Prefix Sum Array in DSA C - Build from Scratch

Prefix Sum Array

📖 Scenario: Imagine you have a list of daily sales numbers for a small shop. You want to quickly find the total sales from the start up to any given day.

🎯 Goal: You will build a prefix sum array that stores the running total of sales up to each day. This helps answer total sales queries efficiently.

📋 What You'll Learn

Create an integer array called sales with exactly these values: 5, 3, 8, 6, 2

Create an integer array called prefix_sum with the same length as sales

Create an integer variable called n and set it to the length of sales

Use a for loop with variable i from 0 to n - 1 to fill prefix_sum

Print the prefix_sum array elements separated by spaces

💡 Why This Matters

🌍 Real World

Prefix sums are used in finance to quickly calculate cumulative totals like sales or expenses over time.

💼 Career

Understanding prefix sums helps in data analysis, algorithm optimization, and solving range query problems efficiently.

1

Create the sales data array

Create an integer array called sales with exactly these values: 5, 3, 8, 6, 2.

DSA C

# Your code here

Hint

Use curly braces to list the values inside the array.

2

Create prefix sum array and length variable

Create an integer array called prefix_sum with length 5 and an integer variable called n set to 5.

DSA C

int sales[5] = {5, 3, 8, 6, 2};
# Your code here

Hint

Declare prefix_sum as an integer array of size 5 and n as an integer with value 5.

3

Fill the prefix sum array

Use a for loop with variable i from 0 to n - 1 to fill prefix_sum so that each element is the sum of all sales elements up to index i. For i == 0, set prefix_sum[0] to sales[0]. For other i, set prefix_sum[i] to prefix_sum[i - 1] + sales[i].

DSA C

int sales[5] = {5, 3, 8, 6, 2};
int prefix_sum[5];
int n = 5;

# Your code here

Hint

Use an if inside the loop to handle the first element separately.

4

Print the prefix sum array

Use a for loop with variable i from 0 to n - 1 to print each element of prefix_sum followed by a space. Then print a newline character.

DSA C

int sales[5] = {5, 3, 8, 6, 2};
int prefix_sum[5];
int n = 5;

for (int i = 0; i < n; i++) {
    if (i == 0) {
        prefix_sum[i] = sales[i];
    } else {
        prefix_sum[i] = prefix_sum[i - 1] + sales[i];
    }
}

# Your code here

Hint

Use printf("%d ", prefix_sum[i]) inside the loop and printf("\n") after the loop.

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