Find maximum product sub-array in a given array

October 12, 2022

Maximum product of sub-array in Python

Here, in this page we will discuss the program to find the maximum product of sub-array in python programming language. We are given with an array and need to return the maximum value of the product of the sub-array.

Maximum product of sub-array in Python

Method Discussed

  • Method 1 : Brute Force solution
  • Method 2 : Efficient solution

Let’s discuss above two methods in brief.

Method 1 :

  • Create a variable say result, set result = arr[0], this variable hold the required maximum product.
  • Run a loop for range(n)
  • Create a variable mul = arr[i], this variable hold the product of sub-array.
  • Run a inner loop, set result = max(result, mul)
  • And, mul *= arr[j]
  • Update, result = max(result, mul)
  • Return result.

Time and Space Complexity :

  • Time Complexity : O(n2)
  • Space Complexity : O(1)

Method 1 : Code in Python

Run 
def maxSubarrayProduct(arr, n):
 
    # Initializing result
    result = arr[0]
 
    for i in range(n):
     
        mul = arr[i]
       
        # traversing in current subarray
        for j in range(i + 1, n):
            result = max(result, mul)
            mul *= arr[j]
         
        # updating the result for (n-1)th index.
        result = max(result, mul)
     
    return result
 
arr = [ 1, -2, -3, 0, 7, -8, -2 ]
n = len(arr)
print("Maximum sub-array product is" , maxSubarrayProduct(arr, n))

Output

Maximum sub-array product is 112

Counting the number of even and odd elements in an array

Find all Symmetric pairs in an array

Finding Arrays are disjoint or not

Determine Array is a subset of another array or not

Determine can all numbers of an array be made equal

Method 2 :

This is the efficient solution and is also similar to Largest Sum Contiguous Subarray problem which uses Kadane’s algorithm.

  • Declare three variables say max_so_far, max_ending_here & min_ending_here.
  • For every index the maximum number ending at that index will be the maximum(arr[i], max_ending_here * arr[i], min_ending_here[i]*arr[i]).
  • Similarly the minimum number ending here will be the minimum of these 3.
  • Thus we get the final value for maximum product subarray.

Time and Space Complexity :

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

Method 2 : Code in Python

def maxSubarrayProduct(arr, n):
    max_ending_here = arr[0];
    min_ending_here = arr[0];
    max_so_far = arr[0];
    
    for i in range(n):
        temp = max({arr[i], arr[i] * max_ending_here, arr[i] * min_ending_here});
        min_ending_here = min({arr[i], arr[i] * max_ending_here, arr[i] * min_ending_here});
        max_ending_here = temp
        max_so_far = max(max_so_far, max_ending_here)
    return max_so_far


arr = [ 1, -2, -3, 0, 7, -8, -2 ]
n = len(arr)
print("Maximum sub-array product is" , maxSubarrayProduct(arr, n))

Output

Maximum sub-array product is 112

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3 comments on “Find maximum product sub-array in a given array”


  • Vidyashree

    x=[1, -2, -3,0,7, -8, -2]
    y=[ ]
    mul=1
    for i in range(len(x)):
    for j in range(i,len(x)):
    mul=mul*x[j]
    y.append(mul)
    print(mul)
    mul=1

    print(“Maximum sub-array product is” , max(y))


  • Prashant

    arr=list(map(int,input().split()))
    sum=1
    for i in range(len(arr)):
    if arr[i]==0:
    pass
    else:sum*=arr[i]
    print(abs(sum))


    • nitesh

      list=[ 1, -2, -3, 0, 7, -8, -2 ,-2]
      multi,max=1,0
      for i in list:
      multi*=i
      if multi==0:
      multi=1
      if max<multi:
      max=multi
      print(max)