Skip to content
Related Articles

Related Articles

Improve Article

Number of sub arrays with negative product

  • Difficulty Level : Hard
  • Last Updated : 03 May, 2021

Given an array arr[] of N integers, the task is to find the count of subarrays with negative product.
Examples: 
 

Input: arr[] = {-1, 2, -2} 
Output:
Subarray with negative product are {-1}, {-2}, {-1, 2} and {2, -2}.
Input: arr[] = {5, -4, -3, 2, -5} 
Output:
 

 

Approach: 
 

  • Replace the positive array elements with 1 and negative array elements with -1.
  • Create a prefix product array pre[] where pre[i] stores the product of all the elements from index arr[0] to arr[i].
  • Now, it can be noted that the sub-array arr[i…j] has a negative product only if pre[i] * pre[j] is negative.
  • Hence, the total count of sub-arrays with negative product will be the product of the count positive and negative elements in the prefix product array.

Below is the implementation of the above approach: 
 



C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the count of
// subarrays with negative product
int negProdSubArr(int arr[], int n)
{
    int positive = 1, negative = 0;
    for (int i = 0; i < n; i++) {
 
        // Replace current element with 1
        // if it is positive else replace
        // it with -1 instead
        if (arr[i] > 0)
            arr[i] = 1;
        else
            arr[i] = -1;
 
        // Take product with previous element
        // to form the prefix product
        if (i > 0)
            arr[i] *= arr[i - 1];
 
        // Count positive and negative elements
        // in the prefix product array
        if (arr[i] == 1)
            positive++;
        else
            negative++;
    }
 
    // Return the required count of subarrays
    return (positive * negative);
}
 
// Driver code
int main()
{
    int arr[] = { 5, -4, -3, 2, -5 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    cout << negProdSubArr(arr, n);
 
    return (0);
}

Java




// Java implementation of the approach
class GFG
{
     
    // Function to return the count of
    // subarrays with negative product
    static int negProdSubArr(int arr[], int n)
    {
        int positive = 1, negative = 0;
        for (int i = 0; i < n; i++)
        {
     
            // Replace current element with 1
            // if it is positive else replace
            // it with -1 instead
            if (arr[i] > 0)
                arr[i] = 1;
            else
                arr[i] = -1;
     
            // Take product with previous element
            // to form the prefix product
            if (i > 0)
                arr[i] *= arr[i - 1];
     
            // Count positive and negative elements
            // in the prefix product array
            if (arr[i] == 1)
                positive++;
            else
                negative++;
        }
     
        // Return the required count of subarrays
        return (positive * negative);
    }
     
    // Driver code
    public static void main (String[] args)
    {
        int arr[] = { 5, -4, -3, 2, -5 };
        int n = arr.length;
     
        System.out.println(negProdSubArr(arr, n));
    }
}
 
// This code is contributed by AnkitRai01

Python3




# Python3 implementation of the approach
 
# Function to return the count of
# subarrays with negative product
def negProdSubArr(arr, n):
    positive = 1
    negative = 0
    for i in range(n):
 
        # Replace current element with 1
        # if it is positive else replace
        # it with -1 instead
        if (arr[i] > 0):
            arr[i] = 1
        else:
            arr[i] = -1
 
        # Take product with previous element
        # to form the prefix product
        if (i > 0):
            arr[i] *= arr[i - 1]
 
        # Count positive and negative elements
        # in the prefix product array
        if (arr[i] == 1):
            positive += 1
        else:
            negative += 1
 
    # Return the required count of subarrays
    return (positive * negative)
 
# Driver code
arr = [5, -4, -3, 2, -5]
n = len(arr)
 
print(negProdSubArr(arr, n))
 
# This code is contributed by Mohit Kumar

C#




// C# implementation of the approach
using System;
 
class GFG
{
         
    // Function to return the count of
    // subarrays with negative product
    static int negProdSubArr(int []arr, int n)
    {
        int positive = 1, negative = 0;
        for (int i = 0; i < n; i++)
        {
     
            // Replace current element with 1
            // if it is positive else replace
            // it with -1 instead
            if (arr[i] > 0)
                arr[i] = 1;
            else
                arr[i] = -1;
     
            // Take product with previous element
            // to form the prefix product
            if (i > 0)
                arr[i] *= arr[i - 1];
     
            // Count positive and negative elements
            // in the prefix product array
            if (arr[i] == 1)
                positive++;
            else
                negative++;
        }
     
        // Return the required count of subarrays
        return (positive * negative);
    }
     
    // Driver code
    static public void Main ()
    {
        int []arr = { 5, -4, -3, 2, -5 };
        int n = arr.Length;
     
        Console.Write(negProdSubArr(arr, n));
    }
}
 
// This code is contributed by Sachin.

Javascript




<script>
 
// Javascript implementation of the approach
 
// Function to return the count of
// subarrays with negative product
function negProdSubArr(arr, n)
{
    let positive = 1, negative = 0;
    for (let i = 0; i < n; i++) {
 
        // Replace current element with 1
        // if it is positive else replace
        // it with -1 instead
        if (arr[i] > 0)
            arr[i] = 1;
        else
            arr[i] = -1;
 
        // Take product with previous element
        // to form the prefix product
        if (i > 0)
            arr[i] *= arr[i - 1];
 
        // Count positive and negative elements
        // in the prefix product array
        if (arr[i] == 1)
            positive++;
        else
            negative++;
    }
 
    // Return the required count of subarrays
    return (positive * negative);
}
 
// Driver code
    let arr = [ 5, -4, -3, 2, -5 ];
    let n = arr.length;
 
    document.write(negProdSubArr(arr, n));
 
</script>
Output: 
8

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :