Maximum Product Subarray in DSA Typescript - Build from Scratch

Maximum Product Subarray

📖 Scenario: You are analyzing daily stock price changes represented as an array of numbers. Each number shows the daily change factor (positive for gain, negative for loss). You want to find the maximum product of a contiguous subarray to understand the best consecutive days for investment growth.

🎯 Goal: Build a TypeScript program that finds the maximum product of any contiguous subarray within a given array of numbers.

📋 What You'll Learn

Create an array called nums with the exact values [2, 3, -2, 4].

Create two variables called maxProd and minProd and set both to the first element of nums.

Use a for loop with variable i starting from 1 to iterate over nums.

Inside the loop, update maxProd and minProd to track the maximum and minimum products ending at the current index.

Create a variable called result and set it to the first element of nums.

Update result inside the loop to keep the maximum product found so far.

Print the value of result at the end.

💡 Why This Matters

🌍 Real World

Finding the maximum product subarray helps in financial analysis to identify the best consecutive days for investment growth based on daily change factors.

💼 Career

This problem is common in technical interviews and helps develop skills in dynamic programming and array manipulation.

1

Create the input array

Create an array called nums with the exact values [2, 3, -2, 4].

DSA Typescript

# Create the array nums with values [2, 3, -2, 4]
// Your code here

Hint

Use const nums = [2, 3, -2, 4]; to create the array.

2

Initialize maxProd, minProd, and result

Create two variables called maxProd and minProd and set both to the first element of nums. Also create a variable called result and set it to the first element of nums.

DSA Typescript

const nums = [2, 3, -2, 4];
// Initialize maxProd, minProd, and result to nums[0]
// Your code here

Hint

Set maxProd, minProd, and result all equal to nums[0].

3

Loop through the array and update maxProd and minProd

Use a for loop with variable i starting from 1 to iterate over nums. Inside the loop, create a variable tempMax to store the current maxProd. Update maxProd to the maximum of nums[i], maxProd * nums[i], and minProd * nums[i]. Update minProd to the minimum of nums[i], tempMax * nums[i], and minProd * nums[i]. Then update result to the maximum of result and maxProd.

DSA Typescript

const nums = [2, 3, -2, 4];
let maxProd = nums[0];
let minProd = nums[0];
let result = nums[0];
// Loop from i = 1 to nums.length - 1
// Update maxProd, minProd, and result inside the loop
// Your code here

Hint

Use a for loop starting at 1. Use Math.max and Math.min to update maxProd and minProd. Remember to save the old maxProd in tempMax before updating.

4

Print the maximum product result

Print the value of result using console.log(result).

DSA Typescript

const nums = [2, 3, -2, 4];
let maxProd = nums[0];
let minProd = nums[0];
let result = nums[0];

for (let i = 1; i < nums.length; i++) {
    const tempMax = maxProd;
    maxProd = Math.max(nums[i], maxProd * nums[i], minProd * nums[i]);
    minProd = Math.min(nums[i], tempMax * nums[i], minProd * nums[i]);
    result = Math.max(result, maxProd);
}
// Print the result
// Your code here

Hint

Use console.log(result) to print the maximum product.

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