题目

代码（首刷看解析 2024年5月6日）

class Solution {
public:
    // 动态规划
    int calculateMinimumHP(vector<vector<int>>& dungeon) {
        // dp[i][j]从(i,j)出发，到达终点所需要的最少血量
        int m = dungeon.size();
        int n = dungeon[0].size();
        vector<vector<int>> dp(m, vector<int>(n, 0));
        // dp[i][j] = max(0, min(dp[i + 1][j], dp[i][j + 1] - dungeon[i][j]));
        dp[m - 1][n - 1] = max(0, -dungeon[m - 1][n - 1]);
        for (int i = m - 2; i >= 0; i--) {
            dp[i][n - 1] = max(dp[i + 1][n - 1] - dungeon[i][n - 1], 0);
        }
        for (int j = n - 2; j >= 0; j--) {
            dp[m - 1][j] = max(dp[m - 1][j + 1] - dungeon[m - 1][j], 0);
        }

        for (int i = m - 2; i >= 0; i--) {
            for (int j = n - 2; j >= 0; j--) {
                dp[i][j] = max(0, min(dp[i + 1][j], dp[i][j + 1]) - dungeon[i][j]);
            }
        }
        return dp[0][0] + 1;
    }
};

代码（二刷自解 2024年8月12日）

class Solution {
public:
    int calculateMinimumHP(vector<vector<int>>& dungeon) {
        int m = dungeon.size();
        int n = dungeon[0].size();
        vector<vector<int>> dp(m, vector<int>(n, 0));
        dp[m - 1][n - 1] = max(0, -dungeon[m - 1][n - 1]);
        for (int i = m - 2; i >= 0; i--) {
            dp[i][n - 1] = max(dp[i + 1][n - 1] - dungeon[i][n - 1], 0);
        }
        for (int j = n - 2; j >= 0; j--) {
            dp[m - 1][j] = max(dp[m - 1][j + 1] - dungeon[m - 1][j], 0);
        }

        for (int i = m - 2; i >= 0; i--) {
            for (int j = n - 2; j >= 0; j--) {
                dp[i][j] = max(0, min(dp[i + 1][j], dp[i][j + 1]) - dungeon[i][j]);
                // cout<<"dp["<<i<<"]["<<j<<"]:"<<dp[i][j]<<" ";
            }
            // cout<<endl;
        }
        return dp[0][0] + 1;
    }
};