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  • [leetcode]Unique Paths

    Unique Paths

    A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

    The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

    How many possible unique paths are there?

    Above is a 3 x 7 grid. How many possible unique paths are there?

    Note: m and n will be at most 100.

    算法思路:

    典型的二维DP,dp[i][j]表示从左上角(0,0)到(i,j)的paths。状态转移方程:dp[i][j] = dp[i - 1][j] + dp[i][j - 1];

    代码如下:

     1 public class Solution {
     2     public int uniquePaths(int m, int n) {
     3         if(m == 1 || n == 1) return 1;
     4         int[][] dp = new int[m][n];
     5         for(int i = 0; i < n; dp[0][i++] = 1);
     6         for(int i = 0; i < m; dp[i++][0] = 1);
     7         for(int i = 1; i < m; i++){
     8             for(int j = 1; j < n; j++){
     9                 dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
    10             }
    11         }
    12         return dp[m - 1][n - 1];
    13     }
    14 }
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  • 原文地址:https://www.cnblogs.com/huntfor/p/3900262.html
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