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Explore Simple Game Algorithms With Color Walk: Part 12
We've now been exploring and discussing game algorithms using the simple game Color Walk for months over the course of 11 posts. We started out extremely simple with random and round-robin algorithms, advanced to some obvious greedy algorithms, and wound up discussing a number of graph algorithms. We've discovered a ton of stuff along the way, so it would be nice to step back and review the ground we've covered to see the big picture in all of the experimentation and details of the various algorithms we found along the way.
The algorithms started out very simple so that some of the tooling structure could be built for running and evaluating the different algorithms. It would have been difficult to debug the batch run code and a complicated algorithm at the same time, so we gradually ramped up the difficulty of the algorithms after making sure all of the tooling was in place to evaluate the different algorithms.
Round-Robin
The simplest algorithm possible is purely cycling through the colors for each successive move without putting any thought into what would be a good color choice. Predictably, this algorithm does not perform well at all, but that's not the point. It's an easy algorithm to get right when building up the tooling around the game, and it provides a baseline measurement of performance that any algorithm worth its salt should be able to beat.
Round-Robin with Skipping
Once we have an algorithm in place, it's natural to immediately start thinking about how to improve it. One obvious thing to notice about the round-robin algorithm is that sometimes at the beginning or end of the game it picks a color that doesn't remove any blocks. We can fix this imperfection. Instead of blindly picking the next color in the rotation every time, it's easy to check if the next color will remove any blocks, and if it doesn't, to skip that color and move on to the next color in the rotation. This optimization makes an incremental improvement to the basic round-robin algorithm, and it's an idea we can use throughout our algorithm development.
Random Choice
Round-robin is not the only choice for a basic algorithm. Another option for a baseline algorithm is to randomly choose the next color with no thought whatsoever. This strategy may seem useless, but in some cases it's very hard to beat a random algorithm. It's always worth a shot to try it out, and then you at least have a simple baseline measurement of what you want your algorithm to beat. If you can't do any better than random, then you might as well use the random choice with its fast execution. Obviously, in this case random is not a good choice.
Random Choice with Skipping
As with round-robin, we can employ the strategy of avoiding moves that don't remove blocks with random choice. We simply keep picking another random color until we chance upon one that removes blocks before committing to the move. This strategy is a better way to implement random choice, as it's more along the lines of make a random move, but not a stupid move. With this type of random choice, saying that an algorithm under consideration does no better than random will actually mean something.
The Greedy Algorithm
The first "real" algorithm that actually does calculations to attempt to determine the next best move also turns out to be a fairly powerful algorithm. The greedy algorithm looks at how many blocks are removed with each color, and then picks the color that removes the most blocks. This strategy significantly improves on the basic algorithms in every way while still being quite fast because it's light on computation. The greedy strategy is great when it works because it's easy to understand, easy to implement, and it tends to execute fast because it only considers immediately available information.
Greedy Look Ahead (GLA)
The GLA algorithm is an extension of the greedy algorithm. Instead of picking the move that removes the most blocks, why not look ahead and pick the move that will open up the board to remove the most blocks on the next move? This algorithm gets more complicated to implement because now we need to track which move has removed which blocks to figure out how the most blocks can be removed in a two-move sequence. Also, this algorithm is no longer technically a greedy algorithm because by definition a greedy algorithm always chooses the most of something with immediately available information, and GLA is incorporating some foresight. However, since it's an extension of a greedy algorithm and still tries to maximize block removal, we'll refer to it in the same terms. It does manage to improve upon the base algorithm, too.
Greedy Look Ahead-N (GLA-N)
Once we've looked ahead one extra move, there's nothing stopping us from looking ahead more moves, except for the fact that as we look more moves ahead, the exponential explosion of moves to be considered will overwhelm us. In a sense, the GLA-N algorithm, with 'N' denoting how many moves we're looking ahead, is just a generalization of the last two algorithms, with GLA-1 being equivalent to the greedy algorithm that only looks at the next move, and GLA-2 being equivalent to GLA that looks at the next two moves. GLA-3 improves upon the previous algorithms, but then the performance plateaus while taking much longer to run for each game.
Max Perimeter
It turns out that the strategy of looking for the move that removes the most blocks is only one of many related strategies that can be plugged into the same basic algorithm structure. The way of deciding which move is the best is called a heuristic, and we have other heuristics to choose from for that purpose. Instead of choosing the move that removes the most blocks, which maximizes the cleared area, we can choose the move that maximizes the perimeter between the cleared space and the leftover blocks. This new algorithm has the same structure as the greedy algorithm, but with a different heuristic for deciding on the optimal color choice. This heuristic manages to outperform the base greedy algorithm.
Max Perimeter Look Ahead
Since we're plugging in a different heuristic for the greedy algorithm, we can also do the same thing for the GLA algorithm, and look ahead some number of moves before choosing the move that will maximize the perimeter in the future. The structure of the algorithm was done in a way that made it easy to swap in any heuristic that we could think of when assessing how to make the next move, so evaluating it for looking ahead was easy. We found that the max perimeter heuristic didn't improve as much here, and actually started to backtrack in performance when it looked too far ahead.
Perimeter-Area Hybrid
With two heuristics, we can think about ways of combining them to make a different determination about what the next move is. One way of combining heuristics is to run one for some number of moves first, and then finish off the game with the other one. When we run the max perimeter heuristic for 20 moves and then run the max area heuristic, we get a different performance profile than either one on its own. Unfortunately, it's not better.
Perimeter-Area Hybrid Look Ahead
Even though the first hybrid attempt wasn't better than the perimeter or area heuristics on their own, we still want to see how it does when looking ahead. We see that here it does improve on the max perimeter heuristic a little—likely because maximizing the perimeter at the end of the game doesn't help as much as maximizing the number of blocks removed—but it can't surpass the powerful GLA algorithm.
Deep-Path (and Look Ahead)
Another idea for solving a board efficiently is to quickly clear a path to the middle of the board before spreading out and clearing away more blocks. While this exact strategy would be complicated to implement, we can approximate it by maximizing the perimeter-to-area ratio. If the perimeter of the cleared section is large and the area is small, that would be equivalent to having a deep path cleared into the board. Testing out a pure deep-path heuristic showed some pretty disappointing results, but that makes sense because such a strategy should perform poorly in the second half of the game, even with look-ahead.
Path-Area Hybrid (and Look Ahead)
Combining the deep-path heuristic with a max area heuristic is what we really want to see with this strategy, and we do see significant improvements compared to a pure deep-path heuristic. However, this approach still does not best the GLA algorithm. While it may be easier for a human to play with this strategy, it's not the best one when you have the raw computational power of a computer playing the game.
Breadth-First Search (BFS)
When you picture the color choices available for each sequential move in the game, the moves can easily be drawn as a graph with start and end vertices. A path from start to end corresponds to a set of moves that makes up a game, and there are a number of algorithms available for searching this graph. One basic algorithm is BFS, which searches each vertex that's one edge away, then two edges away, and so on until the end vertex is found. Because the graph is unmanageably large, we need to give BFS a head start with GLA-5 for the first moves. With this hybrid algorithm, we actually best GLA-5 by itself, on average, and we have a new best algorithm to beat.
Depth-First Search (DFS)
Instead of searching the move graph in order of how far away the moves are, we can follow each path of moves to its end before backing up and going down the next path. This strategy is depth-first instead of breadth-first, and we need to be careful to limit the search so that it doesn't take forever on this type of graph. We can limit the search to only follow paths that remove blocks on every move, we can stop the search on a particular path if we've already found one that's shorter, and we can run GLA-5 first to shrink the graph that we end up searching with DFS. With these limitations we get pretty good performance, although not quite as good as BFS or GLA.
Dijkstra's Algorithm
While both BFS and DFS would search the entire graph if we didn't limit them in some way, it is possible to optimize the search to try to find a nearly shortest path more quickly. Dijkstra's algorithm does just that by assigning a value to each vertex in the graph that it comes to and putting those vertices in a priority queue. Then it will pull the maximum-valued vertex out of the queue, assess the children of that vertex, and put them in the queue. The algorithm continues until it finds the end vertex, and it does pretty well against the competition. Dijkstra's algorithm is especially consistent at finding a good solution, with a low standard deviation between games.
GLA-Dijkstra Hybrid
We can pair Dijkstra's algorithm with other algorithms to make new hybrids and try to improve performance further. Pairing it with the powerful GLA algorithm ends up besting every other algorithm we've explored. The ultimate strategy seems to be to clear about half the board with moves that maximize the number of blocks removed, then carefully select the optimal path to the end of the game with Dijkstra's algorithm. We could further optimize this algorithm by tweaking the switch-over point between the two sub-algorithms.
Dijkstra-GLA Hybrid
Another idea was to try switching the order of GLA and Dijkstra's algorithm, and seeing how that performed. Alas, it did not do as well, so it appears that Dijkstra's algorithm really shines at optimizing moves at the end of the game while GLA is best at clearing the way at the beginning of the game.
Max-Perimeter-Dijkstra Hybrid
For one last attempt at another hybrid algorithm, we looked at combining the max perimeter heuristic with Dijkstra's algorithm. This strategy makes some sense by trying to increase the possibilities of clearing blocks in the future by maximizing the perimeter of blocks adjacent to the empty zone, and then searching for that optimal path to the end. It ended up working pretty well, doing better than GLA and BFS in the worst case, but falling slightly short on boards that had potential for less moves.
We've summarized 20 or more algorithms here, depending on how you count them, and that's far from a complete list of possibilities. Other combinations of these algorithms could be explored, we could come up with other heuristics to help decide on move values, and we could mix-and-match more algorithms in complex and intricate ways with varying parameters to try to find that one perfect move sequence for each game. The solution space is incredibly large.
Exploring all of these different algorithms teaches us a lot about what the solution space looks like, and how the problem (the Color Walk game in this case) behaves when attacked in different ways. We've seen that some foresight is important, making good assessments of the progress in the game on any given move is quite helpful, and combining strengths of different algorithms works well. And we can do much better than random or a simple round-robin approach!
We also have developed an understanding of a number of classic algorithms and learned some good problem-solving strategies. The articles behind all of these algorithm summaries go into much more depth and detail on each of them, and they show how to develop an algorithm within the constraints of a specific problem. You can also look at the complete code here, and experiment with it for yourself. Have some fun with it, and see if you can beat the GLA-Dijkstra Hybrid algorithm.
Article Index
Part 1: Introduction & Setup
Part 2: Tooling & Round-Robin
Part 3: Random & Skipping
Part 4: The Greedy Algorithm
Part 5: Greedy Look Ahead
Part 6: Heuristics & Hybrids
Part 7: Breadth-First Search
Part 8: Depth-First Search
Part 9: Dijkstra's Algorithm
Part 10: Dijkstra's Hybrids
Part 11: Priority Queues
Part 12: Summary
Simple Beginnings
The algorithms started out very simple so that some of the tooling structure could be built for running and evaluating the different algorithms. It would have been difficult to debug the batch run code and a complicated algorithm at the same time, so we gradually ramped up the difficulty of the algorithms after making sure all of the tooling was in place to evaluate the different algorithms.
Round-Robin
The simplest algorithm possible is purely cycling through the colors for each successive move without putting any thought into what would be a good color choice. Predictably, this algorithm does not perform well at all, but that's not the point. It's an easy algorithm to get right when building up the tooling around the game, and it provides a baseline measurement of performance that any algorithm worth its salt should be able to beat.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Round Robin | 37 | 48.3 | 62 | 4.5 |
Round-Robin with Skipping
Once we have an algorithm in place, it's natural to immediately start thinking about how to improve it. One obvious thing to notice about the round-robin algorithm is that sometimes at the beginning or end of the game it picks a color that doesn't remove any blocks. We can fix this imperfection. Instead of blindly picking the next color in the rotation every time, it's easy to check if the next color will remove any blocks, and if it doesn't, to skip that color and move on to the next color in the rotation. This optimization makes an incremental improvement to the basic round-robin algorithm, and it's an idea we can use throughout our algorithm development.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| RR with Skipping | 37 | 46.9 | 59 | 4.1 |
Random Choice
Round-robin is not the only choice for a basic algorithm. Another option for a baseline algorithm is to randomly choose the next color with no thought whatsoever. This strategy may seem useless, but in some cases it's very hard to beat a random algorithm. It's always worth a shot to try it out, and then you at least have a simple baseline measurement of what you want your algorithm to beat. If you can't do any better than random, then you might as well use the random choice with its fast execution. Obviously, in this case random is not a good choice.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Random Choice | 60 | 80.2 | 115 | 10.5 |
Random Choice with Skipping
As with round-robin, we can employ the strategy of avoiding moves that don't remove blocks with random choice. We simply keep picking another random color until we chance upon one that removes blocks before committing to the move. This strategy is a better way to implement random choice, as it's more along the lines of make a random move, but not a stupid move. With this type of random choice, saying that an algorithm under consideration does no better than random will actually mean something.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Random with Skipping | 43 | 53.1 | 64 | 4.5 |
The Algorithm to Beat
The Greedy Algorithm
The first "real" algorithm that actually does calculations to attempt to determine the next best move also turns out to be a fairly powerful algorithm. The greedy algorithm looks at how many blocks are removed with each color, and then picks the color that removes the most blocks. This strategy significantly improves on the basic algorithms in every way while still being quite fast because it's light on computation. The greedy strategy is great when it works because it's easy to understand, easy to implement, and it tends to execute fast because it only considers immediately available information.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Greedy | 31 | 39.8 | 48 | 3.5 |
Greedy Look Ahead (GLA)
The GLA algorithm is an extension of the greedy algorithm. Instead of picking the move that removes the most blocks, why not look ahead and pick the move that will open up the board to remove the most blocks on the next move? This algorithm gets more complicated to implement because now we need to track which move has removed which blocks to figure out how the most blocks can be removed in a two-move sequence. Also, this algorithm is no longer technically a greedy algorithm because by definition a greedy algorithm always chooses the most of something with immediately available information, and GLA is incorporating some foresight. However, since it's an extension of a greedy algorithm and still tries to maximize block removal, we'll refer to it in the same terms. It does manage to improve upon the base algorithm, too.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Greedy Look Ahead | 28 | 37.0 | 45 | 3.1 |
Greedy Look Ahead-N (GLA-N)
Once we've looked ahead one extra move, there's nothing stopping us from looking ahead more moves, except for the fact that as we look more moves ahead, the exponential explosion of moves to be considered will overwhelm us. In a sense, the GLA-N algorithm, with 'N' denoting how many moves we're looking ahead, is just a generalization of the last two algorithms, with GLA-1 being equivalent to the greedy algorithm that only looks at the next move, and GLA-2 being equivalent to GLA that looks at the next two moves. GLA-3 improves upon the previous algorithms, but then the performance plateaus while taking much longer to run for each game.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Greedy Look-Ahead-3 | 25 | 34.2 | 40 | 2.7 |
| Greedy Look-Ahead-4 | 25 | 33.3 | 39 | 2.6 |
| Greedy Look-Ahead-5 | 25 | 33.1 | 41 | 2.8 |
Plugging in Heuristics
Max Perimeter
It turns out that the strategy of looking for the move that removes the most blocks is only one of many related strategies that can be plugged into the same basic algorithm structure. The way of deciding which move is the best is called a heuristic, and we have other heuristics to choose from for that purpose. Instead of choosing the move that removes the most blocks, which maximizes the cleared area, we can choose the move that maximizes the perimeter between the cleared space and the leftover blocks. This new algorithm has the same structure as the greedy algorithm, but with a different heuristic for deciding on the optimal color choice. This heuristic manages to outperform the base greedy algorithm.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Max Perimeter | 29 | 37.4 | 44 | 3.2 |
Max Perimeter Look Ahead
Since we're plugging in a different heuristic for the greedy algorithm, we can also do the same thing for the GLA algorithm, and look ahead some number of moves before choosing the move that will maximize the perimeter in the future. The structure of the algorithm was done in a way that made it easy to swap in any heuristic that we could think of when assessing how to make the next move, so evaluating it for looking ahead was easy. We found that the max perimeter heuristic didn't improve as much here, and actually started to backtrack in performance when it looked too far ahead.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Max Perimeter Look-Ahead-2 | 27 | 35.0 | 44 | 2.8 |
| Max Perimeter Look-Ahead-3 | 27 | 35.0 | 41 | 2.9 |
| Max Perimeter Look-Ahead-4 | 26 | 34.8 | 43 | 3.3 |
| Max Perimeter Look-Ahead-5 | 28 | 34.9 | 46 | 2.9 |
Perimeter-Area Hybrid
With two heuristics, we can think about ways of combining them to make a different determination about what the next move is. One way of combining heuristics is to run one for some number of moves first, and then finish off the game with the other one. When we run the max perimeter heuristic for 20 moves and then run the max area heuristic, we get a different performance profile than either one on its own. Unfortunately, it's not better.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Perimeter-Area Hybrid | 31 | 39.0 | 49 | 3.8 |
Perimeter-Area Hybrid Look Ahead
Even though the first hybrid attempt wasn't better than the perimeter or area heuristics on their own, we still want to see how it does when looking ahead. We see that here it does improve on the max perimeter heuristic a little—likely because maximizing the perimeter at the end of the game doesn't help as much as maximizing the number of blocks removed—but it can't surpass the powerful GLA algorithm.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Perim-Area Hybrid Look-Ahead-2 | 27 | 35.2 | 43 | 3.2 |
| Perim-Area Hybrid Look-Ahead-3 | 27 | 33.5 | 41 | 2.7 |
| Perim-Area Hybrid Look-Ahead-4 | 26 | 33.2 | 41 | 3.1 |
| Perim-Area Hybrid Look-Ahead-5 | 28 | 33.0 | 41 | 2.5 |
Deep-Path (and Look Ahead)
Another idea for solving a board efficiently is to quickly clear a path to the middle of the board before spreading out and clearing away more blocks. While this exact strategy would be complicated to implement, we can approximate it by maximizing the perimeter-to-area ratio. If the perimeter of the cleared section is large and the area is small, that would be equivalent to having a deep path cleared into the board. Testing out a pure deep-path heuristic showed some pretty disappointing results, but that makes sense because such a strategy should perform poorly in the second half of the game, even with look-ahead.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Deep-Path | 51 | 74.8 | 104 | 9.4 |
| Deep-Path Look-Ahead-2 | 50 | 74.9 | 112 | 9.8 |
| Deep-Path Look-Ahead-3 | 50 | 75.2 | 112 | 9.8 |
| Deep-Path Look-Ahead-4 | 50 | 75.4 | 112 | 9.5 |
Path-Area Hybrid (and Look Ahead)
Combining the deep-path heuristic with a max area heuristic is what we really want to see with this strategy, and we do see significant improvements compared to a pure deep-path heuristic. However, this approach still does not best the GLA algorithm. While it may be easier for a human to play with this strategy, it's not the best one when you have the raw computational power of a computer playing the game.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Path-Area Hybrid | 35 | 44.2 | 54 | 3.5 |
| Path-Area Hybrid Look-Ahead-2 | 34 | 40.8 | 49 | 3.0 |
| Path-Area Hybrid Look-Ahead-3 | 31 | 39.0 | 47 | 3.2 |
| Path-Area Hybrid Look-Ahead-4 | 32 | 38.7 | 45 | 2.7 |
The Graph Algorithms
Breadth-First Search (BFS)
When you picture the color choices available for each sequential move in the game, the moves can easily be drawn as a graph with start and end vertices. A path from start to end corresponds to a set of moves that makes up a game, and there are a number of algorithms available for searching this graph. One basic algorithm is BFS, which searches each vertex that's one edge away, then two edges away, and so on until the end vertex is found. Because the graph is unmanageably large, we need to give BFS a head start with GLA-5 for the first moves. With this hybrid algorithm, we actually best GLA-5 by itself, on average, and we have a new best algorithm to beat.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| BFS with Greedy Look-Ahead-5 | 26 | 32.7 | 40 | 2.8 |
Depth-First Search (DFS)
Instead of searching the move graph in order of how far away the moves are, we can follow each path of moves to its end before backing up and going down the next path. This strategy is depth-first instead of breadth-first, and we need to be careful to limit the search so that it doesn't take forever on this type of graph. We can limit the search to only follow paths that remove blocks on every move, we can stop the search on a particular path if we've already found one that's shorter, and we can run GLA-5 first to shrink the graph that we end up searching with DFS. With these limitations we get pretty good performance, although not quite as good as BFS or GLA.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| DFS with Greedy Look-Ahead-5 | 25 | 34.8 | 43 | 3.9 |
Dijkstra's Algorithm
While both BFS and DFS would search the entire graph if we didn't limit them in some way, it is possible to optimize the search to try to find a nearly shortest path more quickly. Dijkstra's algorithm does just that by assigning a value to each vertex in the graph that it comes to and putting those vertices in a priority queue. Then it will pull the maximum-valued vertex out of the queue, assess the children of that vertex, and put them in the queue. The algorithm continues until it finds the end vertex, and it does pretty well against the competition. Dijkstra's algorithm is especially consistent at finding a good solution, with a low standard deviation between games.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Dijkstra's Algorithm | 29 | 33.1 | 40 | 1.9 |
GLA-Dijkstra Hybrid
We can pair Dijkstra's algorithm with other algorithms to make new hybrids and try to improve performance further. Pairing it with the powerful GLA algorithm ends up besting every other algorithm we've explored. The ultimate strategy seems to be to clear about half the board with moves that maximize the number of blocks removed, then carefully select the optimal path to the end of the game with Dijkstra's algorithm. We could further optimize this algorithm by tweaking the switch-over point between the two sub-algorithms.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| GLA-Dijkstra Hybrid | 25 | 31.8 | 37 | 2.2 |
Dijkstra-GLA Hybrid
Another idea was to try switching the order of GLA and Dijkstra's algorithm, and seeing how that performed. Alas, it did not do as well, so it appears that Dijkstra's algorithm really shines at optimizing moves at the end of the game while GLA is best at clearing the way at the beginning of the game.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Dijkstra-GLA Hybrid | 28 | 36.3 | 44 | 3.1 |
Max-Perimeter-Dijkstra Hybrid
For one last attempt at another hybrid algorithm, we looked at combining the max perimeter heuristic with Dijkstra's algorithm. This strategy makes some sense by trying to increase the possibilities of clearing blocks in the future by maximizing the perimeter of blocks adjacent to the empty zone, and then searching for that optimal path to the end. It ended up working pretty well, doing better than GLA and BFS in the worst case, but falling slightly short on boards that had potential for less moves.
| Min | Mean | Max | Stdev | |
|---|---|---|---|---|
| Max-Perimeter-Dijkstra Hybrid | 27 | 32.8 | 38 | 2.3 |
A Big Solution Space
We've summarized 20 or more algorithms here, depending on how you count them, and that's far from a complete list of possibilities. Other combinations of these algorithms could be explored, we could come up with other heuristics to help decide on move values, and we could mix-and-match more algorithms in complex and intricate ways with varying parameters to try to find that one perfect move sequence for each game. The solution space is incredibly large.
Exploring all of these different algorithms teaches us a lot about what the solution space looks like, and how the problem (the Color Walk game in this case) behaves when attacked in different ways. We've seen that some foresight is important, making good assessments of the progress in the game on any given move is quite helpful, and combining strengths of different algorithms works well. And we can do much better than random or a simple round-robin approach!
We also have developed an understanding of a number of classic algorithms and learned some good problem-solving strategies. The articles behind all of these algorithm summaries go into much more depth and detail on each of them, and they show how to develop an algorithm within the constraints of a specific problem. You can also look at the complete code here, and experiment with it for yourself. Have some fun with it, and see if you can beat the GLA-Dijkstra Hybrid algorithm.
Article Index
Part 1: Introduction & Setup
Part 2: Tooling & Round-Robin
Part 3: Random & Skipping
Part 4: The Greedy Algorithm
Part 5: Greedy Look Ahead
Part 6: Heuristics & Hybrids
Part 7: Breadth-First Search
Part 8: Depth-First Search
Part 9: Dijkstra's Algorithm
Part 10: Dijkstra's Hybrids
Part 11: Priority Queues
Part 12: Summary
Rex Nebular - Final Rating
Written by TBD
Having said that, I enjoyed the game a lot more at the beginning. I was wondering if it was just that the humour got stale after a while, but I really think it's more because much more effort was put into the beginning of the game than the late game. More items seem to have unique and detailed descriptions earlier whereas later in the game there are a lot more generic or shorter responses.
Puzzles and Solvability
The puzzles in this game are fine. They're mostly inventory based.
Another slightly below par score here. A somewhat interesting back-story and a third of the game taking place in an interesting but tonally odd setting are countered by the unimpressive characterization and lackluster story as a whole.
Final score: 4
Sound and Graphics
The game surprised me by only having talking during the opening cutscene. Even the end cutscene, with Rex and Stone, where Rex knocks over the vase after they have a two-line conversation doesn't have speech – strange choice.
Anyway, the sound in this game was... not good. Gee, in coming up with these ratings I've been a lot harsher than I expected. And listening to some of the sounds again, it's really years behind the times.The dog sounds nothing like a dog. Even the gender bender machine itself sounds like it could be made with PC Speaker in the 80s. (I'm possibly slightly exaggerating the quality of 1980s PC Speaker sounds, but it's certainly not actually good.)
The music was (and I say this a lot in my final ratings) not very memorable. The music is all very background and not at all interesting or emotion-inducing. I've been playing a Youtube longplay in the background while writing this and none of the music is reminding me of the game or evoking emotions in me. Perhaps this is the most forgettable game soundtrack of all time!
As for the graphics, they're acceptable and things look like what they are supposed to look like. The animation I spoke so well of in the introduction post was indeed only an indication of the opening cutscene quality.
I'm once again going for a 4 in this section. It's not quite okay.
Final score: 4
Environment and Atmosphere
This is always a hard one to rate. I suppose it can be defined as the feel of the game. How do all the facets of the game combine to make a cohesive and fun experience.
The game tries to do the funny sci-fi humour thing and succeeds sometimes. It's not bad, but oh, let's just get to the crux of it – the whole game is mediocre.
A medicre game deserves a mediocre score. I'll go with a 5 here.
Final score: 5
Dialogue and Acting
After the first section I played, I was impressed with the writing, and the acting of the opening cutscene.
But the more I played the less impressed I became. The verbose funny responses to things are largely the same. Trying to look at something the first time gives me a funny response. Looking at the eleventh item on a screen that gives the same funny response as the previous ten quickly makes the response lose its humour.
There's very little actual dialogue in the game as Rex rarely interacts with other people. Most of this category is referring to the narrator's lines when trying to interact with items.
It's fair to say, if I rated this game after my first gameplay post, I would have gone higher for many of the categories and it probably would have hit 50 or so. I've heard that first impressions are more important, but in the case of a final rating the first impression barely makes a dent if the game can't keep up the quality for its entirety. Sorry, Rex Nebular and the Cosmic Gender Bender, but I find you to be a below average game. At first I thought 45 might be a bit low but then I looked at some of our other games and it's the fourth 45 we've given for 1992, and the third 45 in a row! Maybe 1992 is the year of 45!
And to give an indication of my Overall Fun Factor, I found that thinking more on the game for the purpose of rating it actually made me think less of the game. I don't think that's happened to me before. There must have been something about the game that kept it interesting enough not to notice its flaws as I played. Having played this game once, I can't see myself ever wanting to play it again – I enjoyed Space Quest IV and even Leather Goddesses of Phobos 2 more than this game and really can't see myself playing this game again. Sorry, Rex. I'll give the game a 4 out of 10 for Overall Fun Factor, which gives a PISSEDOFF rating of... 4+5+4+4+5+5+4+4+4/.9 which equals 43!
100 CAPs to TBD
31 CAPs to Leo Velles
 |
| It seems weird to make a big deal about your manual being written by an award winning game designer when he had nothing to do with the game itself. |
So let's get to rating Rex Nebular and the Cosmic Gender Bender. I'll start with some general thoughts. I was really surprised (and rather pleased) that the game didn't contain a whole heap of sex-based jokes. That type of humour can very quickly become repetitive and boring so well done.
Having said that, I enjoyed the game a lot more at the beginning. I was wondering if it was just that the humour got stale after a while, but I really think it's more because much more effort was put into the beginning of the game than the late game. More items seem to have unique and detailed descriptions earlier whereas later in the game there are a lot more generic or shorter responses.
Puzzles and Solvability
The puzzles in this game are fine. They're mostly inventory based.
The most memorable puzzles in this game were puzzles that didn't happen. What I mean by that, was that I spent much of the game pondering the use of things that ended up having no use at all.
There is one area on the surface that I can't get through because I'm a man. One of the first things I did after changing my gender was to go past that area, wondering what excitement I'd find beyond.
Well, I found some more huts just like the one on the screen before, a chicken roasting over a fire, and a stream that I can't cross because of the piranhas. I spent much of the rest of the game wondering how I would get past the piranhas and what I'd find beyond it. Then the game ended. The only reason to go to the surface as a woman was to get a roast chicken that wasn't useful until the very last section of the game. Thinking about it now it's rather baffling. The piranha stream wasn't the only red herring in the game. There are a lot of items that serve no purpose whatsoever, and don't even have interesting comments when interacted with (but I'll get to that later)
I feel that they had planned a much larger game but ran out of time or money. Some of the things that make me think so are the above section, and also the software store that is only useful for getting penlight batteries but contains a security system and various types of software. I felt sure I'd have to either get an item through the security system of the software store or take parts of the security system to trick someone else at some point. More puzzling possibilities that are strangely not there.
Adding to my bafflement of non-puzzles was the entire gender changing thing? It's a massive missed opportunity. It's used twice. Once to get to the southern section of the female base (and the go back to the surface for a chicken - can't forget that one) and once to be able to activate the car in Machopolis. Despite finding a teleporter in the southern section of the female base, I die when I tried to get through as a man so I don't even have the chance to enter the women's section as a man for comedy value.
The one positive in the puzzles and solvability section is the lack of negatives. Mazes, bad mini-games, and timed sequences don't exist. The manual hinted that hard mode could have dead-ends, but I didn't find any, and wouldn't blame a game for including them if they also included difficulty levels that don't have any dead-ends, so another good here.
The difficulty levels are quite a positive, or at least could have been. Difficulty levels can really help a game by making it easier or harder depending on each player's wishes. I did solve one puzzle by spoiling myself in easy mode, but when I redid the first half of the game in medium difficulty I was surprised at the limited amount of times it was used. Using it for more than a handful of puzzles is something else I felt was a good idea but largely ignored in development.
Overall, I wasn't terribly impressed with the puzzles in general in this game. So a slightly below par 4 seems appropriate.
Final score: 4
Interface and Inventory
The interface has some nice ease-of-use features. Holding down the mouse button acts as a "What is" or tooltip option so you don't get stuck pixel hunting. I appreciated that.
I was annoyed that the game never made it clear that the explosives couldn't be used without a detonator. I wasted a lot of time attempting to blow things up – the game even made of point of me having to be careful with it, reminding me about Professor Pyro blowing herself up whenever I looked at them. Come on game, if the cases won't blow up without detonators, you could have told me that every time I try to throw them or put them on something.
Each inventory item had a funny (potentially) description, and at least one special action. Some of the actions are obvious, like 'read' for the repair list and most were there for a single joke, like 'fondle'. The spinning inventory, which was so exciting it was touted as a feature in the manual, isn't terribly exciting but does add some movement to a section of the screen that would otherwise be static, so well done, I guess? The downside is that the section becomes very drab and grey. I assume the spinning meant they couldn't also do much with colour, because all items are just light shades of grey over a darker grey background.
So, a thumbs up for the tooltips and the funny descriptions, but otherwise nothing special.
Final score: 5
Story and Setting
The background story of a gender war was interesting, as long as I didn't think too much about the logistics of it, but of course most comedy game stories fall apart if you try to think about them logically. Machopolis was by far the most fleshed out setting in the game.
In fact, the post-apocalyptic style setting of Machopolis is a weird contrast to the attempted tone of the game as a whole. The game descriptions are full of jokes and it's clear the game doesn't want me to take it seriously, but the empty husk of a city that was Machopolis on its own is rarely funny at all. I'm not sure I'd call it bad but... it's just very strange, and didn't click with me.
I'm a fan of the Fallout series and that's something that has a largely serious post-apocalyptic setting that also manages to do plenty of silly comedy and have the two mesh very well. So it can be done, but this game just didn't succeed as well.
There is one area on the surface that I can't get through because I'm a man. One of the first things I did after changing my gender was to go past that area, wondering what excitement I'd find beyond.
Well, I found some more huts just like the one on the screen before, a chicken roasting over a fire, and a stream that I can't cross because of the piranhas. I spent much of the rest of the game wondering how I would get past the piranhas and what I'd find beyond it. Then the game ended. The only reason to go to the surface as a woman was to get a roast chicken that wasn't useful until the very last section of the game. Thinking about it now it's rather baffling. The piranha stream wasn't the only red herring in the game. There are a lot of items that serve no purpose whatsoever, and don't even have interesting comments when interacted with (but I'll get to that later)
I feel that they had planned a much larger game but ran out of time or money. Some of the things that make me think so are the above section, and also the software store that is only useful for getting penlight batteries but contains a security system and various types of software. I felt sure I'd have to either get an item through the security system of the software store or take parts of the security system to trick someone else at some point. More puzzling possibilities that are strangely not there.
 |
| Seriously. With the security stands at the front, and the software on the special stand in the middle, how can the small penlight on the shelf be the ONLY interactive element in the entire store. |
The one positive in the puzzles and solvability section is the lack of negatives. Mazes, bad mini-games, and timed sequences don't exist. The manual hinted that hard mode could have dead-ends, but I didn't find any, and wouldn't blame a game for including them if they also included difficulty levels that don't have any dead-ends, so another good here.
The difficulty levels are quite a positive, or at least could have been. Difficulty levels can really help a game by making it easier or harder depending on each player's wishes. I did solve one puzzle by spoiling myself in easy mode, but when I redid the first half of the game in medium difficulty I was surprised at the limited amount of times it was used. Using it for more than a handful of puzzles is something else I felt was a good idea but largely ignored in development.
Overall, I wasn't terribly impressed with the puzzles in general in this game. So a slightly below par 4 seems appropriate.
Final score: 4
Interface and Inventory
The interface has some nice ease-of-use features. Holding down the mouse button acts as a "What is" or tooltip option so you don't get stuck pixel hunting. I appreciated that.
I was annoyed that the game never made it clear that the explosives couldn't be used without a detonator. I wasted a lot of time attempting to blow things up – the game even made of point of me having to be careful with it, reminding me about Professor Pyro blowing herself up whenever I looked at them. Come on game, if the cases won't blow up without detonators, you could have told me that every time I try to throw them or put them on something.
Each inventory item had a funny (potentially) description, and at least one special action. Some of the actions are obvious, like 'read' for the repair list and most were there for a single joke, like 'fondle'. The spinning inventory, which was so exciting it was touted as a feature in the manual, isn't terribly exciting but does add some movement to a section of the screen that would otherwise be static, so well done, I guess? The downside is that the section becomes very drab and grey. I assume the spinning meant they couldn't also do much with colour, because all items are just light shades of grey over a darker grey background.
 |
| Grey chicken looks much less appetizing than brown chicken. |
Final score: 5
Story and Setting
The background story of a gender war was interesting, as long as I didn't think too much about the logistics of it, but of course most comedy game stories fall apart if you try to think about them logically. Machopolis was by far the most fleshed out setting in the game.
In fact, the post-apocalyptic style setting of Machopolis is a weird contrast to the attempted tone of the game as a whole. The game descriptions are full of jokes and it's clear the game doesn't want me to take it seriously, but the empty husk of a city that was Machopolis on its own is rarely funny at all. I'm not sure I'd call it bad but... it's just very strange, and didn't click with me.
I'm a fan of the Fallout series and that's something that has a largely serious post-apocalyptic setting that also manages to do plenty of silly comedy and have the two mesh very well. So it can be done, but this game just didn't succeed as well.
The fact that the MacGuffin of the game, the vase, was something I kept forgetting about shows the game gave me no reason to care. It never told me why the vase was important - did it have power or was its rarity and value its only use (I strongly suspected the second)? Again, in a comedy game the MacGuffin is often secondary and unimportant but even in a good comedy story it should at least play some role in my motivation to solve the puzzles. The vase is mentioned in the Audio Log booklet that came with the game documentation as something Rex's rich employer had fond memories playing with as a kid (A reference to a rather popular old movie, most likely)
Rex himself isn't terribly well characterised either -
- Is he clumsy? Well yes, but I only found that out in the ending cutscene, when he knocks over the vase.
- Is he unlucky in love? It seems so, due largely to his stereotypical single-bachelor style living conditions, but it's not something that defines him like Larry Laffer.
- Is he competent? I'm really not sure - I suppose so but how much of that was just me successfully solving puzzles rather than part of his personality?
I actually don't know much about Rex at all. It's possible I missed or forgot a lot, but the lack of characters for Rex to have conversations with limit the amount I learn about him, which makes me less interested in his success or otherwise in this story. He does say a lot more in the Audio Log and has more of a personality there but none of that personality seemed to make it into the game itself.
 |
| Perhaps Rex's personality would have made more of an impact on me if he was the one narrating rather than a separate narrator |
Final score: 4
Sound and Graphics
The game surprised me by only having talking during the opening cutscene. Even the end cutscene, with Rex and Stone, where Rex knocks over the vase after they have a two-line conversation doesn't have speech – strange choice.
Anyway, the sound in this game was... not good. Gee, in coming up with these ratings I've been a lot harsher than I expected. And listening to some of the sounds again, it's really years behind the times.The dog sounds nothing like a dog. Even the gender bender machine itself sounds like it could be made with PC Speaker in the 80s. (I'm possibly slightly exaggerating the quality of 1980s PC Speaker sounds, but it's certainly not actually good.)
 |
| Well, at least we know who to blame for the dog sounding so bad. |
As for the graphics, they're acceptable and things look like what they are supposed to look like. The animation I spoke so well of in the introduction post was indeed only an indication of the opening cutscene quality.
I'm once again going for a 4 in this section. It's not quite okay.
Final score: 4
Environment and Atmosphere
This is always a hard one to rate. I suppose it can be defined as the feel of the game. How do all the facets of the game combine to make a cohesive and fun experience.
Well, the opening of the game gave me a very good impression. The verbose funny responses amused me. The animations impressed me and the dialogue was written and acted well.
 |
| Ah, the times when I had a much higher impression of the game. |
A medicre game deserves a mediocre score. I'll go with a 5 here.
Final score: 5
Dialogue and Acting
After the first section I played, I was impressed with the writing, and the acting of the opening cutscene.
But the more I played the less impressed I became. The verbose funny responses to things are largely the same. Trying to look at something the first time gives me a funny response. Looking at the eleventh item on a screen that gives the same funny response as the previous ten quickly makes the response lose its humour.
 |
| This is one of 11 items on this screen alone that has the exact same description when looked at. |
There were, if they can be called that, a few dialogue puzzles – two if my memory's correct; We had to answer the doctor's questions without being a smartarse or die, and we had to convince the surface woman that we were a real man by giving her the cliché man responses. Neither of those were too taxing on the brain but some of the responses were worth the comedy value.
Possibly the best writing was actually in the confusingly named Audio Log that came with the game documentation and was written by Steve Meretzky. The Audio Log is a 23 page booklet and contained a rather funny text version of an audio-captured Captain's Log.
The writing and dialogue as a whole was okay, and it had enough funny dialogue that it kept me amused for a decent portion of the game. I'm sitting on a completely average 5 again here.
Final Rating: 5
Final Rating
This gives us a Final rating of… 4+5+4+4+5+5*10/6, which equals…
Possibly the best writing was actually in the confusingly named Audio Log that came with the game documentation and was written by Steve Meretzky. The Audio Log is a 23 page booklet and contained a rather funny text version of an audio-captured Captain's Log.
 |
| The Audio Log ends in the middle of the opening cutscene! |
Final Rating: 5
Final Rating
This gives us a Final rating of… 4+5+4+4+5+5*10/6, which equals…
And to give an indication of my Overall Fun Factor, I found that thinking more on the game for the purpose of rating it actually made me think less of the game. I don't think that's happened to me before. There must have been something about the game that kept it interesting enough not to notice its flaws as I played. Having played this game once, I can't see myself ever wanting to play it again – I enjoyed Space Quest IV and even Leather Goddesses of Phobos 2 more than this game and really can't see myself playing this game again. Sorry, Rex. I'll give the game a 4 out of 10 for Overall Fun Factor, which gives a PISSEDOFF rating of... 4+5+4+4+5+5+4+4+4/.9 which equals 43!
CAP Distribution
100 CAPs to TBD
- Blogger Award - 100 CAPs - For playing Rex Nebular and the Cosmic Gender Bender for everyone's enjoyment
- Bad Motivator Award - 5 CAPs - for letting Charles know that the vase is entirely uninteresting as a motivation
- True Companion Award - 20 CAPs - for playing along and sharing thoughts on the game
- Assistance Confirmed Award - 6 CAPs - for giving me confirmation that I'd need Charles' help, and some extra help that I didn't end up needing
- Underused Award - 5 CAPs - for noticing and lamenting the lack of puzzles related to the Gender Bender
- Assistance Granted Award - 10 CAPs - for helping when I was stuck for a second time soon after the first
- In Conclusion Award - 6 CAPs - for a nice series of random comments on the Won! Post that I must have agreed with, seeing as many of those comments were echoed in this final rating.
- Assistance Dog Award - 10 CAPs – for helping me when I was throwing the bone at the wrong thing
- Observation Award - 5 CAPs - for further pointing out that my not noticing the hermit alley just meant I wasn't paying attention at all.
10 CAPs to Alex Romanov
- Psychic Prediction Award – 10 CAPs – for correctly guessing the PISSED Rating Rex Nebular would get.
- Pantene Award – 5 CAPs - for Noticing how full-bodied and 80s Rox's hair is
- Underused Award - 5 CAPs - for noticing and lamenting that the Gender Bender appears to be just a keycard
- Patron of the Arts Award - 10 CAPs - for donating to Tony Longworth, a musician who's done Infocom-inspired music on The Adventure Gamer's behalf
- Snoo-Snoo Award – 5 Caps – for putting an extremely appropriate Futurama reference in the comments
- Fine Art Award - 5 CAPs - for telling us a little about the late Kenn Nishiuye, an artist for this game who also worked for Sierra.
- Sorry Award - 5 CAPs - as compensation for having rose tinted memories tarnished by someone judging a 1992 game in 2019. Sorry.
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