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.

Analysis:

This is a DP problem.

Init: A[0][i] = A[0][i-1]+grid[0][i];

A[i][0] = A[i-1][0]+grid[i][0];

State Change func:

A[i][j] = min(A[i-1][j]+grid[i][j], A[i][j-1]+grid[i][j]);

Source Code:

class Solution { public: int minPathSum(vector<vector<int> > &grid) { // Start typing your C/C++ solution below // DO NOT write int main() function if (grid.empty()){return 0;} int m=grid.size(); int n=(*grid.begin()).size(); vector<vector<int> > a(m,vector<int>(n,0)); a[0][0]=grid[0][0]; for (int i=1;i<n;i++){ a[0][i]=a[0][i-1]+grid[0][i];} for (int i=1;i<m;i++){ a[i][0]=a[i-1][0]+grid[i][0];} for(int i=1;i<m;i++){ for (int j=1;j<n;j++){ a[i][j]= min( a[i][j-1]+grid[i][j], a[i-1][j]+grid[i][j]); } } return a[m-1][n-1]; } };

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