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Maximum Product Subarray | Set 3

• Difficulty Level : Hard
• Last Updated : 26 Aug, 2022

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}```
Recommended Practice

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++

 `// C++ program to find maximum product subarray` `#include ` `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;` `}`

Java

 `// 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.`

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`

C#

 `// 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.`

PHP

 ``

Javascript

 ``

Output

```Maximum Subarray product is 60
```

Complexity Analysis:

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

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