Create unique_paths.md

Author: 17020021029

unique_paths.md

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+# Unique Paths
+## Problem
+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?
+
+![图片](https://leetcode.com/static/images/problemset/robot_maze.png)
+
+Above is a 3 x 7 grid. How many possible unique paths are there?
+
+Note: m and n will be at most 100.
+## 问题分析
+向下走和向右走的步数是一定的,一共走m+n-2步，其中m-1步往一个方向走，n-1步往另一个方向走，该题就转化为了排列组合的问题，从m+n-2步中选出m-1步来或从m+n-2选出n-1步来，结果都是一样的
+## 代码实现
+```ruby
+int uniquePaths(int m, int n) {
+    long x m+n-2;  //一定要用long，阶乘数太大了
+    long y=(m<n?m:n)-1;
+    long up=1,down=1;   
+    if(m==1||n==1) 
+        return 1;
+    for(int i=0;i<y;i++){
+        up *= x--;
+    }
+    for(int i=y;i>0 ;i--){
+        down *= i;
+    }
+    return (int)(up/down);
+}
+```