leetcode

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.

//利用dp解决，动态转移方程为：
// dp[i][j] = min(dp[i-1][j],dp[i][j-1]) + grid[i][j].
class Solution {
public:
    int minPathSum(std::vector<std::vector<int> > &grid) {
        std::vector<std::vector<int>> dp(grid.size(),std::vector<int>(grid[0].size(),0));
		dp[0][0] = grid[0][0];

		for (int i = 1; i < grid.size(); i++)
		{
			dp[i][0] = dp[i-1][0] + grid[i][0];
		}
		for (int i = 1; i < grid[0].size(); i++)
		{
			dp[0][i] = dp[0][i-1] + grid[0][i];
		}
		for (int i = 1; i < grid.size(); i++)
		{
			for (int j = 1; j < grid[0].size(); j++)
			{
				dp[i][j] = std::min(dp[i-1][j],dp[i][j-1]) + grid[i][j];
			}
		}
		return dp[grid.size()-1][grid[0].size()-1];
    }
};

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