Prefix Sum Array in DSA Java - Build from Scratch

Prefix Sum Array

📖 Scenario: You are working with a list of daily sales numbers for a small shop. To quickly find the total sales between any two days, you want to create a prefix sum array.

🎯 Goal: Build a prefix sum array from the daily sales array. This array will help you find the sum of sales from the start up to any day efficiently.

📋 What You'll Learn

Create an integer array called sales with the exact values: 5, 3, 8, 6, 2

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

Fill prefixSum so that each element at index i is the sum of sales[0] to sales[i]

Print the prefixSum array elements separated by spaces

💡 Why This Matters

🌍 Real World

Prefix sum arrays are used in finance to quickly calculate cumulative totals, in gaming for score tracking, and in data analysis for fast range queries.

💼 Career

Understanding prefix sums helps in optimizing algorithms for performance, a key skill in software development and data engineering roles.

1

Create the sales array

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

DSA Java

// Create the sales array with exact values
// Your code here

Hint

Use int[] sales = {5, 3, 8, 6, 2}; to create the array.

2

Create the prefixSum array

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

DSA Java

public class Main {
    public static void main(String[] args) {
        int[] sales = {5, 3, 8, 6, 2};
        // Create prefixSum array with same length as sales
        // Your code here
    }
}

Hint

Use new int[sales.length] to create the array.

3

Fill the prefixSum array with sums

Fill the prefixSum array so that each element at index i is the sum of sales[0] to sales[i]. Use a for loop with variable i from 0 to sales.length - 1. For i == 0, set prefixSum[0] to sales[0]. For other i, set prefixSum[i] to prefixSum[i - 1] + sales[i].

DSA Java

public class Main {
    public static void main(String[] args) {
        int[] sales = {5, 3, 8, 6, 2};
        int[] prefixSum = new int[sales.length];
        // Use a for loop with i from 0 to sales.length - 1
        // For i == 0, prefixSum[0] = sales[0]
        // For i > 0, prefixSum[i] = prefixSum[i - 1] + sales[i]
        // Your code here
    }
}

Hint

Use a for loop and an if statement to fill the prefixSum array.

4

Print the prefixSum array

Print the elements of the prefixSum array separated by spaces using a for loop with variable i from 0 to prefixSum.length - 1. Use System.out.print(prefixSum[i] + " ") inside the loop and System.out.println() after the loop.

DSA Java

public class Main {
    public static void main(String[] args) {
        int[] sales = {5, 3, 8, 6, 2};
        int[] prefixSum = new int[sales.length];
        for (int i = 0; i < sales.length; i++) {
            if (i == 0) {
                prefixSum[i] = sales[i];
            } else {
                prefixSum[i] = prefixSum[i - 1] + sales[i];
            }
        }
        // Use a for loop to print prefixSum elements separated by spaces
        // Your code here
    }
}

Hint

Use a for loop and System.out.print to print each element followed by a space.

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 up to that index in arr

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

Solution

1. Step 1: Understand prefix sum definition

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

2. Step 2: Compare options with definition

   Only An array where each element is the sum of all elements up to that index in arr matches this definition exactly.

3. Final Answer:

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

4. Quick Check:

   Prefix sum = cumulative sum [OK]

Hint: Prefix sum means cumulative sum from start to current index [OK]

Common Mistakes:

• Confusing prefix sum with product or max operations
• Thinking prefix sum stores differences
• Mixing prefix sum with suffix sum

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

easy

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

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

C. int[] prefix = new int[arr.length]; prefix[0] = arr[0]; for(int i=1; i

D. int[] prefix = new int[arr.length]; for(int i=0; i

Solution

1. Step 1: Check initialization of prefix array

   Prefix sum array must start with prefix[0] = arr[0] to include first element sum.

2. Step 2: Verify loop calculation

   Loop from i=1 to end adds previous prefix sum plus current arr element, which is correct.

3. Final Answer:

   int[] prefix = new int[arr.length]; prefix[0] = arr[0]; for(int i=1; i -> Option C

4. Quick Check:

   Initialize first element, then add previous sums [OK]

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

Common Mistakes:

• Starting prefix[0] with 0 instead of arr[0]
• Multiplying instead of adding elements
• Reversing array elements instead of summing

3. What is the output of the following Java code?

int[] arr = {2, 4, 6, 8};
int[] prefix = new int[arr.length];
prefix[0] = arr[0];
for(int i = 1; i < arr.length; i++) {
    prefix[i] = prefix[i-1] + arr[i];
}
System.out.println(java.util.Arrays.toString(prefix));

medium

A. [2, 6, 12, 20]

B. [2, 4, 6, 8]

C. [0, 2, 6, 12]

D. [2, 8, 14, 22]

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: Verify final prefix array

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

3. Final Answer:

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

4. Quick Check:

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

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

Common Mistakes:

• Printing original array instead of prefix sum
• Starting prefix sum with 0 incorrectly
• Adding wrong elements in loop

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

int[] arr = {1, 3, 5};
int[] prefix = new int[arr.length];
prefix[0] = 0;
for(int i = 1; i <= arr.length; i++) {
    prefix[i] = prefix[i-1] + arr[i];
}

medium

A. Loop condition should be i < arr.length instead of i <= arr.length

B. prefix[0] should be initialized to arr[0] instead of 0

C. Array index arr[i] will cause an error when i equals arr.length

D. All of the above

Solution

1. Step 1: Check loop boundary

   The loop uses i <= arr.length, which causes index out of bounds because valid indices are 0 to arr.length-1.

2. Step 2: Check prefix[0] initialization and array access

   prefix[0] should be arr[0] to start sums correctly; also arr[i] access fails at i = arr.length.

3. Step 3: Combine all errors

   All issues cause runtime errors or incorrect prefix sums.

4. Final Answer:

   All of the above -> Option D

5. Quick Check:

   Loop bounds, initialization, and indexing errors combined [OK]

Hint: Check loop limits and array indices carefully [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Initializing prefix[0] incorrectly
• Accessing array out of bounds

5. Given an integer array arr of length 5: {3, 1, 4, 1, 5}, you want to find the sum of elements from index 1 to 3 (inclusive) efficiently using a prefix sum array. Which expression correctly calculates this sum using the prefix sum array prefix where prefix[i] is the sum of elements from index 0 to i?

hard

A. prefix[3] - prefix[2]

B. prefix[3] - prefix[0]

C. prefix[3] - prefix[1]

D. prefix[3] - prefix[0] + arr[1]

Solution

1. Step 1: Understand prefix sum usage for range sums

   Sum from index l to r = prefix[r] - prefix[l-1]. Here l=1, r=3.

2. Step 2: Apply formula with given indices

   Sum = prefix[3] - prefix[0]. prefix[0] is sum up to index 0, so subtracting it leaves sum from 1 to 3.

3. Final Answer:

   prefix[3] - prefix[0] -> Option B

4. Quick Check:

   Range sum = prefix[r] - prefix[l-1] [OK]

Hint: Range sum = prefix[end] - prefix[start - 1] [OK]

Common Mistakes:

• Subtracting prefix at wrong index
• Adding extra elements unnecessarily
• Confusing inclusive indices