Leetcode: Minimum Path Sum

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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.

與Unique Path問題相似，是一個DP問題，問題的解決方案依然是建造一個新矩陣，每個元素值是從top left到該點的最短距離。遞迴式可以根據這個寫出來，並且一旦計算出了到該點的最短距離，就把它存起來以備其他點使用。

 1 public class Solution { 2     public int minPathSum(int[][] grid) { 3         int m = grid.length; 4         int n = grid[0].length; 5         if (m == 0 || n == 0) return 0; 6         int[][] matrix = new int[m][n]; 7         return FindMinPath(m-1, n-1, grid, matrix); 8     } 9     10     public int FindMinPath(int i, int j, int[][]grid, int[][]matrix) {11         if (matrix[i][j] != 0) return matrix[i][j];12         if (i == 0 && j == 0) {13             matrix[i][j] = grid[0][0];14             return matrix[i][j];15         }16         if (i == 0 && j != 0) {17             matrix[i][j] = FindMinPath(i, j-1, grid, matrix) + grid[i][j];18             return matrix[i][j];19         }20         if (i != 0 && j == 0) {21             matrix[i][j] = FindMinPath(i-1, j, grid, matrix) + grid[i][j];22             return matrix[i][j];23         }24         else {25             matrix[i][j] = Math.min(FindMinPath(i, j-1, grid, matrix), FindMinPath(i-1, j, grid, matrix)) + grid[i][j];26             return matrix[i][j];27         }28     }29 }

 

Leetcode: Minimum Path Sum