Prefix Sum Array in DSA C - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Prefix Sum Array Construction

What is the output of the prefix sum array after running the following code?

DSA C

int arr[] = {2, 4, 6, 8};
int n = 4;
int prefix[n];
prefix[0] = arr[0];
for(int i = 1; i < n; i++) {
    prefix[i] = prefix[i-1] + arr[i];
}
for(int i = 0; i < n; i++) {
    printf("%d ", prefix[i]);
}

A 2 4 6 8

B 2 6 12 20

C 2 8 14 22

D 0 2 6 12

💡 Hint

Remember prefix sum at index i is sum of all elements from 0 to i.

The prefix sum array stores cumulative sums. Starting with 2, then 2+4=6, then 6+6=12, then 12+8=20.

🧠 Conceptual

intermediate

Understanding Prefix Sum Array Usage

Which of the following is the main advantage of using a prefix sum array?

A It reduces the array size by half.

B It sorts the array elements in ascending order.

C It allows quick calculation of sum of any subarray in constant time after preprocessing.

D It finds the maximum element in the array.

💡 Hint

Think about how prefix sums help in range sum queries.

Prefix sums let you find sum of elements between two indices quickly by subtracting prefix sums.

🔧 Debug

advanced

Identify the Error in Prefix Sum Calculation

What error will this code produce when calculating prefix sums?

DSA C

int arr[] = {1, 3, 5};
int n = 3;
int prefix[n];
for(int i = 0; i <= n; i++) {
    if(i == 0) prefix[i] = arr[i];
    else prefix[i] = prefix[i-1] + arr[i];
}
for(int i = 0; i < n; i++) {
    printf("%d ", prefix[i]);
}

A Output: 1 3 5

B Output: 1 4 9

C Compilation error due to missing semicolon

D Runtime error: Array index out of bounds

💡 Hint

Check the loop condition carefully for array indexing.

The loop runs from i=0 to i=3 (inclusive), but array indices go only up to 2, causing out of bounds access.

🚀 Application

advanced

Calculate Sum of Subarray Using Prefix Sum Array

Given prefix sum array prefix = {3, 8, 15, 21, 28}, what is the sum of elements from index 2 to 4 (0-based)?

A 20

B 13

C 15

D 28

💡 Hint

Use formula: sum(l, r) = prefix[r] - prefix[l-1]

Sum from index 2 to 4 = prefix[4] - prefix[1] = 28 - 8 = 20.

❓ Predict Output

expert

Output of Prefix Sum with Negative Numbers

What is the output of the prefix sum array after running this code?

DSA C

int arr[] = {5, -2, 7, -3, 4};
int n = 5;
int prefix[n];
prefix[0] = arr[0];
for(int i = 1; i < n; i++) {
    prefix[i] = prefix[i-1] + arr[i];
}
for(int i = 0; i < n; i++) {
    printf("%d ", prefix[i]);
}

A 5 3 10 7 11

B 0 5 3 10 7

C 5 3 10 13 17

D 5 -2 7 -3 4

💡 Hint

Add each element to the sum of all previous elements.

Prefix sums: 5, 5+(-2)=3, 3+7=10, 10+(-3)=7, 7+4=11.