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];
  }
};