Maximum Product Subarray | Set 3

Given an array A[] that contains both positive and negative integers, find the maximum product subarray.

Examples :

Input: A[] = { 6, -3, -10, 0, 2 }
Output: 180  // The subarray is {6, -3, -10}

Input: A[] = {-1, -3, -10, 0, 60 }
Output: 60  // The subarray is {60}

Input: A[] = { -2, -3, 0, -2, -40 }
Output: 80  // The subarray is {-2, -40}

The idea is to traverse array from left to right keeping two variables minVal and maxVal which represents the minimum and maximum product value till the ith index of the array. Now, if the ith element of the array is negative that means now the values of minVal and maxVal will be swapped as value of maxVal will become minimum by multiplying it with a negative number. Now, compare the minVal and maxVal.
The value of minVal and maxVal depends on the current index element or the product of the current index element and the previous minVal and maxVal respectively.

Below is the implementation of above approach:

C++

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// C++ program to find maximum product subarray
#include <bits/stdc++.h>
using namespace std;
  
// Function to find maximum product subarray
int maxProduct(int* arr, int n)
{
    // Variables to store maximum and minimum
    // product till ith index.
    int minVal = arr[0];
    int maxVal = arr[0];
  
    int maxProduct = arr[0];
  
    for (int i = 1; i < n; i++) {
  
        // When multiplied by -ve number,
        // maxVal becomes minVal
        // and minVal becomes maxVal.
        if (arr[i] < 0)
            swap(maxVal, minVal);
  
        // maxVal and minVal stores the
        // product of subarray ending at arr[i].
        maxVal = max(arr[i], maxVal * arr[i]);
        minVal = min(arr[i], minVal * arr[i]);
  
        // Max Product of array.
        maxProduct = max(maxProduct, maxVal);
    }
  
    // Return maximum product found in array.
    return maxProduct;
}
  
// Driver Code
int main()
{
    int arr[] = { -1, -3, -10, 0, 60 };
  
    int n = sizeof(arr) / sizeof(arr[0]);
  
    cout << "Maximum Subarray product is "
         << maxProduct(arr, n) << endl;
  
    return 0;
}

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Java

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// Java program to find maximum product subarray
import java.io.*;
  
class GFG {
  
    // Function to find maximum product subarray
    static int maxProduct(int arr[], int n)
    {
          
        // Variables to store maximum and minimum
        // product till ith index.
        int minVal = arr[0];
        int maxVal = arr[0];
      
        int maxProduct = arr[0];
      
        for (int i = 1; i < n; i++)
        {
      
            // When multiplied by -ve number,
            // maxVal becomes minVal
            // and minVal becomes maxVal.
            if (arr[i] < 0)
            {
                int temp = maxVal;
                maxVal = minVal;
                minVal =temp;
              
            }
      
            // maxVal and minVal stores the
            // product of subarray ending at arr[i].
            maxVal = Math.max(arr[i], maxVal * arr[i]);
            minVal = Math.min(arr[i], minVal * arr[i]);
      
            // Max Product of array.
            maxProduct = Math.max(maxProduct, maxVal);
        }
      
        // Return maximum product found in array.
        return maxProduct;
    }
      
    // Driver Code
    public static void main (String[] args)
    {
        int arr[] = { -1, -3, -10, 0, 60 };
        int n = arr.length;
      
        System.out.println( "Maximum Subarray product is "
                                    + maxProduct(arr, n));
    }
}
  
// This code is contributed by anuj_67.

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Python3

# Python 3 program to find maximum
# product subarray

# Function to find maximum
# product subarray
def maxProduct(arr, n):

# Variables to store maximum and
# minimum product till ith index.
minVal = arr[0]
maxVal = arr[0]

maxProduct = arr[0]

for i in range(1, n, 1):

# When multiplied by -ve number,
# maxVal becomes minVal
# and minVal becomes maxVal.
if (arr[i] < 0): temp = maxVal maxVal = minVal minVal = temp # maxVal and minVal stores the # product of subarray ending at arr[i]. maxVal = max(arr[i], maxVal * arr[i]) minVal = min(arr[i], minVal * arr[i]) # Max Product of array. maxProduct = max(maxProduct, maxVal) # Return maximum product # found in array. return maxProduct # Driver Code if __name__ == '__main__': arr = [-1, -3, -10, 0, 60] n = len(arr) print("Maximum Subarray product is", maxProduct(arr, n)) # This code is contributed by # Surendra_Gangwar [tabby title="C#"]

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// C# program to find 
// maximum product subarray
using System;
  
class GFG 
{
  
    // Function to find maximum
    // product subarray
    static int maxProduct(int []arr, 
                          int n)
    {
          
        // Variables to store 
        // maximum and minimum 
        // product till ith index.
        int minVal = arr[0];
        int maxVal = arr[0];
      
        int maxProduct = arr[0];
      
        for (int i = 1; i < n; i++)
        {
      
            // When multiplied by -ve 
            // number, maxVal becomes 
            // minVal and minVal 
            // becomes maxVal.
            if (arr[i] < 0)
            {
                int temp = maxVal;
                maxVal = minVal;
                minVal = temp;
              
            }
      
            // maxVal and minVal stores 
            // the product of subarray 
            // ending at arr[i].
            maxVal = Math.Max(arr[i], 
                              maxVal * arr[i]);
            minVal = Math.Min(arr[i], 
                              minVal * arr[i]);
      
            // Max Product of array.
            maxProduct = Math.Max(maxProduct, 
                                  maxVal);
        }
      
        // Return maximum product
        // found in array.
        return maxProduct;
    }
      
    // Driver Code
    public static void Main ()
    {
        int []arr = {-1, -3, -10, 0, 60};
        int n = arr.Length;
      
        Console.WriteLine("Maximum Subarray " +
                                "product is " +
                           maxProduct(arr, n));
    }
}
  
// This code is contributed by anuj_67.

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PHP

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<?php 
// PHP program to find maximum 
// product subarray
  
// Function to find maximum 
// product subarray
function maxProduct(&$arr, $n)
{
    // Variables to store maximum and 
    // minimum product till ith index.
    $minVal = $arr[0];
    $maxVal = $arr[0];
  
    $maxProduct = $arr[0];
  
    for ($i = 1; $i < $n; $i++)
    {
  
        // When multiplied by -ve number,
        // maxVal becomes minVal
        // and minVal becomes maxVal.
        if ($arr[$i] < 0)
        {
            $temp = $maxVal;
            $maxVal = $minVal;
            $minVal = $temp;
        }
  
        // maxVal and minVal stores the
        // product of subarray ending at arr[i].
        $maxVal = max($arr[$i], $maxVal * $arr[$i]);
        $minVal = min($arr[$i], $minVal * $arr[$i]);
  
        // Max Product of array.
        $maxProduct = max($maxProduct, $maxVal);
    }
  
    // Return maximum product found in array.
    return $maxProduct;
}
  
// Driver Code
$arr = array( -1, -3, -10, 0, 60 );
$n = sizeof($arr);
echo "Maximum Subarray product is " .
         maxProduct($arr, $n) . "\n";
  
// This code is contributed by ita_c
?>

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Output:

Maximum Sub array product is 60

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

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Improved By : vt_m, Ita_c, SURENDRA_GANGWAR



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