[动态规划] leetcode 174 Dungeon Game

problem:https://leetcode.com/problems/dungeon-game

        看了这道题的tag我用了二分 + 简化dp（只需求特定血量能否达到）来做，能过但是速度好慢。一看评论区发现大家都是用纯dp过的，我哭了。

class Solution {
public:
    int m, n;
    bool canSave(vector<vector<int>>& dungeon, int life)
    {
        vector<vector<int>> health(m, vector<int>(n, -1));
        health[0][0] = life + dungeon[0][0];
        for(int i = 0;i < m ;i++)
        {
            for(int j = 0;j < n;j++)
            {
                if(i > 0 && health[i - 1][j] > 0)
                {
                    health[i][j] = health[i - 1][j] + dungeon[i][j];
                }
                if(j > 0 && health[i][j - 1] > 0)
                {
                    health[i][j] = max(health[i][j], health[i][j - 1] + dungeon[i][j]);
                }
            }
        }
        return health[m - 1][n - 1] > 0;
    }
    int calculateMinimumHP(vector<vector<int>>& dungeon) {
        m = dungeon.size();
        if(!m) return 0;
        n = dungeon[0].size();
        
        int high = 1;
        int low = 1;
      
        for(int i = 0; i < m; i++)
        {
            for(int j = 0;j < n; j++)
            {
                if(dungeon[i][j] < 0)
                {
                    high += -dungeon[i][j];
                }
            }
        }
        
        while(low < high)
        {
            int mid = low + (high - low) / 2;
            if(canSave(dungeon, mid))
            {
                high = mid;
            }
            else
            {
                low = mid + 1;
            }
        }
        return low;
    }
};