70. Climbing Stairs

浅浅的花香味﹌ 2022-05-16 15:56 192阅读 0赞

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

Example 1:

  1. Input: 2
  2. Output: 2
  3. Explanation: There are two ways to climb to the top.
  4. 1. 1 step + 1 step
  5. 2. 2 steps

Example 2:

  1. Input: 3
  2. Output: 3
  3. Explanation: There are three ways to climb to the top.
  4. 1. 1 step + 1 step + 1 step
  5. 2. 1 step + 2 steps
  6. 3. 2 steps + 1 step

题意：有n阶楼梯， 每次可以爬1层或2层，总有多少种走法。

方法一：动态规划，状态转移方程是 count[i] = count[i-1] + count[i-2]; count[i]表示i个台阶有多少种走法。

  1. class Solution {
  2. public:
  3.     int climbStairs(int n) {
  4.          if(n<=2)
  5.           return n;
  7.         vector<int> count(n);
  8.         count[0] =1;
  9.         count[1] =2;
  11.         for(int i=2;i<n;i++)
  12.         {
  13.           count[i] = count[i-1] + count[i-2];
  14.         }      
  15.         return  count[n-1];
  16.     }
  17. };

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