Prefix Sum Array in DSA Go - 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 between any two days without adding each day every time.

🎯 Goal: You will build a prefix sum array in Go. This array helps you find the sum of sales between any two days quickly.

📋 What You'll Learn

Create a slice called sales with exact daily sales values

Create a slice called prefixSums to store prefix sums

Calculate prefix sums using a for loop

Print the prefixSums slice to show the result

💡 Why This Matters

🌍 Real World

Prefix sums are used in finance, data analysis, and gaming to quickly calculate sums over ranges without repeated addition.

💼 Career

Understanding prefix sums helps in coding interviews and real-world tasks where performance matters for large data.

1

Create the sales data slice

Create a slice called sales with these exact daily sales values: 5, 8, 6, 3, 7.

DSA Go

package main

func main() {
    // Create the sales slice with values 5, 8, 6, 3, 7
    // Your code here
}

Hint

Use sales := []int{5, 8, 6, 3, 7} to create the slice.

2

Create the prefix sums slice

Create a slice called prefixSums with the same length as sales and initialize all values to zero.

DSA Go

package main

import "fmt"

func main() {
    sales := []int{5, 8, 6, 3, 7}
    // Create prefixSums slice with length equal to sales
    // Your code here
}

Hint

Use make([]int, len(sales)) to create the slice.

3

Calculate prefix sums

Use a for loop with variable i from 0 to len(sales)-1 to fill prefixSums. Set prefixSums[0] to sales[0]. For other indices, set prefixSums[i] to prefixSums[i-1] + sales[i].

DSA Go

package main

import "fmt"

func main() {
    sales := []int{5, 8, 6, 3, 7}
    prefixSums := make([]int, len(sales))
    // Calculate prefix sums using a for loop
    // Your code here
}

Hint

Remember to set the first prefix sum before the loop.

4

Print the prefix sums slice

Use fmt.Println(prefixSums) to print the prefixSums slice.

DSA Go

package main

import "fmt"

func main() {
    sales := []int{5, 8, 6, 3, 7}
    prefixSums := make([]int, len(sales))

    prefixSums[0] = sales[0]
    for i := 1; i < len(sales); i++ {
        prefixSums[i] = prefixSums[i-1] + sales[i]
    }
    // Print the prefixSums slice
    // Your code here
}

Hint

Use fmt.Println(prefixSums) to display the result.

Practice

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

easy

A. To find the maximum element in the array

B. To sort the array elements in ascending order

C. To reverse the array elements efficiently

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

Solution

1. Step 1: Understand prefix sum array concept

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

2. Step 2: Use prefix sums for subarray sums

   Using prefix sums, sum of any subarray can be found quickly by subtracting two prefix sums.

3. Final Answer:

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

4. Quick Check:

   Prefix sum array helps fast subarray sums [OK]

Hint: Prefix sums store cumulative sums for fast subarray queries [OK]

Common Mistakes:

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

2. Which of the following Go code snippets correctly initializes a prefix sum array prefix from an integer slice arr?

easy

A. prefix := make([]int, len(arr))
for i := 0; i < len(arr); i++ {
prefix[i] = prefix[i-1] + arr[i]
}

B. prefix := make([]int, len(arr)+1)
for i := 1; i <= len(arr); i++ {
prefix[i] = prefix[i-1] + arr[i-1]
}

C. prefix := make([]int, len(arr)+1)
for i := 0; i < len(arr); i++ {
prefix[i] = prefix[i-1] + arr[i]
}

D. prefix := make([]int, len(arr))
for i := 1; i < len(arr); i++ {
prefix[i] = prefix[i-1] + arr[i]
}

Solution

1. Step 1: Check prefix array size and indexing

   Prefix sum array usually has length one more than original to handle zero prefix sum at start.

2. Step 2: Verify loop and indexing logic

   Loop from 1 to len(arr), prefix[i] = prefix[i-1] + arr[i-1] correctly accumulates sums.

3. Final Answer:

   prefix := make([]int, len(arr)+1) for i := 1; i <= len(arr); i++ { prefix[i] = prefix[i-1] + arr[i-1] } -> Option B

4. Quick Check:

   Correct prefix sum initialization uses offset indexing [OK]

Hint: Prefix array length = original length + 1, loop starts at 1 [OK]

Common Mistakes:

• Using prefix array same length as original
• Starting loop at 0 and accessing prefix[-1]
• Incorrect indexing of arr inside loop

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

arr := []int{2, 4, 6, 8}
prefix := make([]int, len(arr)+1)
for i := 1; i <= len(arr); i++ {
  prefix[i] = prefix[i-1] + arr[i-1]
}
fmt.Println(prefix)

medium

A. [0 2 6 12 20]

B. [2 6 12 20 28]

C. [0 2 4 6 8]

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: Write final prefix array

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

3. Final Answer:

   [0 2 6 12 20] -> Option A

4. Quick Check:

   Sum accumulates correctly in prefix array [OK]

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

Common Mistakes:

• Forgetting initial zero in prefix array
• Adding wrong elements at each step
• Confusing prefix array length

4. Identify the error in this Go code that tries to build a prefix sum array:

arr := []int{1, 3, 5}
prefix := make([]int, len(arr))
for i := 1; i < len(arr); i++ {
  prefix[i] = prefix[i-1] + arr[i]
}
fmt.Println(prefix)

medium

A. prefix array size should be len(arr)+1

B. Loop should start from i=0 instead of i=1

C. prefix[0] is not initialized before use

D. arr indexing is out of range

Solution

1. Step 1: Check prefix array initialization

   Prefix array is size len(arr), which can work but prefix[0] must be set before use.

2. Step 2: Analyze loop and prefix[0]

   Loop starts at i=1, prefix[1] = prefix[0] + arr[1]. prefix[0] is zero by default in Go, but it should be explicitly set to arr[0] before the loop.

3. Step 3: Check correctness of prefix sums

   prefix[0] is zero, but arr[0] is never added, so prefix sums are incomplete.

4. Final Answer:

   prefix[0] is not initialized before use -> Option C

5. Quick Check:

   Missing prefix[0] initialization causes wrong sums [OK]

Hint: Initialize prefix[0] before loop to avoid wrong sums [OK]

Common Mistakes:

• Not initializing prefix[0]
• Wrong prefix array size
• Incorrect loop start index

5. Given an integer slice arr, how can you use a prefix sum array to find the sum of elements between indices l and r (inclusive) efficiently?

hard

A. sum = prefix[r+1] - prefix[l]

B. sum = prefix[r] - prefix[l-1]

C. sum = prefix[r] + prefix[l]

D. sum = prefix[r+1] + prefix[l-1]

Solution

1. Step 1: Understand prefix sum indexing

   Prefix sum array usually has length len(arr)+1 with prefix[0]=0, prefix[i] = sum of arr[0..i-1].

2. Step 2: Calculate subarray sum using prefix sums

   Sum from l to r = prefix[r+1] - prefix[l] because prefix[r+1] sums up to arr[r].

3. Final Answer:

   sum = prefix[r+1] - prefix[l] -> Option A

4. Quick Check:

   Subarray sum = prefix[r+1] - prefix[l] [OK]

Hint: Use prefix[r+1] - prefix[l] for sum between l and r [OK]

Common Mistakes:

• Using prefix[r] - prefix[l-1] without offset
• Adding prefix sums instead of subtracting
• Confusing indices by 1