Climbing Stairs

 1 import java.math.BigInteger;
 2 
 3 public class Solution {
 4     public int climbStairs(int n) {
 5         int num2s = n / 2;
 6         int ways = 0;
 7         int num1s = n - num2s * 2;
 8         for(int i = num2s; i >= 0; i--){
 9             ways += selectMFromN(num2s + num1s, num2s);
10             num2s--;
11             num1s += 2;
12         }
13         return ways;
14     }
15     /**
16      * 计算C(N,M) = n * (n - 1) *...(n - m + 1) / m!
17      * @param n
18      * @param m
19      * @return
20      */
21     public int selectMFromN(int n, int m){
22         BigInteger fenzi = new BigInteger("1");
23         BigInteger fenmu = new BigInteger("1");
24         for(int i = n ; i >= n - m + 1;i--){
25             fenzi = fenzi.multiply(new BigInteger(String.valueOf(i)));
26         }
27         for(int i = m ; i >= 1;i--){
28             fenmu = fenmu.multiply(new BigInteger(String.valueOf(i)));
29         }
30         return (fenzi.divide(fenmu)).intValue();
31     }
32 }