Prefix Sum Array in DSA C# - 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 C#

int[] prefixSum = new int[arr.Length];
prefixSum[0] = arr[[1]];

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

A{0}

B(0)

C[0]

D<0>

Attempts:

3 left

💡 Hint

Common Mistakes

Using parentheses or curly braces instead of square brackets for indexing.

Trying to assign the whole array instead of a single element.

We use square brackets [ ] to access array elements by index in C#.

2fill in blank

medium

Complete the for loop header to iterate from the second element to the end of the array.

DSA C#

for (int i = [1]; i < arr.Length; i++)
{
    prefixSum[i] = prefixSum[i - 1] + arr[i];
}

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

A0

B1

Carr.Length

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Starting the loop at 0 which overwrites the first prefix sum.

Starting at arr.Length which is out of bounds.

We start from index 1 because prefixSum[0] is already set.

3fill in blank

hard

Fix the error in the prefix sum calculation inside the loop.

DSA C#

prefixSum[i] = prefixSum[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 + instead of - which causes index out of range or wrong sums.

Using * or / which are not correct for indexing.

We subtract 1 to get the previous prefix sum element.

4fill in blank

hard

Fill both blanks to compute the sum of elements from index left to right using the prefix sum array.

DSA C#

int rangeSum = prefixSum[[1]] - prefixSum[[2]];

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

Aright

Bleft

Cleft - 1

Dright - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using left instead of left - 1 for the second index.

Using right - 1 instead of right for the first index.

Sum from left to right is prefixSum[right] - prefixSum[left - 1].

5fill in blank

hard

Fill all three blanks to safely compute the sum from left to right, handling the case when left is zero.

DSA C#

int rangeSum = (left == 0) ? prefixSum[[1]] : prefixSum[[2]] - prefixSum[[3]];

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

Aright

Cleft - 1

Dleft

Attempts:

3 left

💡 Hint

Common Mistakes

Not handling left == 0 case causing index errors.

Using left instead of left - 1 in subtraction.

If left is zero, sum is prefixSum[right]. Otherwise, subtract prefixSum[left - 1].

Practice

1. What is the main purpose of a Prefix Sum Array in algorithms?

easy

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

B. To sort the array elements in ascending order

C. To find the maximum element in the array

D. To reverse the array elements

Solution

1. Step 1: Understand what prefix sums represent

   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 in any subarray -> Option A

4. Quick Check:

   Prefix Sum Array = Fast subarray sums [OK]

Hint: Prefix sums help sum subarrays fast by subtraction [OK]

Common Mistakes:

• Thinking prefix sums sort the array
• Confusing prefix sums with maximum element search
• Assuming prefix sums reverse the array

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

easy

A. int[] prefix = new int[arr.Length+1]; for(int i=1; i<=arr.Length; i++) prefix[i] = prefix[i-1] + arr[i];

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

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

D. int[] prefix = new int[arr.Length]; prefix[0] = 0; for(int i=1; i

Solution

1. Step 1: Check initialization of prefix array

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

2. Step 2: Verify loop for cumulative sum

   The loop starts from 1 and adds prefix[i-1] + arr[i], correctly building prefix sums.

3. Final Answer:

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

4. Quick Check:

   Correct prefix sum initialization = int[] prefix = new int[arr.Length]; prefix[0] = arr[0]; for(int i=1; i

Hint: Start prefix[0] = arr[0], then add previous prefix + current element [OK]

Common Mistakes:

• Using wrong array length for prefix
• Starting loop from 0 instead of 1
• Accessing arr out of bounds (like arr[i] when i == arr.Length)

3. Given the array arr = new int[] {2, 4, 6, 8} and its prefix sum array prefix computed as usual, what is the output of prefix[3] - prefix[1]?

medium

A. 18

B. 10

C. 12

D. 14

Solution

1. Step 1: Compute prefix sum array

   prefix[0]=2, prefix[1]=2+4=6, prefix[2]=6+6=12, prefix[3]=12+8=20

2. Step 2: Calculate prefix[3] - prefix[1]

   20 - 6 = 14

3. Final Answer:

   14 -> Option D

4. Quick Check:

   Sum from index 2 to 3 = 6+8 = 14 [OK]

Hint: Subtract prefix sums to get subarray sum [OK]

Common Mistakes:

• Confusing indices and subtracting wrong prefix values
• Adding prefix sums instead of subtracting
• Forgetting prefix sums start at index 0

4. Consider the following code snippet to build a prefix sum array. Identify the error:

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 should start from i = 0, not 1

B. prefix[0] should be arr[0], not 0

C. Array prefix should have length arr.Length + 1

D. No error, code is correct

Solution

1. Step 1: Check initialization of prefix[0]

   Setting prefix[0] = 0 is incorrect; it should be arr[0] to start cumulative sum correctly.

2. Step 2: Verify loop and array length

   The loop starting at 1 and array length are fine; only prefix[0] initialization is wrong.

3. Final Answer:

   prefix[0] should be arr[0], not 0 -> Option B

4. Quick Check:

   Correct prefix start = arr[0] [OK]

Hint: Initialize prefix[0] with arr[0], not zero [OK]

Common Mistakes:

• Starting loop at 0 causing index errors
• Using wrong prefix array size
• Assuming zero initialization is always correct

5. You have an integer array arr of length 6: {3, 1, 4, 1, 5, 9}. You want to find the sum of elements from index 2 to 5 inclusive using a prefix sum array prefix where prefix[i] stores sum of elements from index 0 to i. Which expression correctly computes this sum?

hard

A. prefix[5] - prefix[1]

B. prefix[5] - prefix[2]

C. prefix[4] - prefix[1]

D. prefix[5] + prefix[1]

Solution

1. Step 1: Understand prefix sum indexing

   prefix[i] = sum of arr[0] to arr[i]. To get sum from index 2 to 5, subtract prefix[1] (sum up to index 1) from prefix[5].

2. Step 2: Write the correct expression

   Sum = prefix[5] - prefix[1]

3. Final Answer:

   prefix[5] - prefix[1] -> Option A

4. Quick Check:

   Sum(2 to 5) = prefix[5] - prefix[1] [OK]

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

Common Mistakes:

• Subtracting prefix[i] instead of prefix[i-1]
• Adding prefix sums instead of subtracting
• Using wrong indices for prefix array