64.最小路徑和

Minimum Path Sum

問題描述：

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

測試代碼（python）：

class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m = len(grid)
        n = len(grid[0])
        dp = [[sys.maxint for col in range(n+1)] for row in range(m+1)]
        dp[0][1] = 0
        dp[0][0] = 0
        dp[1][0] = 0
        for i in range(1,m+1):
            for j in range(1,n+1):
                dp[i][j] = min(dp[i-1][j],dp[i][j-1])+grid[i-1][j-1]
        return dp[m][n]        

性能：

參考答案：

class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        sum = list(grid[0])
        for j in range(1, len(grid[0])):
            sum[j] = sum[j - 1] + grid[0][j]
        for i in range(1, len(grid)):
            sum[0] += grid[i][0]
            for j in range(1,len(grid[0])):
                sum[j] = min(sum[j - 1], sum[j]) + grid[i][j]
        return sum[-1]

性能：

測試代碼（c++）：

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

性能：