70. Climbing Stairs

You are climbing a staircase. It takes n steps to reach 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: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: n = 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

Solution:

class Solution {
    public int climbStairs(int n) {
        /*

        dp[i] means how many step to current i staircase
2                _
1           _ 
0        _ 
                 2 + 1
            1+1
dp[i]    1   


        */
        if (n == 1){
            return 1;
        }
        int[] dp = new int[n];

        dp[0] = 1;
        dp[1] = 2;
        for (int i = 2; i < n; i++){
            dp[i] = dp[i - 1] + dp[i - 2];
        }   

        return dp[n - 1];
    }
}

// TC: O(n)
// SC: O(n)

Brute Force

class Solution {
    public int climbStairs(int n) {
        return help(0, n);
    }

    public int help(int i, int n){
        if (i > n){
            return 0;
        }

        if (i == n){
            return 1;
        }

        return help(i+1, n) + help(i+2, n);
    }
}

//TLE

//TC: O(2^n)
//SC: O(n)

Dynamic:

class Solution {
    public int climbStairs(int n) {
        if (n == 0 || n == 1 || n == 2 || n == 3){
            return  n;
        }

        int[] dp = new int[n + 1];
        dp[0] = 0;
        dp[1] = 1;
        dp[2] = 2;
        dp[3] = 3;
        for (int i = 4; i < n + 1; i++){
            dp[i] = dp[i-1] + dp[i-2];
        }

        return dp[n];
    }
}


// TC: O(n)
// SC: O(n)

/*
        n = 4

        dp: 0,1,2,3,4
            [0,1,2,3, ]

            dp[i] = dp[i-1] + dp[i-2]


             0 
             / \
           1     2
          / \    / \
         2   3   3  4
       /  \  /   / 
      3   4  4    4
    /
    4         


*/

https://leetcode.cn/problems/climbing-stairs/solutions/2560716/jiao-ni-yi-bu-bu-si-kao-dong-tai-gui-hua-7zm1/