Modify array by replacing elements with the nearest power of its previous or next element

Given a circular array arr[] consisting of N positive integers, the task is to modify the array by replacing each array element with the nearest power of its previous or next array element.

Examples:

Input: arr[] = {2, 3, 4, 1, 2}
Output: {2, 4, 3, 1, 2}
Explanation:
For arr[0](= 2): The previous and the next array elements are 2 and 3 respectively. Therefore, nearest power is 2¹.
For arr[1](= 3): The previous and the next elements are 2 and 4 respectively. Therefore, the nearest power is 4¹.
For arr[2](= 4): The previous and the next elements are 3 and 1 respectively. Therefore, the nearest power is 3¹.
For arr[3](= 1): The previous and the next elements are 4, and 2. Therefore, the nearest power is 4⁰.
For arr[4](= 2): The previous and the next elements are 1, and 2. Therefore, the nearest power of 1 is 2¹.

Input: arr[] = {21, 3, 54, 78, 9}
Output: {27, 1, 78, 81, 1}

Approach: The idea is to traverse the array and replace each array element with the nearest power of its previous element or next array element. 
Follow the steps below to solve this problem:

• Traverse the array arr[] and perform the following steps:
  • Find the value of K for which X^K will be closest to Y.
  • For calculating K, take the floor value of log_x(Y).
  • Therefore, K and K + 1 will be the two integers for which the nearest power is the closest.
  • Calculate Y^K and Y^{(K + 1)} and check which is closest to X and update the array element arr[i] with the closest value.
• After completing the above steps, print the array arr[] as the modified array   .

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;

// Function to calculate the power
// of y which is nearest to x
int nearestPow(int x, int y)
{

    // Base Case
    if (y == 1)
        return 1;

    // Stores the logarithmic
    // value of x with base y
    int k = log10(x) / log10(y);

    if (abs(pow(y, k) - x) <
        abs(pow(y, (k + 1)) - x))
        return pow(y, k);

    return pow(y, (k + 1));
}

// Function to replace each array
// element by the nearest power of
// its previous or next element
void replacebyNearestPower(vector<int> arr)
{

    // Stores the previous
    // and next element
    int prev = arr[arr.size() - 1];
    int lastNext = arr[0];
    int next = 0;

    // Traverse the array
    for(int i = 0; i < arr.size(); i++)
    {
        int temp = arr[i];
        if (i == arr.size() - 1)
            next = lastNext;
        else
            next = arr[(i + 1) % arr.size()];

        // Calculate nearest power for
        // previous and next elements
        int prevPow = nearestPow(arr[i], prev);
        int nextPow = nearestPow(arr[i], next);

        // Replacing the array values
        if (abs(arr[i] - prevPow) <
            abs(arr[i] - nextPow))
            arr[i] = prevPow;
        else
            arr[i] = nextPow;

        prev = temp;
    }

    // Print the updated array
    for(int i = 0; i < arr.size(); i++)
        cout << arr[i] << " ";
}

// Driver Code
int main()
{

    // Given array
    vector<int> arr{ 2, 3, 4, 1, 2 };

    replacebyNearestPower(arr);
}

// This code is contributed by ipg2016107

Java

// Java program for the above approach
class GFG{

// Function to calculate the power
// of y which is nearest to x
static int nearestPow(int x, int y)
{

    // Base Case
    if (y == 1)
        return 1;

    // Stores the logarithmic
    // value of x with base y
    int k = (int)(Math.log10(x) /
                  Math.log10(y));

    if (Math.abs(Math.pow(y, k) - x) <
        Math.abs(Math.pow(y, (k + 1)) - x))
        return (int)(Math.pow(y, k));

    return (int)(Math.pow(y, (k + 1)));
}

// Function to replace each array
// element by the nearest power of
// its previous or next element
static void replacebyNearestPower(int[] arr)
{

    // Stores the previous
    // and next element
    int prev = arr[arr.length - 1];
    int lastNext = arr[0];
    int next = 0;

    // Traverse the array
    for(int i = 0; i < arr.length; i++)
    {
        int temp = arr[i];
        if (i == arr.length - 1)
            next = lastNext;
        else
            next = arr[(i + 1) % arr.length];

        // Calculate nearest power for
        // previous and next elements
        int prevPow = nearestPow(arr[i], prev);
        int nextPow = nearestPow(arr[i], next);

        // Replacing the array values
        if (Math.abs(arr[i] - prevPow) <
            Math.abs(arr[i] - nextPow))
            arr[i] = prevPow;
        else
            arr[i] = nextPow;

        prev = temp;
    }

    // Print the updated array
    for(int i = 0; i < arr.length; i++)
        System.out.print(arr[i] + " ");
}

// Driver Code
public static void main(String args[])
{

    // Given array
    int[] arr = { 2, 3, 4, 1, 2 };

    replacebyNearestPower(arr);
}
}

// This code is contributed by abhinavjain194

Python3

# Python3 program for the above approach

import math

# Function to calculate the power
# of y which is nearest to x
def nearestPow(x, y):

    # Base Case
    if y == 1:
        return 1

    # Stores the logarithmic
    # value of x with base y
    k = int(math.log(x, y))

    if abs(y**k - x) < abs(y**(k + 1) - x):
        return y**k

    return y**(k + 1)

# Function to replace each array
# element by the nearest power of
# its previous or next element
def replacebyNearestPower(arr):

    # Stores the previous
    # and next element
    prev = arr[-1]

    lastNext = arr[0]

    # Traverse the array
    for i in range(len(arr)):

        temp = arr[i]
        if i == len(arr)-1:
            next = lastNext
        else:
            next = arr[(i + 1) % len(arr)]

        # Calculate nearest power for
        # previous and next elements
        prevPow = nearestPow(arr[i], prev)
        nextPow = nearestPow(arr[i], next)

        # Replacing the array values
        if abs(arr[i]-prevPow) < abs(arr[i]-nextPow):
            arr[i] = prevPow
        else:
            arr[i] = nextPow
        prev = temp

    # Print the updated array
    print(arr)

# Driver Code

# Given array
arr = [2, 3, 4, 1, 2]

replacebyNearestPower(arr)

C#

// C# program for the above approach
using System;

class GFG{

// Function to calculate the power
// of y which is nearest to x
static int nearestPow(int x, int y)
{

    // Base Case
    if (y == 1)
        return 1;

    // Stores the logarithmic
    // value of x with base y
    int k = (int)(Math.Log(x, y));

    if (Math.Abs(Math.Pow(y, k) - x) <
        Math.Abs(Math.Pow(y, (k + 1)) - x))
        return (int)(Math.Pow(y, k));

    return (int)(Math.Pow(y, (k + 1)));
}

// Function to replace each array
// element by the nearest power of
// its previous or next element
static void replacebyNearestPower(int[] arr)
{

    // Stores the previous
    // and next element
    int prev = arr[arr.Length - 1];
    int lastNext = arr[0];
    int next = 0;

    // Traverse the array
    for(int i = 0; i < arr.Length; i++)
    {
        int temp = arr[i];
        if (i == arr.Length - 1)
            next = lastNext;
        else
            next = arr[(i + 1) % arr.Length];

        // Calculate nearest power for
        // previous and next elements
        int prevPow = nearestPow(arr[i], prev);
        int nextPow = nearestPow(arr[i], next);

        // Replacing the array values
        if (Math.Abs(arr[i] - prevPow) <
            Math.Abs(arr[i] - nextPow))
            arr[i] = prevPow;
        else
            arr[i] = nextPow;

        prev = temp;
    }

    // Print the updated array
    for(int i = 0; i < arr.Length; i++)
        Console.Write(arr[i] + " ");
}

// Driver Code
public static void Main()
{

    // Given array
    int[] arr = { 2, 3, 4, 1, 2 };

    replacebyNearestPower(arr);
}
}

// This code is contributed by ukasp

Javascript

<script>

// JavaScript program for the above approach

// Function to calculate the power
// of y which is nearest to x
function nearestPow(x, y) {

    // Base Case
    if (y == 1)
        return 1

    // Stores the logarithmic
    // value of x with base y
    var k = Math.floor(Math.log(x) / Math.log(y))

    if (Math.abs(Math.pow(y,k) - x) <
        Math.abs(Math.pow(y,(k + 1)) - x))
        return Math.pow(y,k)

    return Math.pow(y,(k + 1))
}

// Function to replace each array
// element by the nearest power of
// its previous or next element
function replacebyNearestPower(arr) {

    // Stores the previous
    // and next element
    var prev = arr[arr.length -1]

    var lastNext = arr[0]

    // Traverse the array
    for (var i = 0; i < arr.length; i++){

        var temp = arr[i]
        if (i == arr.length -1)
            var next = lastNext
        else
            var next = arr[(i + 1) % arr.length]

        // Calculate nearest power for
        // previous and next elements
        var prevPow = nearestPow(arr[i], prev)
        var nextPow = nearestPow(arr[i], next)

        // Replacing the array values
        if (Math.abs(arr[i]-prevPow) <
            Math.abs(arr[i]-nextPow))
            arr[i] = prevPow
        else
            arr[i] = nextPow

        prev = temp
    }

    // Print the updated array
    document.write(arr)
}
// Driver Code
// Given array
var arr = [2, 3, 4, 1, 2]

replacebyNearestPower(arr)

// This code is contributed by AnkThon

</script>

Output:

[2, 4, 3, 1, 2]

Time Complexity: O(N)
Auxiliary Space: O(1)