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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?Input FormatInput from stdin will be processed as follows and passed to the function.The first line contains an integer n, the number of steps.Constraints0 <= n <= 1000Output FormatThe output is the number of waysSample Input 02Sample Output 02

Question

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?Input FormatInput from stdin will be processed as follows and passed to the function.The first line contains an integer n, the number of steps.Constraints0 <= n <= 1000Output FormatThe output is the number of waysSample Input 02Sample Output 02

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Solution

This problem can be solved using dynamic programming. Here are the steps:

  1. Create an array dp of size n+1 to store the number of ways to reach a step. Initialize dp[0] and dp[1] as 1 because there is only one way to reach the first and second step.

  2. For each step from 2 to n, calculate the number of ways to reach that step. The number of ways to reach a step is the sum of the number of ways to reach the previous step and the number of ways to reach the second previous step. This is because at each step, you can either take one step from the previous step or two steps from the second previous step. So, dp[i] = dp[i-1] + dp[i-2].

  3. The number of ways to reach the top (step n) is stored in dp[n].

Here is a Python code snippet that implements the above steps:

def climbStairs(n):
    if n <= 1:
        return n
    dp = [0]*(n+1)
    dp[0] = dp[1] = 1
    for i in range(2, n+1):
        dp[i] = dp[i-1] + dp[i-2]
    return dp[n]

This function takes an integer n as input and returns the number of distinct ways to climb to the top of the staircase.

This problem has been solved

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