174. Dungeon Game

class Solution {
    public int calculateMinimumHP(int[][] dungeon) {
        int rows = dungeon.length;
        int cols = dungeon[0].length;
        
        int[][] dp = new int[rows][cols]; // dp[i][j] 为进入 dungeon[i][j] 所需要的最小血量以通过 dungeon[i][j] 以及后续 dungeon
        
        dp[rows - 1][cols - 1] = Math.max(1, 1 - dungeon[rows - 1][cols - 1]);
        
        // last column
        for (int i = rows - 2; i >= 0; i--) {
            dp[i][cols - 1] = Math.max(1, dp[i + 1][cols - 1] - dungeon[i][cols - 1]);
        }
        
        // last row
        for (int i = cols - 2; i >= 0; i--) {
            dp[rows - 1][i] = Math.max(1, dp[rows - 1][i + 1] - dungeon[rows - 1][i]);
        }
        
        for (int i = rows - 2; i >= 0; i--) {
            for (int j = cols - 2; j >= 0; j--) {
                int right = Math.max(1, dp[i][j + 1] - dungeon[i][j]);
                int down = Math.max(1, dp[i + 1][j] - dungeon[i][j]);
                dp[i][j] = Math.min(right, down);
            }
        }
        
        return dp[0][0];
    }
}