Maximum Product Subarray in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Maximum Product Subarray Calculation

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

DSA Javascript

function maxProduct(nums) {
  let maxProd = nums[0];
  let minProd = nums[0];
  let result = nums[0];
  for (let i = 1; i < nums.length; i++) {
    if (nums[i] < 0) {
      [maxProd, minProd] = [minProd, maxProd];
    }
    maxProd = Math.max(nums[i], maxProd * nums[i]);
    minProd = Math.min(nums[i], minProd * nums[i]);
    result = Math.max(result, maxProd);
  }
  return result;
}

console.log(maxProduct([2,3,-2,4]));

A 6

B 4

C -2

D 0

💡 Hint

Think about how negative numbers affect the product and why swapping max and min helps.

The maximum product subarray is [2,3] with product 6. The negative number -2 resets the product, but the max product remains 6.

❓ Predict Output

intermediate

Result of Maximum Product Subarray with Zeroes

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

DSA Javascript

function maxProduct(nums) {
  let maxProd = nums[0];
  let minProd = nums[0];
  let result = nums[0];
  for (let i = 1; i < nums.length; i++) {
    if (nums[i] < 0) {
      [maxProd, minProd] = [minProd, maxProd];
    }
    maxProd = Math.max(nums[i], maxProd * nums[i]);
    minProd = Math.min(nums[i], minProd * nums[i]);
    result = Math.max(result, maxProd);
  }
  return result;
}

console.log(maxProduct([0, -2, 0, -1, 0]));

A -2

B -1

C 1

D 0

💡 Hint

Zero resets the product, so consider subarrays around zero.

The maximum product subarray is [0] or any zero element, product is 0.

🔧 Debug

advanced

Identify the Error in Maximum Product Subarray Implementation

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

DSA Javascript

function maxProduct(nums) {
  let maxProd = 1;
  let minProd = 1;
  let result = -Infinity;
  for (let i = 0; i < nums.length; i++) {
    if (nums[i] < 0) {
      [maxProd, minProd] = [minProd, maxProd];
    }
    maxProd = Math.max(nums[i], maxProd * nums[i]);
    minProd = Math.min(nums[i], minProd * nums[i]);
    result = Math.max(result, maxProd);
  }
  return result;
}

console.log(maxProduct([2,3,-2,4]));

A Returns 12 incorrectly

B Returns 6 correctly

C Returns 4 incorrectly

D Returns -Infinity

💡 Hint

Check initial values of maxProd and minProd and how they affect the first iteration.

Initializing maxProd and minProd to 1 causes incorrect multiplication on first element, leading to wrong max product 12 instead of 6.

🧠 Conceptual

advanced

Why Swap maxProd and minProd When Encountering Negative Number?

In the maximum product subarray algorithm, why do we swap maxProd and minProd when the current number is negative?

A Because negative numbers reset the product to zero

B Because multiplying by a negative flips max and min, so swapping keeps track of correct values

C Because swapping avoids division by zero errors

D Because it sorts the array to handle negatives first

💡 Hint

Think about how a negative number changes the sign of the product.

Multiplying by a negative number turns the largest product into the smallest and vice versa, so swapping maxProd and minProd keeps track of correct values.

❓ Predict Output

expert

Maximum Product Subarray Output with Mixed Signs and Zeroes

What is the output of this code for the input array with mixed positive, negative numbers and zeroes?

DSA Javascript

function maxProduct(nums) {
  let maxProd = nums[0];
  let minProd = nums[0];
  let result = nums[0];
  for (let i = 1; i < nums.length; i++) {
    if (nums[i] < 0) {
      [maxProd, minProd] = [minProd, maxProd];
    }
    maxProd = Math.max(nums[i], maxProd * nums[i]);
    minProd = Math.min(nums[i], minProd * nums[i]);
    result = Math.max(result, maxProd);
  }
  return result;
}

console.log(maxProduct([2, -5, -2, -4, 3]));

A 40

B -2

C 24

D 120

💡 Hint

Consider how multiple negatives multiply to positive and track max product carefully.

The maximum product subarray is [-5, -2, -4, 3] with product 24.

Practice

1. What does the Maximum Product Subarray problem ask you to find in an array of integers?

easy

A. The subarray with the largest difference between elements

B. The contiguous subarray with the largest sum of its elements

C. The subarray with the smallest product of its elements

D. The contiguous subarray with the largest product of its elements

Solution

1. Step 1: Understand the problem goal

   The problem asks for the contiguous subarray (elements next to each other) that has the maximum product when multiplied together.

2. Step 2: Differentiate from sum problems

   This is different from maximum sum subarray problems because it focuses on multiplication, which can be affected by negative numbers and zeros.

3. Final Answer:

   The contiguous subarray with the largest product of its elements -> Option D

4. Quick Check:

   Maximum Product Subarray = largest product subarray [OK]

Hint: Look for the subarray with the highest multiplication result [OK]

Common Mistakes:

• Confusing product with sum
• Ignoring negative numbers impact
• Thinking about non-contiguous subarrays

2. Which of the following JavaScript code snippets correctly initializes variables to track the maximum product subarray?

easy

A. let maxProd = Infinity, minProd = -Infinity, result = 0;

B. let maxProd = 0, minProd = 0, result = 0;

C. let maxProd = nums[0], minProd = nums[0], result = nums[0];

D. let maxProd = [], minProd = [], result = [];

Solution

1. Step 1: Understand variable roles

   maxProd and minProd track the max and min products ending at current index; result stores the overall max product.

2. Step 2: Correct initialization

   Initializing all three to the first element of the array ensures correct comparison and handling of negative numbers.

3. Final Answer:

   let maxProd = nums[0], minProd = nums[0], result = nums[0]; -> Option C

4. Quick Check:

   Initialize with first element for correct tracking [OK]

Hint: Start tracking with first element, not zero or arrays [OK]

Common Mistakes:

• Initializing with zero causes wrong results if first element is negative
• Using arrays instead of numbers for tracking
• Using Infinity values incorrectly

3. What will be the output of the following JavaScript code?

const nums = [2, 3, -2, 4];
function maxProduct(nums) {
  let maxProd = nums[0], minProd = nums[0], result = nums[0];
  for (let i = 1; i < nums.length; i++) {
    if (nums[i] < 0) [maxProd, minProd] = [minProd, maxProd];
    maxProd = Math.max(nums[i], maxProd * nums[i]);
    minProd = Math.min(nums[i], minProd * nums[i]);
    result = Math.max(result, maxProd);
  }
  return result;
}
console.log(maxProduct(nums));

medium

A. 4

B. 6

C. -2

D. 8

Solution

1. Step 1: Trace the loop and variable updates

   Start with maxProd=2, minProd=2, result=2.
   i=1 (3): maxProd=max(3,2*3)=6, minProd=min(3,2*3)=3, result=max(2,6)=6.
   i=2 (-2): nums[i]<0 so swap maxProd and minProd: maxProd=3, minProd=6.
   maxProd=max(-2,3*(-2))=max(-2,-6)=-2, minProd=min(-2,6*(-2))=min(-2,-12)=-12, result=max(6,-2)=6.
   i=3 (4): maxProd=max(4,-2*4)=4, minProd=min(4,-12*4)=-48, result=max(6,4)=6.

2. Step 2: Determine final result

   The maximum product found is 6 from subarray [2,3].

3. Final Answer:

   6 -> Option B

4. Quick Check:

   Max product subarray = 6 [OK]

Hint: Swap max and min when negative to track products correctly [OK]

Common Mistakes:

• Not swapping max and min on negative numbers
• Confusing max product with sum
• Incorrectly updating result

4. Identify the bug in the following code for Maximum Product Subarray and select the fix:

function maxProduct(nums) {
  let maxProd = 0, minProd = 0, result = 0;
  for (let i = 0; i < nums.length; i++) {
    if (nums[i] < 0) [maxProd, minProd] = [minProd, maxProd];
    maxProd = Math.max(nums[i], maxProd * nums[i]);
    minProd = Math.min(nums[i], minProd * nums[i]);
    result = Math.max(result, maxProd);
  }
  return result;
}

medium

A. Initialize maxProd, minProd, and result with nums[0] instead of 0

B. Remove the swap of maxProd and minProd when nums[i] < 0

C. Start loop from i = 1 instead of 0

D. Use Math.min instead of Math.max for result update

Solution

1. Step 1: Check variable initialization

   Initializing maxProd, minProd, and result to 0 causes wrong results if nums[0] is negative or non-zero. They should start at nums[0].

2. Step 2: Confirm loop start and swap logic

   Loop starting at 0 is okay if initialization is correct. Swap on negative is needed to handle sign changes.

3. Final Answer:

   Initialize maxProd, minProd, and result with nums[0] instead of 0 -> Option A

4. Quick Check:

   Correct initialization fixes wrong product tracking [OK]

Hint: Always initialize tracking vars with first array element [OK]

Common Mistakes:

• Starting loop at 0 with zero initialization
• Removing swap logic on negative numbers
• Updating result with min instead of max

5. Given the array nums = [1, -2, -3, 0, 7, -8, -2], what is the maximum product of any contiguous subarray?

hard

A. 112

B. 48

C. 7

D. 0

Solution

1. Step 1: Trace subarrays and products

   Check subarrays:
   - [1] = 1
   - [1,-2] = -2
   - [1,-2,-3] = 6
   - [-2,-3] = 6
   - [7] = 7
   - [7,-8] = -56
   - [7,-8,-2] = 112 (max so far)
   Zero resets product.
   Other subarrays have smaller products.

2. Step 2: Identify max product

   The maximum product is 112 from subarray [7, -8, -2].

3. Final Answer:

   112 -> Option A

4. Quick Check:

   Max product subarray = 112 [OK]

Hint: Consider negative pairs and zeros to find max product [OK]

Common Mistakes:

• Ignoring zeros resetting product
• Not considering negative number pairs
• Only checking positive subarrays