Prefix Sum Array in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the prefix sum array with the first element of the input array.

DSA Python

prefix_sum = [[1]]

Drag options to blanks, or click blank then click option'

Aarr[0]

B0

C[]

Darr

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing prefix_sum as an empty list instead of starting with the first element.

Using 0 instead of the first element of the array.

The prefix sum array starts with the first element of the input array.

2fill in blank

medium

Complete the code to append the sum of the last prefix sum and the current element to the prefix sum array.

DSA Python

for i in range(1, len(arr)):
    prefix_sum.append(prefix_sum[-1] [1] arr[i])

Drag options to blanks, or click blank then click option'

A/

B-

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of addition.

Using the wrong operator causing incorrect prefix sums.

Each prefix sum is the sum of the previous prefix sum and the current element.

3fill in blank

hard

Fix the error in the code to correctly compute the prefix sum array.

DSA Python

prefix_sum = [arr[0]]
for i in range(1, len(arr)):
    prefix_sum.append(prefix_sum[i-1] [1] arr[i])

Drag options to blanks, or click blank then click option'

A*

B-

C+

D//

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of addition.

Using integer division which changes the sum.

The prefix sum at index i is the sum of prefix_sum at i-1 and arr at i.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each element to its prefix sum if the element is greater than 0.

DSA Python

{word: [1] for word in arr if word [2] 0}

Drag options to blanks, or click blank then click option'

Aprefix_sum[arr.index(word)]

Bprefix_sum[word]

C>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using the word itself as index causing errors.

Using wrong comparison operators.

The dictionary maps each word to its prefix sum using the index, and filters words greater than 0.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps the uppercase of each key to its prefix sum value if the value is positive.

DSA Python

result = [1]: [2] for k, v in data.items() if v [3] 0}

Drag options to blanks, or click blank then click option'

Ak.upper()

Bv

C>

Dk.lower()

Attempts:

3 left

💡 Hint

Common Mistakes

Using lowercase keys instead of uppercase.

Including values that are zero or negative.

The dictionary comprehension maps uppercase keys to their values only if the value is greater than zero.

Practice

1. What does a prefix sum array represent for a given array arr?

easy

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

B. An array where each element is the maximum value found in arr up to that index.

C. An array where each element is the difference between consecutive elements in arr.

D. An array where each element is the sum of all elements from the start 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 original array up to each index.

2. Step 2: Compare options with definition

   Only An array where each element is the sum of all elements from the start up to that index in arr. correctly describes this sum accumulation; others describe different operations.

3. Final Answer:

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

4. Quick Check:

   Prefix sum = cumulative sum [OK]

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

Common Mistakes:

• Confusing prefix sum with product or max operations
• Thinking prefix sum stores differences
• Assuming prefix sum stores original array values

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

easy

A. prefix = [arr[0]]
for i in range(1, len(arr)):
prefix.append(arr[i] - prefix[i-1])

B. prefix = []
for i in range(len(arr)):
prefix.append(arr[i] + arr[i-1])

C. prefix = [arr[0]]
for i in range(1, len(arr)):
prefix.append(prefix[i-1] + arr[i])

D. prefix = [0] * len(arr)
for i in range(len(arr)):
prefix[i] = arr[i] * prefix[i-1]

Solution

1. Step 1: Analyze code for prefix sum logic

   prefix = [arr[0]] for i in range(1, len(arr)): prefix.append(prefix[i-1] + arr[i]) starts prefix with first element and adds current element to previous prefix sum correctly.

2. Step 2: Check other options for errors

   prefix = [] for i in range(len(arr)): prefix.append(arr[i] + arr[i-1]) adds current and previous array elements incorrectly; C multiplies instead of sums; A subtracts instead of sums.

3. Final Answer:

   prefix = [arr[0]]\nfor i in range(1, len(arr)):\n prefix.append(prefix[i-1] + arr[i]) -> Option C

4. Quick Check:

   Prefix sum uses cumulative addition [OK]

Hint: Start prefix with first element, then add previous prefix sum [OK]

Common Mistakes:

• Using multiplication instead of addition
• Adding wrong elements or indices
• Initializing prefix array incorrectly

3. What is the output of the following code?

arr = [3, 1, 4, 1, 5]
prefix = [arr[0]]
for i in range(1, len(arr)):
    prefix.append(prefix[i-1] + arr[i])
print(prefix)

medium

A. [3, 4, 8, 9, 14]

B. [3, 1, 4, 1, 5]

C. [3, 3, 7, 8, 13]

D. [0, 3, 4, 8, 9]

Solution

1. Step 1: Calculate prefix sums step-by-step

   Start with prefix = [3]. Then add 1: 3+1=4, add 4: 4+4=8, add 1: 8+1=9, add 5: 9+5=14.

2. Step 2: Form the final prefix array

   prefix = [3, 4, 8, 9, 14]

3. Final Answer:

   [3, 4, 8, 9, 14] -> Option A

4. Quick Check:

   Sum accumulates correctly [OK]

Hint: Add current element to last prefix sum [OK]

Common Mistakes:

• Confusing prefix array with original array
• Off-by-one errors in indexing
• Incorrect initial prefix value

4. Find the error in this prefix sum code and choose the corrected version:

arr = [2, 4, 6]
prefix = [0]
for i in range(len(arr)):
    prefix.append(prefix[i] + arr[i])
print(prefix)

medium

A. Change prefix = [0] to prefix = [arr[0]] and loop from 1 to len(arr)-1.

B. Change prefix.append(prefix[i] + arr[i]) to prefix.append(prefix[i-1] + arr[i]).

C. Remove the initial zero from prefix and start loop from 0 as is.

D. No error; code works correctly and prints prefix sums.

Solution

1. Step 1: Identify initialization and loop issues

   Initializing prefix with [0] and looping from 0 adds an extra leading zero. Tracing: i=0 append(0+2)=2 -> [0,2]; i=1 append(2+4)=6 -> [0,2,6]; i=2 append(6+6)=12 -> [0,2,6,12]. This produces prefix sums of length n+1 with prefix[0]=0, whereas standard is length n starting from arr[0].

2. Step 2: Correct initialization and loop range

   Start prefix with first element arr[0], then loop from index 1 to end to add sums correctly.

3. Final Answer:

   Change prefix = [0] to prefix = [arr[0]] and loop from 1 to len(arr)-1. -> Option A

4. Quick Check:

   Proper start and loop fix prefix sums [OK]

Hint: Initialize prefix with first element, loop from second element [OK]

Common Mistakes:

• Starting prefix with zero instead of first element
• Looping from zero causing off-by-one errors
• Using wrong prefix index inside loop

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

hard

A. Calculate sum as prefix[r] * prefix[l].

B. Calculate sum as prefix[r] - prefix[l-1] if l > 0, else prefix[r].

C. Calculate sum as prefix[r] + prefix[l] always.

D. Calculate sum by looping from l to r and adding elements.

Solution

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

   Prefix sum at index r stores sum from start to r. To get sum from l to r, subtract sum from start to l-1.

2. Step 2: Handle edge case when l is zero

   If l is zero, sum is prefix[r] directly since no subtraction needed.

3. Final Answer:

   Calculate sum as prefix[r] - prefix[l-1] if l > 0, else prefix[r]. -> Option B

4. Quick Check:

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

Hint: Subtract prefix before l from prefix at r for range sum [OK]

Common Mistakes:

• Adding prefix sums instead of subtracting
• Ignoring edge case when l = 0
• Using multiplication or looping unnecessarily