Dungeon Princess

• Time : $O(nm)$
• Space : $O(nm)$

c++

int Solution::calculateMinimumHP(vector<vector<int> > &A) {
    int n = A.size(), m = A[0].size();
        vector<vector<int>> dp(n + 1, vector<int>(m + 1, INT_MAX));
        dp[n][m-1] = dp[n-1][m] = 1;
        for(int i = n - 1; i >= 0; i--) {
            for(int j = m - 1; j >= 0; j--) {
                int hp = min(dp[i+1][j], dp[i][j+1]) - A[i][j];
                dp[i][j] = hp <= 0 ? 1 : hp;
            }
        }
        return dp[0][0];
}