Maximum Product Subarray in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Maximum Product Subarray Calculation

What is the output of the following code that finds the maximum product of a contiguous subarray?

DSA Python

def max_product_subarray(nums):
    max_prod = min_prod = result = nums[0]
    for num in nums[1:]:
        candidates = (num, max_prod * num, min_prod * num)
        max_prod = max(candidates)
        min_prod = min(candidates)
        result = max(result, max_prod)
    return result

print(max_product_subarray([2,3,-2,4]))

A 6

B 4

C 8

D -2

💡 Hint

Think about how negative numbers affect the product and why we track both max and min products.

The maximum product subarray is [2,3] with product 6. The code tracks max and min products to handle negative numbers correctly.

❓ Predict Output

intermediate

Result of Maximum Product Subarray with Negative Numbers

What is the output of this code for the input array containing negative numbers?

DSA Python

def max_product_subarray(nums):
    max_prod = min_prod = result = nums[0]
    for num in nums[1:]:
        candidates = (num, max_prod * num, min_prod * num)
        max_prod = max(candidates)
        min_prod = min(candidates)
        result = max(result, max_prod)
    return result

print(max_product_subarray([-2,0,-1]))

A -2

B -1

C 0

D 1

💡 Hint

Remember zero resets the product, so consider subarrays around zero.

The maximum product subarray is [0] with product 0. Negative numbers and zero reset the product tracking.

🔧 Debug

advanced

Identify the Error in Maximum Product Subarray Implementation

What error will this code produce when run, and why?

DSA Python

def max_product_subarray(nums):
    max_prod = min_prod = result = 0
    for num in nums:
        candidates = (num, max_prod * num, min_prod * num)
        max_prod = max(candidates)
        min_prod = min(candidates)
        result = max(result, max_prod)
    return result

print(max_product_subarray([-2]))

A The output is -2

B The output is 0

C The output is 24

D The output is 6

💡 Hint

Check the initial values of max_prod, min_prod, and result.

Initializing max_prod, min_prod, and result to 0 causes incorrect tracking because the first element might be positive and greater than 0, but the code never sets them to the first element's value.

🧠 Conceptual

advanced

Why Track Both Maximum and Minimum Products?

Why does the maximum product subarray algorithm track both the maximum and minimum products at each step?

A Because the minimum product can become maximum if multiplied by a negative number

B Because minimum product helps to find the smallest subarray length

C Because maximum product alone is enough to find the answer

D Because minimum product tracks the sum of negative numbers

💡 Hint

Think about how multiplying two negative numbers affects the product.

Tracking the minimum product is important because multiplying it by a negative number can turn it into a large positive product, which might be the maximum.

🚀 Application

expert

Maximum Product Subarray Length Query

Given the array [1, -2, -3, 0, 7, -8, -2], what is the length of the contiguous subarray with the maximum product?

A 4

B 5

C 2

D 3

💡 Hint

Find the subarray with the maximum product first, then count its length.

The maximum product subarray is [7, -8, -2] with product 112 and length 3. Zero resets the product, so subarrays containing zero are considered separately.