Prefix Sum Array in DSA Typescript - 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 out the total sales from the start up to any given day without adding all the numbers every time.

🎯 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 quickly.

📋 What You'll Learn

Create an array called sales with exact daily sales numbers

Create an empty array called prefixSums to store running totals

Use a for loop with variable i to calculate prefix sums

Print the prefixSums array at the end

💡 Why This Matters

🌍 Real World

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

💼 Career

Understanding prefix sums helps in coding interviews and real-world tasks involving efficient data queries.

1

Create the sales data array

Create an array called sales with these exact daily sales numbers: 10, 20, 15, 5, 30.

DSA Typescript

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

Hint

Use square brackets [] to create the array and separate numbers with commas.

2

Create the prefix sums array

Create an empty array called prefixSums to store the running totals of sales.

DSA Typescript

const sales = [10, 20, 15, 5, 30];
// Create an empty array called prefixSums
// Your code here

Hint

Use [] to create an empty array and specify the type as number[].

3

Calculate prefix sums using a loop

Use a for loop with variable i from 0 to sales.length - 1. Inside the loop, add the current sale to the previous prefix sum (or 0 if i is 0) and store it in prefixSums[i].

DSA Typescript

const sales = [10, 20, 15, 5, 30];
const prefixSums: number[] = [];
// Use a for loop with i to calculate prefix sums
// Your code here

Hint

Use a conditional expression to add the previous prefix sum only if i is greater than 0.

4

Print the prefix sums array

Print the prefixSums array using console.log(prefixSums).

DSA Typescript

const sales = [10, 20, 15, 5, 30];
const prefixSums: number[] = [];
for (let i = 0; i  0 ? prefixSums[i - 1] : 0);
}
// Print the prefixSums array
// Your code here

Hint

The output should show the running totals: 10, 30, 45, 50, 80.

Practice

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

easy

A. To quickly find the sum of elements between any two indices

B. To sort the array elements in ascending order

C. To reverse the array elements

D. To find the maximum element in the array

Solution

1. Step 1: Understand what prefix sum array stores

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

2. Step 2: Identify the use of prefix sums

   Using prefix sums, we can find the sum of any subarray quickly by subtracting two prefix sums.

3. Final Answer:

   To quickly find the sum of elements between any two indices -> Option A

4. Quick Check:

   Prefix sum array = fast range sum queries [OK]

Hint: Prefix sums help answer range sum queries fast [OK]

Common Mistakes:

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

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

easy

A. const prefix = []; for(let i=0; i

B. const prefix = [0]; for(let i=0; i

C. const prefix = [arr[0]]; for(let i=1; i

D. const prefix = [0]; for(let i=1; i<=arr.length; i++) { prefix[i] = prefix[i-1] + arr[i]; }

Solution

1. Step 1: Check initialization and loop indexing

   const prefix = [0]; for(let i=0; i

2. Step 2: Identify errors in other options

   const prefix = []; for(let i=0; i

3. Final Answer:

   const prefix = [0]; for(let i=0; i -> Option B

4. Quick Check:

   Prefix sum array starts with 0 and accumulates sums [OK]

Hint: Start prefix with 0 and add arr[i] in loop [OK]

Common Mistakes:

• Accessing array out of bounds
• Not initializing prefix[0] to 0
• Using negative indices

3. Given the TypeScript code below, what is the output printed?

const arr = [2, 4, 6, 8];
const prefix = [0];
for(let i = 0; i < arr.length; i++) {
  prefix[i + 1] = prefix[i] + arr[i];
}
console.log(prefix);

medium

A. [2, 6, 12, 20]

B. [0, 2, 4, 6, 8]

C. [0, 2, 6, 12, 20]

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: Confirm final prefix array

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

3. Final Answer:

   [0, 2, 6, 12, 20] -> Option C

4. Quick Check:

   Sum accumulates correctly in prefix array [OK]

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

Common Mistakes:

• Forgetting initial 0 in prefix
• Adding wrong elements in loop
• Off-by-one errors in indexing

4. The following TypeScript code attempts to create a prefix sum array but has a bug. What is the error?

const arr = [1, 3, 5];
const prefix = [];
for(let i = 0; i < arr.length; i++) {
  prefix[i + 1] = prefix[i] + arr[i];
}
console.log(prefix);

medium

A. prefix array is not initialized with 0 at index 0

B. Loop runs one time too many

C. arr[i] is accessed out of bounds

D. prefix array is declared with wrong type

Solution

1. Step 1: Check prefix array initialization

   The prefix array is empty initially, so prefix[0] is undefined.

2. Step 2: Identify impact on prefix sum calculation

   prefix[i] is undefined for i=0, so prefix[1] = undefined + arr[0] results in NaN.

3. Final Answer:

   prefix array is not initialized with 0 at index 0 -> Option A

4. Quick Check:

   Initialize prefix[0] = 0 to avoid NaN [OK]

Hint: Always start prefix array with 0 at index 0 [OK]

Common Mistakes:

• Not initializing prefix[0]
• Assuming empty array has prefix[0]
• Ignoring NaN results

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 sums, then sum = prefix[5] - prefix[1]

B. Calculate prefix sums, then sum = prefix[6] - prefix[1]

C. Calculate prefix sums, then sum = prefix[5] - prefix[2]

D. Calculate prefix sums, then sum = prefix[6] - prefix[2]

Solution

1. Step 1: Understand prefix sum indexing

   Prefix sum array prefix has prefix[0] = 0, prefix[i] = sum of arr[0] to arr[i-1].

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

   Sum = prefix[6] - prefix[2], because prefix[6] sums arr[0..5], prefix[2] sums arr[0..1].

3. Final Answer:

   Calculate prefix sums, then sum = prefix[6] - prefix[2] -> Option D

4. Quick Check:

   Sum of arr[2..5] = prefix[6] - prefix[2] [OK]

Hint: Sum(i to j) = prefix[j+1] - prefix[i] [OK]

Common Mistakes:

• Off-by-one errors in prefix indices
• Subtracting wrong prefix sums
• Confusing inclusive/exclusive ranges