LintCode 476. Stone Game

http://www.lintcode.com/en/problem/stone-game/


Game Theory problems are classified as DP problems.

And this is a classic one. Because there are two players gaming and so many possible moves,

that comes with a huge searching space with a lot of overlaps.

So overlaps must be eliminated by Memoization.

And let's see the 4 Elements of the DP:

1. initialization: (or termination)
dp[i][i] = 0;

2. transfer formula:
dp[i][j] = sum[i][j] + (for all the possible k) min(dp(i, k) + dp(k, j));

3. Result:
dp(0, length - 1);