Climb Stair (DP) -[Leetcode]

Prerequisite — Recursion ,memoization ,dp

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

Java Solution :-

class Solution {
public int climbStairs(int n) {
int dp[] = new int [n+1];
for(int i=0;i<=n;i++)
{
dp[i]=-1;
}

return climb(n , dp);
}

public static int climb(int n , int dp[])
{
if(n==0)
{
return 1;
}
if(n<0)
{
return 0;
}
if(dp[n]!=-1)
{
return dp[n];
}
int left=climb(n-1,dp);
int right=climb(n-2,dp);

dp[n]=right+left;

return dp[n];
}
}