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