Editorial for SAC '22 Code Challenge 2 P4 - Cookie Galore

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Author: maxcruickshanks

First, realize that this problem asks for the shortest path from $(1, 1)$ ~(1, 1)~ to $(N, M)$ ~(N, M)~.

Next, decompose the grid of characters into a graph:

If the next position you are travelling to is a . cell, the weight is $0$ ~0~.
If the next position you are travelling to is a C cell, the weight is $1$ ~1~.

Now, run a shortest path algorithm (e.g., Dijkstra's algorithm) to find the shortest path.

Time Complexity: $\mathcal{O}(NM\log(NM))$ ~\mathcal{O}(NM\log(NM))~

Note that a faster time complexity can be achieved by further realizing that the weights are either $0$ ~0~ or $1$ ~1~, allowing you to use 0-1 BFS.

Also, the bounds for $N$ ~N~ and $M$ ~M~ are relatively low because the author believes that distinguishing between a log factor (e.g., Dijkstra's algorithm vs. 0-1 BFS) is unfair to competitors.

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