70. Climbing Stairs

Question

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?

Example 1:

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

Example 2:

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

Constraints:

• 1 <= n <= 45

Summary

It is a simple DP. There is two ways to climb to stair n, 1) from stair n-1 climb 1 step or 2) from stair n-2 climb 2 steps.

climbStairs(n) = climbStairs(n-1) + climbStairs(n-2);

Solution

class Solution {
public:
    map<int,int> memo = { {0,0},{1,1}, {2,2}};
    int climbStairs(int n) {
        if (memo.find(n) != memo.end())
            return memo[n];
        else
            memo[n] = climbStairs(n-1) + climbStairs(n-2);
        return memo[n];
    }
};