【leetcode刷题笔记】动态规划

#【leetcode刷题笔记】动态规划

石子游戏

public boolean stoneGame(int[] piles) {
        int N = piles.length;
        
        // dp[i][j] is the score of Alex's maximum total score when remaining piles are from ith to jth (included).
        int[][] dp = new int[N+2][N+2];
        for(int size = 1; size <= N; size++){
            for(int i = 0; i + size <= N; i++){
                int j = i + size - 1;
                // if the number of rounds have been played are even
                if((N - size) % 2 == 0){
                		// Alex's turn
                    dp[i + 1][j + 1] = Math.max(piles[i] + dp[i + 2][j + 1],
                                               piles[j] + dp[i + 1][j]);
                }
                else{
                		// Lee's turn
                    dp[i + 1][j + 1] = Math.min(dp[i + 2][j + 1], dp[i + 1][j]);
                }
            }
        }
        
        int total = 0;
        for(int i = 0; i < N; i ++){
            total += piles[i];
        }
        // total - dp[1][N] is Lee's total score
        return dp[1][N] > total - dp[1][N]; 
}

弄清动态规划的起止条件，和如何选择最佳值。