路径问题【动态规划】

一、不同路径

 

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector> dp(m+1,vector(n+1));

        dp[0][1] = 1;

        for(int i = 1;i <= m;i++){
            for(int j = 1;j <= n;j++){
                dp[i][j] = dp[i-1][j]+dp[i][j-1];
            }
        }
        return dp[m][n];
    }
};

二、不同路径II 

 

class Solution {
public:
    int uniquePathsWithObstacles(vector>& ob) {
        int m = ob.size();
        int n = ob[0].size();
        vector> dp(m+1,vector(n+1));

        dp[1][0] = 1;

        for(int i = 1;i <= m;i++){
            for(int j = 1;j <= n;j++){
                if(ob[i-1][j-1] == 0) 
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        } 
        return dp[m][n];
    }
};

 三、礼物的最大价值

class Solution {
public:
    int maxValue(vector>& grid) {
        int m = grid.size();
        int n = grid[0].size();

        vector> dp(m+1,vector(n+1));

        for(int i = 1;i <= m;i++){
            for(int j = 1;j <= n;j++){
                dp[i][j] = max(dp[i-1][j],dp[i][j-1])+grid[i-1][j-1];
            }
        }
        return dp[m][n];
    }
};

 四、下降路径最小和

 

 

 

class Solution {
public:
    int minFallingPathSum(vector>& matrix) {
        int n = matrix.size();
        vector> dp(n+1,vector (n+2,INT_MAX));

        for(int j = 0;j < n+2;j++){
            dp[0][j] = 0;
        }
        for(int i = 1;i <= n;i++){
            for(int j = 1;j <= n;j++){
                dp[i][j] = min(dp[i-1][j-1],min(dp[i-1][j],dp[i-1][j+1]))+matrix[i-1][j-1];
            }
        }
        int ret = INT_MAX;
        for(int i = 1;i <= n;i++)
            ret = min(ret,dp[n][i]);
        return ret;
    }
};

 五、最小路径和

 

此题跟前面差不多，略。

六、地下城游戏 【以[i,j]位置为起点】

        

 

 

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