Skip to content
Related Articles

Related Articles

Improve Article

Minimum steps to reach the Nth stair in jumps of perfect power of 2

  • Difficulty Level : Medium
  • Last Updated : 07 Apr, 2021

Given N stairs, the task is to find the minimum number of jumps of perfect power of 2 requires to reach the Nth stair.

Examples: 

Input: N = 5 
Output: 
Explanation: 
We can take jumps from 0->1->4
So the minimum jumps require are 2.

Input: N = 23 
Output:
Explanation: 
We can take jumps from 0->1->2->4->16
So the minimum jumps required are 4. 
 

Approach: Since the jumps are required to be in perfect power of 2. So the count of set bit in the given number N is the minimum number of jumps required to reach Nth stair as the summation of 2i for all set bit index i is equals to N.



Below is the implementation of the above approach:  

C++




// C++ program for the above approach
#include "bits/stdc++.h"
using namespace std;
 
// Function to count the number of jumps
// required to reach Nth stairs.
int stepRequired(int N)
{
 
    int cnt = 0;
 
    // Till N becomes 0
    while (N) {
 
        // Removes the set bits from
        // the right to left
        N = N & (N - 1);
        cnt++;
    }
 
    return cnt;
}
 
// Driver Code
int main()
{
 
    // Number of stairs
    int N = 23;
 
    // Function Call
    cout << stepRequired(N);
    return 0;
}

Java




// Java program for the above approach
 
import java.util.*;
 
class GFG{
 
// Function to count the number of jumps
// required to reach Nth stairs.
static int stepRequired(int N)
{
 
    int cnt = 0;
 
    // Till N becomes 0
    while (N > 0) {
 
        // Removes the set bits from
        // the right to left
        N = N & (N - 1);
        cnt++;
    }
 
    return cnt;
}
 
// Driver Code
public static void main(String[] args)
{
 
    // Number of stairs
    int N = 23;
 
    // Function Call
    System.out.print(stepRequired(N));
}
}
 
// This code is contributed by PrinciRaj1992

Python3




# Python3 program for the above approach
 
# Function to count the number of jumps
# required to reach Nth stairs.
def stepRequired(N):
 
    cnt = 0;
 
    # Till N becomes 0
    while (N > 0):
 
        # Removes the set bits from
        # the right to left
        N = N & (N - 1);
        cnt += 1;
    return cnt;
 
# Driver Code
if __name__ == '__main__':
 
    # Number of stairs
    N = 23;
 
    # Function Call
    print(stepRequired(N));
     
# This code is contributed by 29AjayKumar

C#




// C# program for the above approach
using System;
 
class GFG{
 
// Function to count the number of
// jumps required to reach Nth stairs.
static int stepRequired(int N)
{
    int cnt = 0;
 
    // Till N becomes 0
    while (N > 0)
    {
 
        // Removes the set bits from
        // the right to left
        N = N & (N - 1);
        cnt++;
    }
 
    return cnt;
}
 
// Driver Code
public static void Main(String[] args)
{
 
    // Number of stairs
    int N = 23;
 
    // Function Call
    Console.Write(stepRequired(N));
}
}
 
// This code is contributed by 29AjayKumar

Javascript




<script>
 
// JavaScript program for the above approach
 
// Function to count the number of jumps
// required to reach Nth stairs.
function stepRequired(N)
{
    let cnt = 0;
 
    // Till N becomes 0
    while (N)
    {
         
        // Removes the set bits from
        // the right to left
        N = N & (N - 1);
        cnt++;
    }
 
    return cnt;
}
 
// Driver Code
 
// Number of stairs
let N = 23;
 
// Function Call
document.write(stepRequired(N));
 
// This code is contributed by Surbhi Tyagi
 
</script>
Output: 
4

 

Time Complexity: O(log N)
 

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.




My Personal Notes arrow_drop_up