Prefix Sum Array in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the prefix sum array's first element.

DSA C

prefix_sum[0] = [1];

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A-1

Barr[0]

Carr[1]

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Setting prefix_sum[0] to 0 instead of arr[0]

Using arr[1] which is the second element

Initializing with -1 which is incorrect

The first element of the prefix sum array should be the first element of the original array.

2fill in blank

medium

Complete the code to compute the prefix sum at index i inside the loop.

DSA C

prefix_sum[i] = prefix_sum[i - 1] [1] arr[i];

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

3fill in blank

hard

Fix the error in the loop condition to correctly iterate over the array elements.

DSA C

for (int i = 1; i [1] n; i++) {

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A>

B<=

C>=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>=' or '>' which causes no iterations or wrong iterations

Using '<=' which causes out-of-bounds access

The loop should run while i is less than n to avoid going out of array bounds.

4fill in blank

hard

Fill both blanks to compute the prefix sum array using a for loop.

DSA C

for (int [1] = 1; [2] < n; [1]++) {
    prefix_sum[[1]] = prefix_sum[[1] - 1] + arr[[1]];
}

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Ai

Bj

Ck

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names in loop parts causing errors

Using uncommon variable names that confuse the logic

The loop variable should be consistent; 'i' is commonly used for indexing.

5fill in blank

hard

Fill all three blanks to create a prefix sum array and print its elements.

DSA C

int prefix_sum[n];
prefix_sum[0] = arr[0];
for (int [1] = 1; [2] < n; [1]++) {
    prefix_sum[[1]] = prefix_sum[[1] - 1] + arr[[1]];
}
for (int [3] = 0; [3] < n; [3]++) {
    printf("%d ", prefix_sum[[3]]);
}

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

Ai

Bj

Ck

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Using the same variable for both loops causing logic errors

Using inconsistent variable names inside loops

Use 'i' for the prefix sum loop and 'j' for the print loop to avoid confusion.

Practice

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

easy

A. To quickly find the sum of elements in any subarray

B. To sort the array elements in ascending order

C. To store the product of all elements

D. To reverse the array efficiently

Solution

1. Step 1: Understand prefix sum array definition

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

2. Step 2: Identify its use

   This allows quick calculation of sums for any subarray by subtracting prefix sums.

3. Final Answer:

   To quickly find the sum of elements in any subarray -> Option A

4. Quick Check:

   Prefix sum = fast subarray sums [OK]

Hint: Prefix sums help find subarray sums fast [OK]

Common Mistakes:

• Confusing prefix sum with sorting
• Thinking it stores products
• Assuming it reverses arrays

2. Which of the following is the correct way to initialize a prefix sum array prefix for an integer array arr of size n in C?

easy

A. prefix[0] = arr[1]; for(int i=1; i

B. prefix[0] = arr[0]; for(int i=1; i

C. for(int i=0; i

D. prefix[0] = 0; for(int i=1; i<=n; i++) prefix[i] = prefix[i-1] + arr[i];

Solution

1. Step 1: Initialize first prefix element

   Set prefix[0] to arr[0] to start sums correctly.

2. Step 2: Loop from 1 to n-1 adding previous prefix and current arr

   Use prefix[i] = prefix[i-1] + arr[i] for correct cumulative sums.

3. Final Answer:

   prefix[0] = arr[0]; for(int i=1; i -> Option B

4. Quick Check:

   Start at arr[0], add cumulatively [OK]

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

Common Mistakes:

• Starting prefix at 0 and indexing arr out of bounds
• Copying arr directly without summing
• Using wrong starting index for arr

3. Given the array arr = {2, 4, 6, 8}, what is the prefix sum array after running the code:

int prefix[4];
prefix[0] = arr[0];
for(int i = 1; i < 4; i++) {
    prefix[i] = prefix[i-1] + arr[i];
}

medium

A. [0, 2, 6, 12]

B. [2, 4, 6, 8]

C. [2, 6, 12, 20]

D. [2, 8, 14, 22]

Solution

1. Step 1: Calculate prefix[0]

   prefix[0] = arr[0] = 2

2. Step 2: Calculate prefix sums for i=1 to 3

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

3. Final Answer:

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

4. Quick Check:

   Sum accumulates: 2, 6, 12, 20 [OK]

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

Common Mistakes:

• Confusing prefix sums with original array
• Starting sums from zero incorrectly
• Adding wrong elements in loop

4. Identify the error in the following code snippet that attempts to create a prefix sum array for arr of size n:

int prefix[n];
prefix[0] = 0;
for(int i = 1; i < n; i++) {
    prefix[i] = prefix[i-1] + arr[i];
}

medium

A. prefix[0] should be initialized to arr[0], not 0

B. Loop should start from i = 0, not 1

C. Array prefix should be of size n+1

D. The code will cause a runtime error

Solution

1. Step 1: Check prefix[0] initialization

   prefix[0] must hold arr[0] to start sums correctly, not zero.

2. Step 2: Analyze loop correctness

   Loop starting at 1 is correct if prefix[0] is set properly.

3. Final Answer:

   prefix[0] should be initialized to arr[0], not 0 -> Option A

4. Quick Check:

   prefix[0] = arr[0] starts sums right [OK]

Hint: Initialize prefix[0] with arr[0], not zero [OK]

Common Mistakes:

• Setting prefix[0] to zero causes wrong sums
• Starting loop at wrong index
• Assuming prefix array size must be n+1

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[5] + prefix[2]

B. Sum elements from arr[2] to arr[5] directly every time

C. Use prefix[6] - prefix[2] to get the sum

D. Calculate prefix[5] - prefix[1] after building prefix sums

Solution

1. Step 1: Build prefix sum array

   prefix[i] = sum of arr[0] to arr[i]. For example, prefix[5] = sum of arr[0..5].

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

   Sum = prefix[5] - prefix[1], because prefix[1] = sum of arr[0..1].

3. Final Answer:

   Calculate prefix[5] - prefix[1] after building prefix sums -> Option D

4. Quick Check:

   Sum(i..j) = prefix[j] - prefix[i-1] [OK]

Hint: Sum subarray = prefix[end] - prefix[start-1] [OK]

Common Mistakes:

• Adding prefix sums instead of subtracting
• Using wrong indices for prefix subtraction
• Summing elements directly ignoring prefix sums