LeetCode: Minimum Path Sum

Problem:

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.

class Solution {
public:
int minPathSum(vector<vector<int> > &grid) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
int y = grid.size();
if (y == 0) return 0;
int x = grid[0].size();

for (int i = 1; i < x; ++i)
grid[0][i] += grid[0][i-1];
for (int i = 1; i < y; ++i)
grid[i][0] += grid[i-1][0];

int a, b;
for(int j = 1; j < y; ++j)
{
for (int i = 1; i < x; ++i)
{
a = grid[j][i] + grid[j-1][i];
b = grid[j][i] + grid[j][i-1];
grid[j][i] = a > b ? b : a;
}
}
return grid[y-1][x-1];
}
};