Count subarrays of atleast size 3 forming a Geometric Progression (GP)

Given an array arr[] of N integers, the task is to find the count of all subarrays from the given array of at least size 3 forming a Geometric Progression.

Examples:

Input: arr[] = {1, 2, 4, 8}
Output: 3
Explanation: The required subarrays forming geometric progression are: 

1. {1, 2, 4}
2. {2, 4, 8}
3. {1, 2, 4, 8}

Input: arr[] = {1, 2, 4, 8, 16, 24}
Output: 6
Explanation: The required subarrays forming geometric progression are: 

1. {1, 2, 4}
2. {2, 4, 8}
3. {4, 8, 16}
4. {1, 2, 4, 8}
5. {2, 4, 8, 16}
6. {1, 2, 4, 8, 16}

Naive Approach: The simplest approach is to generate all the subarrays of size at least 3 and count all those subarrays forming a Geometric Progression. Print the count after checking all the subarrays.

Time Complexity: O(N³)
Auxiliary Space: O(N)

Efficient Approach: The idea is to use a property of Geometric Progression i.e., {a, b, c} is GP if and only if a*c = b. Follow the below steps to solve the problem:

• Initialize a variable, res, and count with 0 to store the total subarrays forming geometric progression and length of the current subarray.
• Traverse the given array over the range [2, N – 1] and increment the value of count if the current element forming a geometric progression i.e., arr[i]*arr[i – 2] = arr[i – 1]*arr[i – 1] Otherwise, set count as zero.
• Add count to res for each iteration in the above steps.
• After the above steps, print the value of res as the resultant count.

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 all the subarrays
// of size at least 3 forming GP
int numberOfGP(int L[], int N)
{
    // If array size is less than 3
    if (N <= 2)
        return 0;

    // Stores the count of subarray
    int count = 0;

    // Stores the count of subarray
    // for each iteration
    int res = 0;

    // Traverse the array
    for (int i = 2; i < N; ++i) {

        // Check if L[i] forms GP
        if (L[i - 1] * L[i - 1]
            == L[i] * L[i - 2]) {
            ++count;
        }

        // Otherwise, update count to 0
        else {
            count = 0;
        }

        // Update the final count
        res += count;
    }

    // Return the final count
    return res;
}

// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 1, 2, 4, 8, 16, 24 };

    int N = sizeof(arr) / sizeof(arr[0]);

    // Function Call
    cout << numberOfGP(arr, N);

    return 0;
}

Java

// Java program for the
// above approach
import java.util.*;
class GFG{

// Function to count all
// the subarrays of size
// at least 3 forming GP
static int numberOfGP(int L[],
                      int N)
{
  // If array size
  // is less than 3
  if (N <= 2)
    return 0;

  // Stores the count
  // of subarray
  int count = 0;

  // Stores the count
  // of subarray for
  // each iteration
  int res = 0;

  // Traverse the array
  for (int i = 2; i < N; ++i)
  {
    // Check if L[i] forms GP
    if (L[i - 1] * L[i - 1] ==
        L[i] * L[i - 2])
    {
      ++count;
    }

    // Otherwise, update
    // count to 0
    else
    {
      count = 0;
    }

    // Update the
    // final count
    res += count;
  }

  // Return the final count
  return res;
}

// Driver Code
public static void main(String[] args)
{
  // Given array arr[]
  int arr[] = {1, 2, 4,
               8, 16, 24};

  int N = arr.length;

  // Function Call
  System.out.print(numberOfGP(arr, N));
}
}

// This code is contributed by gauravrajput1

Python3

# Python3 program for the above approach

# Function to count all the subarrays
# of size at least 3 forming GP
def numberOfGP(L, N):

    # If array size is less than 3
    if (N <= 2):
        return 0

    # Stores the count of subarray
    count = 0

    # Stores the count of subarray
    # for each iteration
    res = 0

    # Traverse the array
    for i in range(2, N):

        # Check if L[i] forms GP
        if (L[i - 1] * L[i - 1] ==
                L[i] * L[i - 2]):
            count += 1

        # Otherwise, update count to 0
        else:
            count = 0

        # Update the final count
        res += count

    # Return the final count
    return res

# Driver Code
if __name__ == '__main__':

    # Given array arr[]
    arr = [ 1, 2, 4, 8, 16, 24 ]

    N = len(arr)

    # Function Call
    print(numberOfGP(arr, N))

# This code is contributed by mohit kumar 29

C#

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

// Function to count all
// the subarrays of size
// at least 3 forming GP
static int numberOfGP(int[] L,
                      int N)
{
  // If array size
  // is less than 3
  if (N <= 2)
    return 0;

  // Stores the count
  // of subarray
  int count = 0;

  // Stores the count
  // of subarray for
  // each iteration
  int res = 0;

  // Traverse the array
  for (int i = 2; i < N; ++i)
  {
    // Check if L[i] forms GP
    if (L[i - 1] * L[i - 1] ==
        L[i] * L[i - 2])
    {
      ++count;
    }

    // Otherwise, update
    // count to 0
    else
    {
      count = 0;
    }

    // Update the
    // final count
    res += count;
  }

  // Return the final
  // count
  return res;
}

// Driver Code
public static void Main(String[] args)
{
  // Given array arr[]
  int[] arr = {1, 2, 4, 8, 16, 24};

  int N = arr.Length;

  // Function Call
  Console.Write(numberOfGP(arr, N));
}
}

// This code is contributed by Chitranayal

Javascript

<script>

// Javascript program for the above approach

// Function to count all the subarrays
// of size at least 3 forming GP
function numberOfGP(L, N)
{
    // If array size is less than 3
    if (N <= 2)
        return 0;

    // Stores the count of subarray
    let count = 0;

    // Stores the count of subarray
    // for each iteration
    let res = 0;

    // Traverse the array
    for (let i = 2; i < N; ++i) {

        // Check if L[i] forms GP
        if (L[i - 1] * L[i - 1]
            == L[i] * L[i - 2]) {
            ++count;
        }

        // Otherwise, update count to 0
        else {
            count = 0;
        }

        // Update the final count
        res += count;
    }

    // Return the final count
    return res;
}

// Driver Code

    // Given array arr[]
    let arr = [ 1, 2, 4, 8, 16, 24];

    let N = arr.length;

    // Function Call
    document.write(numberOfGP(arr, N));

// This code is contributed by Mayank Tyagi

</script>

Output

6

Time Complexity: O(N)
Auxiliary Space: O(1) as it is using constant variables