Maximum Product Subarray in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the maximum product variable.

DSA Typescript

let maxProduct = [1];

Drag options to blanks, or click blank then click option'

A0

Bnums[0]

C1

DNumber.MIN_VALUE

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing maxProduct to 0 ignores negative numbers.

Using 1 ignores the actual first element which might be negative or zero.

We start with the first element as the initial maximum product because the product subarray must include at least one element.

2fill in blank

medium

Complete the code to update the current maximum product at each step.

DSA Typescript

maxEndingHere = Math.max(nums[i], nums[i] * [1], nums[i] * minEndingHere);

Drag options to blanks, or click blank then click option'

Anums[i-1]

BminEndingHere

CmaxProduct

DmaxEndingHere

Attempts:

3 left

💡 Hint

Common Mistakes

Using minEndingHere instead of maxEndingHere causes wrong max calculation.

Using maxProduct instead of maxEndingHere mixes global max with local max.

maxEndingHere is updated by comparing the current number, the product with previous max, and the product with previous min (to handle negatives).

3fill in blank

hard

Fix the error in swapping maxEndingHere and minEndingHere when nums[i] is negative.

DSA Typescript

if (nums[i] < 0) {
    let temp = [1];
    [2] = maxEndingHere;
    maxEndingHere = temp;
}

Drag options to blanks, or click blank then click option'

AmaxEndingHere

BminEndingHere

CmaxProduct

Dnums[i]

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping with wrong variables causes incorrect product calculation.

Not swapping at all misses negative number effect.

When the current number is negative, max and min products swap because multiplying by negative flips signs.

4fill in blank

hard

Fill both blanks to update minEndingHere and maxProduct after processing nums[i].

DSA Typescript

minEndingHere = Math.min(nums[i], nums[i] * [1]);
maxProduct = Math.max(maxProduct, [2]);

Drag options to blanks, or click blank then click option'

AminEndingHere

BmaxEndingHere

Dnums[i]

Attempts:

3 left

💡 Hint

Common Mistakes

Using maxEndingHere to update minEndingHere causes wrong min calculation.

Updating maxProduct with minEndingHere causes wrong global max.

minEndingHere updates with the minimum product ending at i; maxProduct updates with the global maximum product found so far.

5fill in blank

hard

Fill all three blanks to complete the loop for maximum product subarray.

DSA Typescript

for (let i = 1; i < nums.length; i++) {
    if (nums[i] < 0) {
        let temp = [1];
        [2] = maxEndingHere;
        maxEndingHere = temp;
    }
    maxEndingHere = Math.max(nums[i], nums[i] * maxEndingHere, nums[i] * minEndingHere);
    minEndingHere = Math.min(nums[i], nums[i] * [3]);
    maxProduct = Math.max(maxProduct, maxEndingHere);
}

Drag options to blanks, or click blank then click option'

AminEndingHere

CmaxEndingHere

Dnums[i]

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping wrong variables or forgetting to swap.

Using maxEndingHere instead of minEndingHere in min calculation.

Swapping minEndingHere and maxEndingHere handles negatives; minEndingHere updates with previous min; maxProduct tracks global max.

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 sum of its elements

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

C. The longest subarray with all positive numbers

D. The subarray with the smallest product of its elements

Solution

1. Step 1: Understand the problem statement

   The problem asks for a contiguous part of the array where the product of all numbers is as large as possible.

2. Step 2: Differentiate from similar problems

   This is different from finding the largest sum or smallest product; it specifically focuses on the product of elements in a continuous segment.

3. Final Answer:

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

4. Quick Check:

   Maximum product subarray means largest product segment [OK]

Hint: Look for continuous elements with max product, not sum [OK]

Common Mistakes:

• Confusing product with sum
• Ignoring that subarray must be contiguous
• Thinking about longest subarray instead of max product

2. Which of the following TypeScript function signatures correctly represents a function to find the maximum product subarray?

easy

A. function maxProduct(nums: number[]): number

B. function maxProduct(nums: string): number

C. function maxProduct(nums: number): number[]

D. function maxProduct(nums: number[]): string

Solution

1. Step 1: Check input parameter type

   The input should be an array of numbers, so nums: number[] is correct.

2. Step 2: Check return type

   The function returns the maximum product value, which is a number, not an array or string.

3. Final Answer:

   function maxProduct(nums: number[]): number -> Option A

4. Quick Check:

   Input array, output number matches signature [OK]

Hint: Input is number array, output is single number [OK]

Common Mistakes:

• Using string type for input or output
• Returning array instead of number
• Incorrect parameter types

3. What is the output of the following TypeScript code?

function maxProduct(nums: number[]): number {
  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]));

medium

A. 6

B. 4

C. -2

D. 24

Solution

1. Step 1: Initialize variables and start loop

   maxProd, minProd, and result start at 2. Loop from index 1 to 3.

2. Step 2: Iterate and update maxProd, minProd, and result

   At i=1 (3): maxProd = max(3, 2*3)=6, minProd = min(3, 2*3)=3, result=6.
   At i=2 (-2): nums[i]<0, 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.
   At i=3 (4): maxProd = max(4, -2*4) = max(4, -8) = 4.
   minProd = min(4, -12*4) = min(4, -48) = -48.
   result = max(6, 4) = 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Max product subarray is [2,3] = 6 [OK]

Hint: Track max and min products, swap on negative [OK]

Common Mistakes:

• Not swapping max and min on negative number
• Only tracking max product, ignoring min product
• Confusing max product with sum

4. Identify the bug in this TypeScript function for maximum product subarray:

function maxProduct(nums: number[]): number {
  let maxProd = 1;
  let minProd = 1;
  let result = Number.MIN_VALUE;
  for (let num of nums) {
    if (num < 0) {
      let temp = maxProd;
      maxProd = minProd;
      minProd = temp;
    }
    maxProd = Math.max(num, maxProd * num);
    minProd = Math.min(num, minProd * num);
    result = Math.max(result, maxProd);
  }
  return result;
}

medium

A. Initializing maxProd and minProd to 0 instead of 1

B. Not swapping maxProd and minProd when num is positive

C. Using a for loop instead of forEach

D. Using Number.MIN_VALUE instead of Number.NEGATIVE_INFINITY for result

Solution

1. Step 1: Understand Number.MIN_VALUE usage

   Number.MIN_VALUE is the smallest positive number close to zero, not the most negative number.

2. Step 2: Correct initialization for result

   To track maximum product correctly, result should start at Number.NEGATIVE_INFINITY to handle negative products properly.

3. Final Answer:

   Using Number.MIN_VALUE instead of Number.NEGATIVE_INFINITY for result -> Option D

4. Quick Check:

   Use Number.NEGATIVE_INFINITY for max tracking [OK]

Hint: Use Number.NEGATIVE_INFINITY for max initial value [OK]

Common Mistakes:

• Confusing Number.MIN_VALUE with negative infinity
• Not swapping max and min on negative number
• Wrong initial values for maxProd and minProd

5. Given the array [-1, -3, -10, 0, 60], what is the maximum product subarray and its product?

hard

A. Subarray: [-1, -3, -10], Product: -30

B. Subarray: [-3, -10, 0], Product: 0

C. Subarray: [60], Product: 60

D. Subarray: [-10, 0, 60], Product: 0

Solution

1. Step 1: Analyze subarrays and their products

   Check products of contiguous subarrays:
   [-1] = -1
   [-1, -3] = 3
   [-1, -3, -10] = -30
   [-3] = -3
   [-3, -10] = 30
   [-10] = -10
   [0] = 0
   [60] = 60

2. Step 2: Identify maximum product

   The largest product found is 60 from subarray [60].

3. Final Answer:

   Subarray: [60], Product: 60 -> Option C

4. Quick Check:

   Max product is 60 from single element [60] [OK]

Hint: Check single elements and negative pairs carefully [OK]

Common Mistakes:

• Assuming negative product is maximum
• Ignoring single element subarrays
• Confusing zero product with max product