Prefix Sum Array in DSA Typescript - 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 Typescript

const prefixSum: number[] = [];
prefixSum[0] = arr[1];

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

A[1]

B[0]

C[arr.length - 1]

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using index 1 instead of 0 for the first element.

Trying to assign the whole array instead of a single element.

The prefix sum array starts with the first element of the input array, so prefixSum[0] = arr[0].

2fill in blank

medium

Complete the code to calculate the prefix sum for each element starting from the second element.

DSA Typescript

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 or multiplication instead of addition.

Using the wrong index for prefixSum.

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

3fill in blank

hard

Fix the error in the function that returns the sum of elements between two indices using the prefix sum array.

DSA Typescript

function rangeSum(prefixSum: number[], left: number, right: number): number {
  if (left === 0) {
    return prefixSum[right];
  } else {
    return prefixSum[right] [1] prefixSum[left];
  }
}

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

A/

B+

C-

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of subtraction.

Not adjusting the index for prefixSum[left - 1].

To get the sum from left to right, subtract prefixSum[left - 1] from prefixSum[right]. The code mistakenly uses prefixSum[left], so it should subtract prefixSum[left - 1]. But since the blank is for the operator, the correct operator is '-'.

4fill in blank

hard

Fill both blanks to create a prefix sum array using a for loop and the addition operator.

DSA Typescript

const prefixSum: number[] = [arr[0]];
for (let i = 1; i < arr.length; i++) {
  prefixSum[i] = prefixSum[i [1]] [2] arr[i];
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '-' for the index.

Using '-' or '*' instead of '+' for addition.

The prefix sum at index i is the sum of prefixSum[i - 1] and arr[i]. So the first blank is '-' to get the previous index, and the second blank is '+' to add the current element.

5fill in blank

hard

Fill all three blanks to create a function that returns the sum of elements between two indices using prefix sums.

DSA Typescript

function rangeSum(prefixSum: number[], left: number, right: number): number {
  if (left === 0) {
    return prefixSum[right];
  } else {
    return prefixSum[right] [1] prefixSum[left [2] [3]];
  }
}

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

A-

B+

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '-' for subtraction.

Using 0 instead of 1 for index adjustment.

To get the sum from left to right, subtract prefixSum[left - 1] from prefixSum[right]. So the first blank is '-', the second blank is '-', and the third blank is '1' to get left - 1.

Practice

1. What is the main purpose of a prefix sum array in algorithms?

easy

A. To quickly find the sum of elements between any two indices

B. To sort the array elements in ascending order

C. To reverse the array elements

D. To find the maximum element in the array

Solution

1. Step 1: Understand what prefix sum array stores

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

2. Step 2: Identify the use of prefix sums

   Using prefix sums, we can find the sum of any subarray quickly by subtracting two prefix sums.

3. Final Answer:

   To quickly find the sum of elements between any two indices -> Option A

4. Quick Check:

   Prefix sum array = fast range sum queries [OK]

Hint: Prefix sums help answer range sum queries fast [OK]

Common Mistakes:

• Confusing prefix sum with sorting
• Thinking prefix sum reverses array
• Assuming prefix sum finds max element

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

easy

A. const prefix = []; for(let i=0; i

B. const prefix = [0]; for(let i=0; i

C. const prefix = [arr[0]]; for(let i=1; i

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

Solution

1. Step 1: Check initialization and loop indexing

   const prefix = [0]; for(let i=0; i

2. Step 2: Identify errors in other options

   const prefix = []; for(let i=0; i

3. Final Answer:

   const prefix = [0]; for(let i=0; i -> Option B

4. Quick Check:

   Prefix sum array starts with 0 and accumulates sums [OK]

Hint: Start prefix with 0 and add arr[i] in loop [OK]

Common Mistakes:

• Accessing array out of bounds
• Not initializing prefix[0] to 0
• Using negative indices

3. Given the TypeScript code below, what is the output printed?

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

medium

A. [2, 6, 12, 20]

B. [0, 2, 4, 6, 8]

C. [0, 2, 6, 12, 20]

D. [2, 4, 6, 8, 0]

Solution

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

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

2. Step 2: Confirm final prefix array

   The prefix array is [0, 2, 6, 12, 20].

3. Final Answer:

   [0, 2, 6, 12, 20] -> Option C

4. Quick Check:

   Sum accumulates correctly in prefix array [OK]

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

Common Mistakes:

• Forgetting initial 0 in prefix
• Adding wrong elements in loop
• Off-by-one errors in indexing

4. The following TypeScript code attempts to create a prefix sum array but has a bug. What is the error?

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

medium

A. prefix array is not initialized with 0 at index 0

B. Loop runs one time too many

C. arr[i] is accessed out of bounds

D. prefix array is declared with wrong type

Solution

1. Step 1: Check prefix array initialization

   The prefix array is empty initially, so prefix[0] is undefined.

2. Step 2: Identify impact on prefix sum calculation

   prefix[i] is undefined for i=0, so prefix[1] = undefined + arr[0] results in NaN.

3. Final Answer:

   prefix array is not initialized with 0 at index 0 -> Option A

4. Quick Check:

   Initialize prefix[0] = 0 to avoid NaN [OK]

Hint: Always start prefix array with 0 at index 0 [OK]

Common Mistakes:

• Not initializing prefix[0]
• Assuming empty array has prefix[0]
• Ignoring NaN results

5. You have an array arr = [3, 1, 4, 1, 5, 9, 2]. Using a prefix sum array, how would you efficiently find the sum of elements from index 2 to 5 (inclusive)?

hard

A. Calculate prefix sums, then sum = prefix[5] - prefix[1]

B. Calculate prefix sums, then sum = prefix[6] - prefix[1]

C. Calculate prefix sums, then sum = prefix[5] - prefix[2]

D. Calculate prefix sums, then sum = prefix[6] - prefix[2]

Solution

1. Step 1: Understand prefix sum indexing

   Prefix sum array prefix has prefix[0] = 0, prefix[i] = sum of arr[0] to arr[i-1].

2. Step 2: Calculate sum from index 2 to 5

   Sum = prefix[6] - prefix[2], because prefix[6] sums arr[0..5], prefix[2] sums arr[0..1].

3. Final Answer:

   Calculate prefix sums, then sum = prefix[6] - prefix[2] -> Option D

4. Quick Check:

   Sum of arr[2..5] = prefix[6] - prefix[2] [OK]

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

Common Mistakes:

• Off-by-one errors in prefix indices
• Subtracting wrong prefix sums
• Confusing inclusive/exclusive ranges