LitCode--最小経路と

LitCode--minimum-path-sum(最小経路と)
ソースリンク:http://www.lintcode.com/zh-cn/problem/minimum-path-sum/
非負の整数だけを含むm＊nグリッドを指定します.左上から右下にかけて、数字と最小のパスが見つかります.
サンプル
注意
同じ時間に下または右にしか移動できません.
分析:
dp[i＋1][j＋1]=min(dp[i＋1][j],dp[i]、[j＋1]+grid[i]、[j]
****  時間複雑度O(n＊m)、空間複雑度O(n＊m)＊＊＊
コード(C++、Java、Python):

class Solution {
public:
    /**
     * @param grid: a list of lists of integers.
     * @return: An integer, minimizes the sum of all numbers along its path
     */
    int min(int a, int b){
        if (a < b) return a;
        else return b;
    }
    int minPathSum(vector<vector<int> > &grid) {
        // write your code here
        int m = grid.size();
        int n = grid[0].size();
        int dp[m][n];
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; i++)
            dp[i][0] = dp[i-1][0] + grid[i][0];
        for (int j = 1; j < n; j++)
            dp[0][j] = dp[0][j-1] + grid[0][j];
        for (int i = 1; i < m; i++)
            for (int j = 1; j < n; j++)
                dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
        return dp[m-1][n-1];
    }
};

public class Solution {
    /**
     * @param grid: a list of lists of integers.
     * @return: An integer, minimizes the sum of all numbers along its path
     */
    int min(int a, int b){
        if (a < b) return a;
        else return b;
    }
    public int minPathSum(int[][] grid) {
        // write your code here
        int m = grid.length;
        int n = grid[0].length;
        int [][] dp = new int [m][n];
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; i++)
            dp[i][0] = dp[i-1][0] + grid[i][0];
        for (int j = 1; j < n; j++)
            dp[0][j] = dp[0][j-1] + grid[0][j];
        for (int i = 1; i < m; i++)
            for (int j = 1; j < n; j++)
                dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
        return dp[m-1][n-1];
    }
}

class Solution:
    """
    @param grid: a list of lists of integers.
    @return: An integer, minimizes the sum of all numbers along its path
    """
    def minPathSum(self, grid):
        # write your code here
        m = len(grid)
        n = len(grid[0])
        dp = [[0 for i in range(n)] for j in range(m)]
        dp[0][0] = grid[0][0]
        for i in range(1, m):
            dp[i][0] = dp[i-1][0] + grid[i][0]
        for j in range(1, n):
            dp[0][j] = dp[0][j-1] + grid[0][j]
        for i in range(1, m):
            for j in range(1, n):
                dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j]
        return dp[m-1][n-1]
        
def min(a, b):
    if a < b:
        return a
    else:
        return b