Queries to count occurrences of maximum array element in subarrays starting from given indices

Given two arrays arr[] and q[] consisting of N integers, the task is for each query q[i] is to determine the number of times the maximum array element occurs in the subarray [q[i], arr[N – 1]].

Examples:

Input: arr[] = {5, 4, 5, 3, 2}, q[] = {1, 2, 3, 4, 5}
Output: 2 1 1 1 1
Explanation:
For the first query index start from 1. The subarray is [5, 4, 5, 3, 2], the maximum value is 5 and it’s occurrence in subarray is 2.
For the second query index start from 2. The subarray is [4, 5, 3, 2], the maximum value is 5 and it’s occurrence in subarray is 1.
For the third query index start from 3. The subarray is [5, 3, 2], the maximum value is 5 and it’s occurrence in subarray is 1.
For the forth query index start from 4. The subarray is [3, 2], the maximum value is 3 and it’s occurrence in subarray is 1.
For the fifth query index start from 5. The subarray is [2], the maximum value is 2 and it’s occurrence in subarray is 1.

Input: arr[] = {2, 1, 2}, q[] = {1, 2, 3}
Output: 2 1 1

Naive Approach: The simplest approach is to traverse the array and find the maximum array element. Now, for each query q[i], traverse the subarray [q[i], arr[N – 1]], and print the count of occurrences of the maximum element in the subarray. 

Follow the steps below to implement the above idea:

C++

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

// Function to find occurrence of
// max element in given subarray
void FreqOfMaxElement(vector<int> arr, vector<int> q)
{

    // Traverse over each query
    for (int i = 0; i < q.size(); i++) {

        // Find the starting index of each query
        int start = q[i] - 1;
        int count = 0;

        // Find the maximum element in the range of each
        // query
        int maxx
            = *max_element(arr.begin() + start, arr.end());

        // Find the occurrences of maxx element
        for (int j = start; j < arr.size(); j++) {
            if (arr[j] == maxx) {
                count++;
            }
        }

        // Print the count
        cout << count << " ";
    }
}

// Driver Code
int main()
{
    vector<int> arr = { 5, 4, 5, 3, 2 };
    vector<int> q = { 1, 2, 3, 4, 5 };

    // Function Call
    FreqOfMaxElement(arr, q);
}

Java

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


public class Gfg {
    // Function to find occurrence of
    // max element in given subarray
    public static void FreqOfMaxElement(List<Integer> arr,
                                        List<Integer> q)
    {
        // Traverse over each query
        for (int i = 0; i < q.size(); i++) {
            // Find the starting index of each query
            int start = q.get(i) - 1;
            int count = 0;

            // Find the maximum element in the range of each
            // query
            int maxx = Collections.max(arr.subList(start, arr.size()));

            // Find the occurrences of maxx element
            for (int j = start; j < arr.size(); j++) {
                if (arr.get(j) == maxx) {
                    count++;
                }
            }

            // Print the count
            System.out.print(count + " ");
        }
    }

    // Driver Code
    public static void main(String[] args)
    {
        List<Integer> arr = Arrays.asList(5, 4, 5, 3, 2);
        List<Integer> q = Arrays.asList(1, 2, 3, 4, 5);

        // Function Call
        FreqOfMaxElement(arr, q);
    }
}

Python3

from collections import Counter

def FreqOfMaxElement(arr, q):
    # Traverse over each query
    for i in range(len(q)):
        # Find the starting index of each query
        start = q[i] - 1
        count = 0

        # Find the maximum element in the range of each query
        maxx = max(arr[start:])

        # Find the occurrences of maxx element
        for j in range(start, len(arr)):
            if arr[j] == maxx:
                count += 1

        # Print the count
        print(count, end = " ")

# Driver Code
if __name__ == "__main__":
    arr = [5, 4, 5, 3, 2]
    q = [1, 2, 3, 4, 5]
    FreqOfMaxElement(arr, q)

    # This code is contributed by aadityaburujwale.

C#

// C# program for the above approach

using System;
using System.Linq;
using System.Collections.Generic;

class GFG {

    // Function to find occurrence of
    // max element in given subarray
    static void FreqOfMaxElement(int[] arr,int[] q)
    {

        // Traverse over each query
        for (int i = 0; i < q.Length; i++) {

            // Find the starting index of each query
            int start = q[i] - 1;
            int count = 0;

            // Find the maximum element in the range of each
            // query
            int maxx=-1;
            for(int j=start; j<arr.Length; j++)
                maxx=Math.Max(maxx, arr[j]);

            // Find the occurrences of maxx element
            for (int j = start; j < arr.Length; j++) {
                if (arr[j] == maxx) {
                    count++;
                }
            }

            // Print the count
            Console.Write(count + " ");
        }
    }

    // Driver Code
    public static void Main (string[] args)
    {
        int[] arr = { 5, 4, 5, 3, 2 };
        int[] q = { 1, 2, 3, 4, 5 };

        // Function Call
        FreqOfMaxElement(arr, q);
    }
}

Javascript

// Javascript program for the above approach

// Function to find occurrence of
// max element in given subarray
function FreqOfMaxElement(arr, q)
{

    // Traverse over each query
    for (let i = 0; i < q.length; i++) {

        // Find the starting index of each query
        let start = q[i] - 1;
        let count = 0;

        // Find the maximum element in the range of each
        // query
        let maxx=Number.MIN_SAFE_INTEGER;

        for(let i=start; i<arr.length; i++)
        {
            maxx=Math.max(arr[i], maxx);
        }
        // Find the occurrences of maxx element
        for (let j = start; j < arr.length; j++) {
            if (arr[j] == maxx) {
                count++;
            }
        }

        // Print the count
        document.write(count);
        document.write(" ");
    }
}

// Driver Code
let arr = [ 5, 4, 5, 3, 2 ];
let q = [ 1, 2, 3, 4, 5 ];

// Function Call
FreqOfMaxElement(arr, q);

Output

2 1 1 1 1 

Time Complexity: O(N*Q), where N and Q are the lengths of the given array and query respectively.
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, the idea is to use Hashing. Below are the steps:

• Create an array maxFreqVec[] to store the occurrence of the max element from given index q[i] to N.
• Traverse the array arr[] from the right and keep track of the maximum element in the array and update the array maxFreqVec[] at that index with the occurrence of that maximum element.
• After the above steps, traverse over the array q[] and print the value maxFreqVec[q[i] – 1] as the maximum element in each subarray for each query.

Below is the implementation of the above approach:

C++

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

// Function to find occurrence of
// max element in given subarray
void FreqOfMaxElement(vector<int> arr,
                      vector<int> q)
{

    // Store the frequency of maximum
    // element
    vector<int> maxFreqVec(arr.size());

    int maxSoFar = INT_MIN;
    int maxFreq = 0;

    // Traverse over the array arr[]
    // from right to left
    for(int i = arr.size() - 1; i >= 0; i--)
    {

        // If curr element is greater
        // than maxSofar
        if (arr[i] > maxSoFar)
        {

            // Reset maxSofar and maxFreq
            maxSoFar = arr[i];
            maxFreq = 1;
        }

        // If curr is equal to maxSofar
        else if (arr[i] == maxSoFar)
        {

            // Increment the maxFreq
            maxFreq++;
        }

        // Update maxFreqVec[i]
        maxFreqVec[i] = maxFreq;
    }

    // Print occurrence of maximum
    // element for each query
    for(int k : q)
    {
        cout << maxFreqVec[k - 1] << " ";
    }
}

// Driver Code
int main()
{
    vector<int> arr = { 5, 4, 5, 3, 2 };
    vector<int> q = { 1, 2, 3, 4, 5 };

    // Function Call
    FreqOfMaxElement(arr, q);
}

// This code is contributed by mohit kumar 29

Java

// Java program for the above approach
import java.util.*;
import java.lang.*;

class GFG {

    // Function to find occurrence of
    // max element in given subarray
    static void FreqOfMaxElement(
        int[] arr, int[] q)
    {

        // Store the frequency of maximum
        // element
        int[] maxFreqVec
            = new int[arr.length];

        int maxSoFar = Integer.MIN_VALUE;
        int maxFreq = 0;

        // Traverse over the array arr[]
        // from right to left
        for (int i = arr.length - 1;
             i >= 0; i--) {

            // If curr element is greater
            // than maxSofar
            if (arr[i] > maxSoFar) {

                // Reset maxSofar and maxFreq
                maxSoFar = arr[i];
                maxFreq = 1;
            }

            // If curr is equal to maxSofar
            else if (arr[i] == maxSoFar) {

                // Increment the maxFreq
                maxFreq++;
            }

            // Update maxFreqVec[i]
            maxFreqVec[i] = maxFreq;
        }

        // Print occurrence of maximum
        // element for each query
        for (int k : q) {
            System.out.print(
                maxFreqVec[k - 1] + " ");
        }
    }

    // Driver Code
    public static void main(String[] args)
    {
        int[] arr = { 5, 4, 5, 3, 2 };
        int[] q = { 1, 2, 3, 4, 5 };

        // Function Call
        FreqOfMaxElement(arr, q);
    }
}

Python3

# Python3 program for
# the above approach
import sys;

# Function to find occurrence
# of max element in given
# subarray
def FreqOfMaxElement(arr, q):

    # Store the frequency of
    # maximum element
    maxFreqVec = [0] * (len(arr));

    maxSoFar = -sys.maxsize;
    maxFreq = 0;

    # Traverse over the array
    # arr from right to left
    for i in range(len(arr)-1,
                   -1, -1):

        # If curr element is
        # greater than maxSofar
        if (arr[i] > maxSoFar):

            # Reset maxSofar
            # and maxFreq
            maxSoFar = arr[i];
            maxFreq = 1;

        # If curr is equal to
        # maxSofar
        elif (arr[i] == maxSoFar):

            # Increment the
            # maxFreq
            maxFreq += 1;

        # Update maxFreqVec[i]
        maxFreqVec[i] = maxFreq;

    # Print occurrence of maximum
    # element for each query
    for i in range(0, len(q)):
        print(maxFreqVec[q[i] - 1],
              end = " ");

# Driver Code
if __name__ == '__main__':

    arr = [5, 4, 5, 3, 2];
    q = [1, 2, 3, 4, 5];

    # Function Call
    FreqOfMaxElement(arr, q);

# This code is contributed by shikhasingrajput

C#

// C# program for the
// above approach
using System;
class GFG{

// Function to find occurrence of
// max element in given subarray
static void FreqOfMaxElement(int[] arr,
                             int[] q)
{
  // Store the frequency of
  // maximum element
  int[] maxFreqVec = new int[arr.Length];

  int maxSoFar = Int32.MinValue;
  int maxFreq = 0;

  // Traverse over the array arr[]
  // from right to left
  for (int i = arr.Length - 1;
           i >= 0; i--)
  {
    // If curr element is greater
    // than maxSofar
    if (arr[i] > maxSoFar)
    {
      // Reset maxSofar and maxFreq
      maxSoFar = arr[i];
      maxFreq = 1;
    }

    // If curr is equal to maxSofar
    else if (arr[i] == maxSoFar)
    {
      // Increment the maxFreq
      maxFreq++;
    }

    // Update maxFreqVec[i]
    maxFreqVec[i] = maxFreq;
  }

  // Print occurrence of maximum
  // element for each query
  foreach (int k in q)
  {
    Console.Write(maxFreqVec[k - 1] +
                  " ");
  }
}

// Driver code
static void Main()
{
  int[] arr = {5, 4, 5, 3, 2};
  int[] q = {1, 2, 3, 4, 5};

  // Function Call
  FreqOfMaxElement(arr, q);
  }
}

// This code is contributed by divyeshrabadiya07

Javascript

<script>

// Javascript program for the above approach

// Function to find occurrence of
// max element in given subarray
function FreqOfMaxElement(arr, q)
{

    // Store the frequency of maximum
    // element
    var maxFreqVec = new Array(arr.length);
    var maxSoFar = -1000000000;
    var maxFreq = 0;

    // Traverse over the array arr[]
    // from right to left
    for(var i = arr.length - 1; i >= 0; i--)
    {

        // If curr element is greater
        // than maxSofar
        if (arr[i] > maxSoFar)
        {

            // Reset maxSofar and maxFreq
            maxSoFar = arr[i];
            maxFreq = 1;
        }

        // If curr is equal to maxSofar
        else if (arr[i] == maxSoFar)
        {

            // Increment the maxFreq
            maxFreq++;
        }

        // Update maxFreqVec[i]
        maxFreqVec[i] = maxFreq;
    }

    // Print occurrence of maximum
    // element for each query
    q.forEach(k => {
        document.write( maxFreqVec[k - 1] + " ");
    });
}

// Driver Code
var arr = [ 5, 4, 5, 3, 2 ];
var q = [ 1, 2, 3, 4, 5 ];

// Function Call
FreqOfMaxElement(arr, q);

// This code is contributed by rutvik_56

</script>

Output:

2 1 1 1 1

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