Question
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.
Example:
Difficulty:Medium
Category:Array, Dynamic-Programming
Analyze
Solution
// f[i][j]=min(f[i-1][j], f[i][j-1])+grid[i][j]
class Solution {
public:
int minPathSum(vector<vector<int>>& grid) {
if (grid.empty()) return 0;
const unsigned int m = grid.size(), n = grid[0].size();
int f[m][n];
f[0][0] = grid[0][0];
for (unsigned int i = 1; i < m; ++i) {
f[i][0] = f[i-1][0] + grid[i][0];
}
for (unsigned int j = 1; j < n; ++j) {
f[0][j] = f[0][j-1] + grid[0][j];
}
for (int i = 1; i < m; ++i) {
for (int j = 1; j < n; ++j) {
f[i][j] = min(f[i-1][j], f[i][j-1]) + grid[i][j];
}
}
return f[m-1][n-1];
}
};