【LeetCode】62.Unique Paths解题报告

【LeetCode】62.Unique Paths解题报告

tags: Array DP

题目地址：https://leetcode.com/problems/unique-paths/#/description
题目描述：

  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.

题意：机器人从左顶点走到右顶点，问多少种走法，只能向右和向下。

分析：本题其实就是一个组合问题，用公式可以直接得到，然而，题还可以用dp做，但是刚开始刷题，dp解法以后补上。公式其实就是（m+n）!/m!*n!

Solutions:

public class Solution {    public int uniquePaths(int m, int n) {        if(m == 1 || n == 1)            return 1;        m--;        n--;        if(m < n) {              // Swap, so that m is the bigger number            m = m + n;            n = m - n;            m = m - n;        }        long res = 1;        int j = 1;        for(int i = m+1; i <= m+n; i++, j++){       // Instead of taking factorial, keep on multiply & divide            res *= i;            res /= j;        }        return (int)res;    }}

Date：2017年6月23日