LeetCode Minimum Path Sum(动态规划)


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.

题意：给出一个非负矩阵，求从左上角到右下角的路径和的最小值

思路：用dp(i,j)表示从(0,0)到(i,j)的路径的最小和，因为移动路径只能是向下和向右，状态转移方程为

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

代码如下：

class Solution {
public int minPathSum(int[][] grid)
{
int row = grid.length;
int col = row == 0 ? 0 : grid[0].length;

int[][] temp = new int[row][col];

for (int i = 0; i < row; i++)
{
Arrays.fill(temp[i], Integer.MAX_VALUE);
}

temp[0][0] = grid[0][0];

for (int i = 0; i < row; i++)
{
for (int j = 0; j < col; j++)
{
if (i == 0 && j == 0) continue;

if (i > 0)
{
temp[i][j] = Math.min(temp[i][j], temp[i - 1][j] + grid[i][j]);
}

if (j > 0)
{
temp[i][j] = Math.min(temp[i][j], temp[i][j - 1] + grid[i][j]);
}
}
}

return temp[row - 1][col - 1];
}
}