[leetcode] Minimum Path Sum

Minimum Path Sum

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.

分析：动态规划：

状态转移公式为：ret[i][j] = min(ret[i-1][j], ret[i][j-1]) + grid[i][j];

对于矩阵

1	2	3
4	5	6
7	8	9

它所对应的ret矩阵为：

1	1+2	1+2+3
1+4	1+2+5	1+2+3+6
1+4+7	1+2+5+8	1+2+3+6+9

=

1	3	6
5	8	12
12	16	21

代码如下：

class Solution
{
public:
  int minPathSum(vector<vector<int> > &grid)
  {
    if(grid.size() == 0)
      return 0;

    vector<vector<int> > ret(grid);

    for(int i=1; i<grid.size(); i++)
      ret[i][0] += ret[i-1][0];

    for(int j=1; j<grid[0].size(); j++)
      ret[0][j] += ret[0][j-1];

    for(int i=1; i<grid.size(); i++)
      for(int j=1; j<grid[i].size(); j++)
        ret[i][j] = min(ret[i][j-1], ret[i-1][j]) + grid[i][j];

    return ret[grid.size()-1][grid[0].size()-1];
  }
};