Maximum Product Subarray in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the goal of the Maximum Product Subarray problem?

To find the contiguous subarray within an array that has the largest product of its elements.

intermediate

Why do we keep track of both maximum and minimum products at each step in the Maximum Product Subarray problem?

Because a negative number can turn a minimum product into a maximum product when multiplied, so tracking both helps handle negative values correctly.

beginner

In the Maximum Product Subarray problem, what happens when the current number is zero?

The product resets because zero multiplied by anything is zero, so we start fresh from the next element.

intermediate

What is the time complexity of the optimal solution for the Maximum Product Subarray problem?

O(n), where n is the number of elements in the array, because we scan the array once while keeping track of max and min products.

advanced

Explain the role of swapping max and min products when encountering a negative number in the Maximum Product Subarray algorithm.

When a negative number is encountered, the max product becomes min and min becomes max because multiplying by a negative flips signs, so swapping helps maintain correct tracking.

What does the Maximum Product Subarray problem ask you to find?

A The subarray with the largest product

B The subarray with the largest sum

C The subarray with the smallest product

D The subarray with the largest length

The problem is about finding the contiguous subarray with the maximum product of its elements.

Why do we track both maximum and minimum products at each step?

A To handle zeros correctly

B To find the longest subarray

C To handle positive numbers only

D Because a negative number can turn a minimum product into a maximum product

Negative numbers can flip the sign of the product, so tracking both max and min helps find the correct maximum product.

What should you do when the current number is zero in the array?

A Start fresh from the next element

B Reset max and min products to 1

C Reset max and min products to zero

D Multiply it with max product

Zero resets the product, so we start fresh from the next element to find new subarrays.

What is the time complexity of the optimal Maximum Product Subarray solution?

A O(n^2)

B O(n log n)

C O(n)

D O(log n)

The solution scans the array once, so it runs in linear time O(n).

When encountering a negative number, what operation is done on max and min products?

A They are both reset to zero

B They are swapped

C They are both multiplied by zero

D They remain unchanged

Swapping max and min products accounts for sign change caused by multiplying by a negative number.

Describe the approach to solve the Maximum Product Subarray problem and why tracking both max and min products is necessary.

Think about how negative numbers affect product signs.

Explain how zero values in the array affect the Maximum Product Subarray calculation and how the algorithm handles them.

Consider what happens when multiplying by zero.

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