Find highest frequency of non-negative powers that are same as indices of elements in given Array

Given an array arr[] with N non-negative integers, find the maximum number of elements that are the same non-negative powers of their indices.

arr[i] = i^X, where X is a non negative number. 

The task is to return the maximum frequency of X.

Example:

Input: arr = [1, 1, 4, 17]
Output: 2
Explanation:
The element 1 at index 0, is a power of 0
The element 1 at index 1, is a power of 0
The element 4 at index 2, is a power of 2
The element 17 at index 3, is not a power of its index, so it is not considered
Therefore the maximum frequency is of power 0, which is 2 

Input: arr = [0, 1, 1, 9, 1, 25]
Output: 4
Explanation: 
The element 0 at index 0, is a power of 2
The element 1 at index 1, is a power of 2
The element 1 at index 2, is a power of 0
The element 9 at index 3, is a power of 2
The element 1 at index 4, is a power of 0
The element 25 at index 5, is a power of 2
Therefore the maximum frequency is of power 2, which is 4 

Approach: Given problem can be solved by finding the powers of every index and checking if they are equal to the element present at that index. 

Follow the steps below to solve the problem:

• Iterate the array arr from index 2 till the end and at every index:
  • Use a loop to multiply the index by itself until the value is less than the maximum value of integer and less than or equal to the element present at that index
    • If the power becomes equal to the element then check if its present in the hashmap:
      • If the power is not present then add it in the hash map with value 1
      • Else if the power is already present then increment its frequency by 1
• If arr[0] = 1, then increment the frequency of 0 in the hashmap by 1
• Iterate the HashMap and find the value with the maximum frequency:
  • If arr[0] = 1, then the frequency of all values except 0 is increment by 1
• If arr[1] = 1, then return, maxFreq +1, else return maxFreq

Below is the implementation of the above approach:

C++

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

// Function to find count of elements which
// are a non-negative power of their indices
int indPowEqualsEle(vector<int> arr)
{

    // Length of the array
    int len = arr.size();

    // Initialize the hashmap to store
    // the frequency of elements
    unordered_map<int, int> map;

    // Initialize maximum value
    // of integer into long
    long limit = INT_MAX;

    // Iterate the array arr from index 2
    for (int i = 2; i < len; i++)
    {

        // If current element is equal to 1
        // then its equal to index power 0
        if (arr[i] == 1)
        {

            // Increment the frequency of 0 by 1
            map[0]++;
            continue;
        }

        // Initialize a variable to index
        // which is to be multiplied
        // by the index
        long indPow = i;

        // Initialize a variable to
        // store the power of the index
        int p = 1;

        while (indPow <= limit && indPow <= arr[i])
        {

            // Element is equal to
            // a power of its index
            if (arr[i] == indPow)
            {

                // Increment the frequency
                // of p by 1
                map[p]++;

                break;
            }

            // Increment power
            p++;

            // Multiply current value with
            // index to get the next power
            indPow *= i;
        }
    }

    // If arr[0] == 1, then increment
    // the frequency of 0 in the hashmap
    map[0]++;

    // Initialize maxFreq to 0 to calculate
    // maximum frequency of powers
    int maxFreq = 0;

    // Iterate the hashmap
    for (auto it = map.begin(); it != map.end(); it++)
    {
        int power = it->second;
        // If arr[0] == 0, then increment the
        // frequency of all powers except 0
        if (arr[0] == 0 && power != 0)
        {

            maxFreq = max(maxFreq,
                          map[power] + 1);
        }
        else
        {

            maxFreq = max(maxFreq,
                          map[power]);
        }
    }

    // Increment the maximum frequency by 1
    // If arr[1] is equal to 1
    return arr[1] == 1
               ? maxFreq + 1
               : maxFreq;
}

// Driver function
int main()
{

    // Initialize an array
    vector<int> arr = {0, 1, 1, 9, 1, 25};

    // Call the function
    // and print the answer
    cout << (indPowEqualsEle(arr));
}

// This code is contributed by Potta Lokesh

Java

// Java implementation for the above approach

import java.io.*;
import java.util.*;

class GFG {

    // Function to find count of elements which
    // are a non-negative power of their indices
    public static int indPowEqualsEle(int[] arr)
    {

        // Length of the array
        int len = arr.length;

        // Initialize the hashmap to store
        // the frequency of elements
        Map<Integer, Integer> map
            = new HashMap<>();

        // Initialize maximum value
        // of integer into long
        long limit = (long)Integer.MAX_VALUE;

        // Iterate the array arr from index 2
        for (int i = 2; i < len; i++) {

            // If current element is equal to 1
            // then its equal to index power 0
            if (arr[i] == 1) {

                // Increment the frequency of 0 by 1
                map.put(0,
                        map.getOrDefault(0, 0) + 1);
                continue;
            }

            // Initialize a variable to index
            // which is to be multiplied
            // by the index
            long indPow = i;

            // Initialize a variable to
            // store the power of the index
            int p = 1;

            while (indPow <= limit
                   && indPow <= arr[i]) {

                // Element is equal to
                // a power of its index
                if (arr[i] == indPow) {

                    // Increment the frequency
                    // of p by 1
                    map
                        .put(p,
                             map.getOrDefault(p, 0) + 1);

                    break;
                }

                // Increment power
                p++;

                // Multiply current value with
                // index to get the next power
                indPow *= i;
            }
        }

        // If arr[0] == 1, then increment
        // the frequency of 0 in the hashmap
        map.put(0, map.getOrDefault(0, 0) + 1);

        // Initialize maxFreq to 0 to calculate
        // maximum frequency of powers
        int maxFreq = 0;

        // Iterate the hashmap
        for (int power : map.keySet()) {

            // If arr[0] == 0, then increment the
            // frequency of all powers except 0
            if (arr[0] == 0 && power != 0) {

                maxFreq
                    = Math.max(maxFreq,
                               map.get(power) + 1);
            }
            else {

                maxFreq = Math.max(maxFreq,
                                   map.get(power));
            }
        }

        // Increment the maximum frequency by 1
        // If arr[1] is equal to 1
        return arr[1] == 1
            ? maxFreq + 1
            : maxFreq;
    }

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

        // Initialize an array
        int[] arr = { 0, 1, 1, 9, 1, 25 };

        // Call the function
        // and print the answer
        System.out.println(indPowEqualsEle(arr));
    }
}

Python3

# Python 3 code for the above approach
from collections import defaultdict
import sys

# Function to find count of elements which
# are a non-negative power of their indices
def indPowEqualsEle(arr):

    # Length of the array
    length = len(arr)

    # Initialize the hashmap to store
    # the frequency of elements
    map = defaultdict(int)

    # Initialize maximum value
    # of integer into long
    limit = sys.maxsize

    # Iterate the array arr from index 2
    for i in range(2, length):

        # If current element is equal to 1
        # then its equal to index power 0
        if (arr[i] == 1):

            # Increment the frequency of 0 by 1
            map[0] += 1
            continue

        # Initialize a variable to index
        # which is to be multiplied
        # by the index
        indPow = i

        # Initialize a variable to
        # store the power of the index
        p = 1

        while (indPow <= limit and indPow <= arr[i]):

            # Element is equal to
            # a power of its index
            if (arr[i] == indPow):

                # Increment the frequency
                # of p by 1
                map[p] += 1

                break

            # Increment power
            p += 1

            # Multiply current value with
            # index to get the next power
            indPow *= i

    # If arr[0] == 1, then increment
    # the frequency of 0 in the hashmap
    map[0] += 1

    # Initialize maxFreq to 0 to calculate
    # maximum frequency of powers
    maxFreq = 0

    # Iterate the hashmap
    for it in range(len(map)):

        power = map[it]
        # If arr[0] == 0, then increment the
        # frequency of all powers except 0
        if (arr[0] == 0 and power != 0):

            maxFreq = max(maxFreq,
                          map[power] + 1)
        else:

            maxFreq = max(maxFreq,
                          map[power])

    # Increment the maximum frequency by 1
    # If arr[1] is equal to 1
    if(arr[1] == 1):
        return maxFreq + 1
    return maxFreq

# Driver function
if __name__ == "__main__":

    # Initialize an array
    arr = [0, 1, 1, 9, 1, 25]

    # Call the function
    # and print the answer
    print(indPowEqualsEle(arr))

    # This code is contributed by ukasp.

C#

// C# implementation for the above approach
using System;
using System.Collections.Generic;

public class GFG {

    // Function to find count of elements which
    // are a non-negative power of their indices
    public static int indPowEqualsEle(int[] arr)
    {

        // Length of the array
        int len = arr.Length;

        // Initialize the hashmap to store
        // the frequency of elements
        Dictionary<int, int> map
            = new Dictionary<int, int>();

        // Initialize maximum value
        // of integer into long
        long limit = (long)int.MaxValue;

        // Iterate the array arr from index 2
        for (int i = 2; i < len; i++) {

            // If current element is equal to 1
            // then its equal to index power 0
            if (arr[i] == 1) {

                // Increment the frequency of 0 by 1
                if(map.ContainsKey(0))
                    map[0] = map[0]+1;
                else
                    map.Add(0, 1);
                continue;
            }

            // Initialize a variable to index
            // which is to be multiplied
            // by the index
            long indPow = i;

            // Initialize a variable to
            // store the power of the index
            int p = 1;

            while (indPow <= limit
                   && indPow <= arr[i]) {

                // Element is equal to
                // a power of its index
                if (arr[i] == indPow) {

                    // Increment the frequency
                    // of p by 1
                    if(map.ContainsKey(p))
                    map[p] = map[p]+1;
                else
                    map.Add(p, 1);

                    break;
                }

                // Increment power
                p++;

                // Multiply current value with
                // index to get the next power
                indPow *= i;
            }
        }

        // If arr[0] == 1, then increment
        // the frequency of 0 in the hashmap
        if(map.ContainsKey(0))
            map[0] = map[0]+1;
        else
            map.Add(0, 1);

        // Initialize maxFreq to 0 to calculate
        // maximum frequency of powers
        int maxFreq = 0;

        // Iterate the hashmap
        foreach (int power in map.Keys) {

            // If arr[0] == 0, then increment the
            // frequency of all powers except 0
            if (arr[0] == 0 && power != 0) {

                maxFreq
                    = Math.Max(maxFreq,
                               map[power] + 1);
            }
            else {

                maxFreq = Math.Max(maxFreq,
                                   map[power]);
            }
        }

        // Increment the maximum frequency by 1
        // If arr[1] is equal to 1
        return arr[1] == 1
            ? maxFreq + 1
            : maxFreq;
    }

    // Driver function
    public static void Main(String[] args)
    {

        // Initialize an array
        int[] arr = { 0, 1, 1, 9, 1, 25 };

        // Call the function
        // and print the answer
        Console.WriteLine(indPowEqualsEle(arr));
    }
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// Javascript code for the above approach

// Function to find count of elements which
// are a non-negative power of their indices
function indPowEqualsEle(arr) {

  // Length of the array
  let len = arr.length;

  // Initialize the hashmap to store
  // the frequency of elements
  let map = new Map();

  // Initialize maximum value
  // of integer into long
  let limit = Number.MAX_SAFE_INTEGER;

  // Iterate the array arr from index 2
  for (let i = 2; i < len; i++) {

    // If current element is equal to 1
    // then its equal to index power 0
    if (arr[i] == 1) {

      // Increment the frequency of 0 by 1
      if (map.has(0)) {
        map.set(0, map.get(0) + 1)
      } else {
        map.set(0, 1)
      }
      continue;
    }

    // Initialize a variable to index
    // which is to be multiplied
    // by the index
    let indPow = i;

    // Initialize a variable to
    // store the power of the index
    let p = 1;

    while (indPow <= limit && indPow <= arr[i]) {

      // Element is equal to
      // a power of its index
      if (arr[i] == indPow) {

        // Increment the frequency
        // of p by 1
        if (map.has(p)) {
          map.set(p, map.get(p) + 1)
        } else {
          map.set(p, 1)
        }

        break;
      }

      // Increment power
      p++;

      // Multiply current value with
      // index to get the next power
      indPow *= i;
    }
  }

  // If arr[0] == 1, then increment
  // the frequency of 0 in the hashmap
  if (map.has(0)) {
    map.set(0, map.get(0) + 1)
  } else {
    map.set(0, 1)
  }

  // Initialize maxFreq to 0 to calculate
  // maximum frequency of powers
  let maxFreq = 0;

  // Iterate the hashmap
  for (let power of map.keys()) {

    // If arr[0] == 0, then increment the
    // frequency of all powers except 0
    if (arr[0] == 0 && power != 0) {

      maxFreq = Math.max(maxFreq,
        map.get(power) + 1);
    }
    else {

      maxFreq = Math.max(maxFreq,
        map.get(power));
    }
  }

  // Increment the maximum frequency by 1
  // If arr[1] is equal to 1
  return arr[1] == 1
    ? maxFreq + 1
    : maxFreq;
}

// Driver function
// Initialize an array
let arr = [0, 1, 1, 9, 1, 25];

// Call the function
// and print the answer
document.write((indPowEqualsEle(arr)))

// This code is contributed by gfgking.
</script>

Output

4

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