LeetCode Minimum Path Sum(动态规划)
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Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right whichminimizes 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]; }}
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