Prefix Sum Array in DSA Java - 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 Java

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]

D0

Attempts:

3 left

💡 Hint

Common Mistakes

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

In Java, to access the first element of an array, use square brackets with index 0: arr[0].

2fill in blank

medium

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

DSA Java

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 - 1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Starting the loop at 0 which causes incorrect prefix sums.

Starting at 2 which skips the second element.

The prefix sum starts from the second element, so the loop index i should start at 1.

3fill in blank

hard

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

DSA Java

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 '-' causing runtime errors.

Using '*' or '/' which are incorrect for indexing.

To get the previous prefix sum, subtract 1 from i: prefixSum[i - 1].

4fill in blank

hard

Fill both blanks to complete the method that returns the sum of elements between indices left and right (inclusive) using the prefix sum array.

DSA Java

public int rangeSum(int left, int right) {
    if (left == 0) {
        return prefixSum[1];
    } else {
        return prefixSum[right] [2] prefixSum[left - 1];
    }
}

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

A[right]

B[left]

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using prefixSum[left] instead of prefixSum[right] in the first return.

Using addition instead of subtraction in the else return.

If left is 0, return prefixSum[right]. Otherwise, subtract prefixSum[left - 1] from prefixSum[right] to get the sum.

5fill in blank

hard

Fill all three blanks to complete the method that builds the prefix sum array from the input array.

DSA Java

public int[] buildPrefixSum(int[] arr) {
    int[] prefixSum = new int[arr.length];
    prefixSum[0] = arr[1];
    for (int i = [2]; i < arr.length; i++) {
        prefixSum[i] = prefixSum[i [3] 1] + arr[i];
    }
    return prefixSum;
}

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

A[0]

B1

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using parentheses instead of square brackets for array access.

Starting loop at 0 causing incorrect sums.

Using '+' instead of '-' in prefixSum index.

Access first element with arr[0], start loop at 1, and subtract 1 to get previous prefix sum index.

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