Prefix Sum Array in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the prefix sum array with the first element of the input array.

DSA Javascript

const prefixSum = [[1]];

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

Aarr[0]

Barr[1]

C0

Darr.length

Attempts:

3 left

💡 Hint

Common Mistakes

Using arr[1] instead of arr[0]

Starting with 0 instead of the first element

The prefix sum array starts with the first element of the input array to accumulate sums correctly.

2fill in blank

medium

Complete the code to calculate the prefix sum for the current index inside the loop.

DSA Javascript

for (let i = 1; i < arr.length; i++) {
  prefixSum[i] = prefixSum[i - 1] [1] arr[i];
}

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

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction instead of addition

Using multiplication or division which are incorrect here

Each prefix sum is the sum of the previous prefix sum and the current element.

3fill in blank

hard

Fix the error in the code to correctly compute the prefix sum array.

DSA Javascript

const prefixSum = [];
prefixSum[0] = arr[0];
for (let i = 1; [1]; i++) {
  prefixSum[i] = prefixSum[i - 1] + arr[i];
}

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

Ai <= arr.length - 1

Bi <= arr.length

Ci < arr.length - 1

Di < arr.length

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= arr.length causes out-of-bounds error

Using < arr.length - 1 skips last element

The loop should run while i is less than arr.length to avoid accessing undefined elements.

4fill in blank

hard

Fill both blanks to create a function that returns the prefix sum array for a given input array.

DSA Javascript

function prefixSumArray(arr) {
  const prefixSum = [arr[0]];
  for (let i = 1; i [1] arr.length; i++) {
    prefixSum[i] = prefixSum[i - 1] [2] arr[i];
  }
  return prefixSum;
}

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

A<

B+

C-

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= in loop condition causing errors

Using subtraction instead of addition

The loop runs while i is less than arr.length, and sums previous prefix sum with current element.

5fill in blank

hard

Fill all three blanks to create a function that returns the prefix sum array using map and reduce methods.

DSA Javascript

function prefixSumArray(arr) {
  let sum = 0;
  return arr.map(([1]) => {
    sum = sum [2] [3];
    return sum;
  });
}

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

Anum

B+

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong parameter name

Using wrong operator

Using index instead of element

The map function uses 'num' as parameter, adds it to sum, and returns the cumulative sum.

Practice

1. What does a prefix sum array represent for a given array arr?

easy

A. An array where each element is the sum of all elements from the start up to that index in arr.

B. An array where each element is the product of all elements from the start up to that index in arr.

C. An array where each element is the difference between consecutive elements in arr.

D. An array where each element is the maximum value found in arr up to that index.

Solution

1. Step 1: Understand prefix sum array definition

   A prefix sum array stores sums of elements from the start of the original array up to each index.

2. Step 2: Compare options with definition

   Only An array where each element is the sum of all elements from the start up to that index in arr. correctly describes this sum accumulation behavior.

3. Final Answer:

   An array where each element is the sum of all elements from the start up to that index in arr. -> Option A

4. Quick Check:

   Prefix sum = cumulative sum [OK]

Hint: Prefix sum means cumulative addition from start [OK]

Common Mistakes:

• Confusing prefix sum with product or max
• Thinking prefix sum stores differences
• Assuming prefix sum stores original values

2. Which of the following JavaScript code snippets correctly initializes a prefix sum array prefix for an input array arr?

easy

A. const prefix = []; for(let i=0; i<arr.length; i++) { prefix[i] = arr[i] * prefix[i-1]; }

B. const prefix = [0]; for(let i=1; i<arr.length; i++) { prefix[i] = prefix[i-1] + arr[i]; }

C. const prefix = [arr[0]]; for(let i=1; i<arr.length; i++) { prefix[i] = prefix[i-1] + arr[i]; }

D. const prefix = []; for(let i=0; i<arr.length; i++) { prefix[i] = arr[i] - prefix[i-1]; }

Solution

1. Step 1: Check initialization of prefix sum array

   Prefix sum starts with first element of arr, so prefix[0] = arr[0].

2. Step 2: Verify loop logic for prefix sums

   Each prefix[i] = prefix[i-1] + arr[i] correctly accumulates sums.

3. Final Answer:

   const prefix = [arr[0]]; for(let i=1; i<arr.length; i++) { prefix[i] = prefix[i-1] + arr[i]; } -> Option C

4. Quick Check:

   Initialize with arr[0], then add previous prefix [OK]

Hint: Start prefix with arr[0], then add previous sums [OK]

Common Mistakes:

• Starting prefix with 0 instead of arr[0]
• Using multiplication instead of addition
• Accessing prefix[-1] which is undefined

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

const arr = [2, 4, 6, 8];
const prefix = [arr[0]];
for(let i = 1; i < arr.length; i++) {
  prefix[i] = prefix[i-1] + arr[i];
}
console.log(prefix);

medium

A. [2, 6, 10, 18]

B. [2, 4, 6, 8]

C. [2, 8, 14, 22]

D. [2, 6, 12, 20]

Solution

1. Step 1: Calculate prefix sums step-by-step

   prefix[0] = 2; prefix[1] = 2 + 4 = 6; prefix[2] = 6 + 6 = 12; prefix[3] = 12 + 8 = 20.

2. Step 2: Confirm final prefix array

   The prefix array is [2, 6, 12, 20].

3. Final Answer:

   [2, 6, 12, 20] -> Option D

4. Quick Check:

   Sum accumulates correctly [OK]

Hint: Add current element to previous prefix sum [OK]

Common Mistakes:

• Adding elements incorrectly or skipping first element
• Confusing prefix array with original array
• Off-by-one errors in loop

4. Identify the error in the following code that attempts to create a prefix sum array:

const arr = [1, 3, 5, 7];
const prefix = [];
for(let i = 0; i < arr.length; i++) {
  prefix[i] = prefix[i-1] + arr[i];
}
console.log(prefix);

medium

A. prefix array is not initialized with first element, causing prefix[-1] to be undefined.

B. The loop should start from i = 1 instead of 0.

C. The code uses addition instead of multiplication.

D. The array arr is empty, so prefix will be empty.

Solution

1. Step 1: Analyze prefix[-1] usage at i=0

   At i=0, prefix[i-1] is prefix[-1], which is undefined, causing NaN result.

2. Step 2: Fix initialization to avoid undefined

   Initialize prefix[0] = arr[0] before loop or handle i=0 separately.

3. Final Answer:

   prefix array is not initialized with first element, causing prefix[-1] to be undefined. -> Option A

4. Quick Check:

   Accessing prefix[-1] causes undefined [OK]

Hint: Initialize prefix[0] before loop to avoid undefined [OK]

Common Mistakes:

• Starting loop at 0 without initializing prefix[0]
• Ignoring undefined prefix[-1] access
• Assuming prefix[-1] is zero automatically

5. Given an array arr = [3, 1, 4, 1, 5], how can you use a prefix sum array to efficiently find the sum of elements between indices 1 and 3 (inclusive)?

hard

A. Calculate prefix sums, then subtract prefix[0] from prefix[4].

B. Calculate prefix sums, then subtract prefix[0] from prefix[3].

C. Calculate prefix sums, then subtract prefix[0] from prefix[2].

D. Calculate prefix sums, then subtract prefix[1] from prefix[3].

Solution

1. Step 1: Build prefix sum array for arr

   prefix = [3, 4, 8, 9, 14] where prefix[i] = sum of arr[0..i].

2. Step 2: Calculate sum from index 1 to 3

   Sum = prefix[3] - prefix[0] = 9 - 3 = 6 (elements 1,4,1).

3. Final Answer:

   Calculate prefix sums, then subtract prefix[0] from prefix[3]. -> Option B

4. Quick Check:

   Sum(1 to 3) = prefix[3] - prefix[0] [OK]

Hint: Sum(i to j) = prefix[j] - prefix[i-1] [OK]

Common Mistakes:

• Subtracting prefix[i] instead of prefix[i-1]
• Using wrong indices for subtraction
• Not building prefix sums first