Recursion on Arrays and Strings in DSA C++ - Build from Scratch

Sum of Array Elements Using Recursion

📖 Scenario: Imagine you have a list of daily expenses and you want to find the total amount spent. Instead of adding them one by one using a loop, you will use a special technique called recursion to add them up.

🎯 Goal: Build a recursive function in C++ that calculates the sum of all elements in an integer array.

📋 What You'll Learn

Create an integer array named expenses with exact values: 100, 200, 300, 400, 500

Create an integer variable n that stores the size of the expenses array

Write a recursive function sumArray that takes the array and its size as parameters and returns the sum of its elements

Print the total sum returned by sumArray

💡 Why This Matters

🌍 Real World

Recursion helps solve problems like summing expenses, searching, or processing data step-by-step, similar to breaking a big task into smaller tasks.

💼 Career

Understanding recursion is important for software development roles that involve algorithms, data processing, and problem-solving.

1

Create the array of expenses

Create an integer array called expenses with these exact values: 100, 200, 300, 400, 500

DSA C++

// Your code here

Hint

Use curly braces {} to list the values inside the array.

2

Store the size of the array

Create an integer variable called n and set it to the size of the expenses array using sizeof(expenses) / sizeof(expenses[0])

DSA C++

int expenses[] = {100, 200, 300, 400, 500};
// Your code here

Hint

Use sizeof to find the total bytes and divide by one element's size.

3

Write the recursive function to sum the array

Write a recursive function called sumArray that takes parameters int arr[] and int size. It should return 0 if size is 0. Otherwise, return the last element arr[size - 1] plus the result of sumArray(arr, size - 1)

DSA C++

int expenses[] = {100, 200, 300, 400, 500};
int n = sizeof(expenses) / sizeof(expenses[0]);

// Your code here

Hint

Base case: when size is 0, return 0. Recursive case: add last element to sum of rest.

4

Print the total sum of the expenses

Print the result of calling sumArray(expenses, n) using std::cout with the message Total expenses:

DSA C++

int expenses[] = {100, 200, 300, 400, 500};
int n = sizeof(expenses) / sizeof(expenses[0]);

int sumArray(int arr[], int size) {
    if (size == 0) {
        return 0;
    }
    return arr[size - 1] + sumArray(arr, size - 1);
}

// Your code here

Hint

Use std::cout to print the message and the sum.

Practice

1. What does a recursive function on an array typically do to process the array elements?

easy

A. It processes one element and calls itself on the rest of the array

B. It processes all elements at once without calling itself

C. It uses loops instead of calling itself

D. It only processes the last element of the array

Solution

1. Step 1: Understand recursion on arrays

   A recursive function on an array usually handles one element and then calls itself on the remaining elements.

2. Step 2: Compare options

   It processes one element and calls itself on the rest of the array matches this behavior. Options A, C, and D describe non-recursive or incorrect methods.

3. Final Answer:

   It processes one element and calls itself on the rest of the array -> Option A

4. Quick Check:

   Recursion on arrays = process one element + recurse [OK]

Hint: Remember recursion breaks problem into smaller parts [OK]

Common Mistakes:

• Thinking recursion processes all elements at once
• Confusing recursion with loops
• Assuming recursion only processes last element

2. Which of the following is the correct base case for a recursive function that sums elements of an integer array arr of size n?

easy

A. if (n == 0) return 0;

B. if (n == 1) return arr[1];

C. if (arr == NULL) return 0;

D. if (n < 0) return 0;

Solution

1. Step 1: Identify base case for recursion on array size

   The base case should stop recursion when no elements are left, which is when n == 0.

2. Step 2: Check each option

   if (n == 0) return 0; returns 0 when n == 0, which is correct. if (n == 1) return arr[1]; incorrectly accesses arr[1] instead of arr[0]. if (arr == NULL) return 0; checks pointer but not size. if (n < 0) return 0; uses invalid negative size.

3. Final Answer:

   if (n == 0) return 0; -> Option A

4. Quick Check:

   Base case for empty array = return 0 [OK]

Hint: Base case usually when size is zero [OK]

Common Mistakes:

• Using wrong index in base case
• Checking pointer instead of size
• Allowing negative sizes

3. What is the output of the following C++ code?

int sumArray(int arr[], int n) {
  if (n == 0) return 0;
  return arr[n-1] + sumArray(arr, n-1);
}

int main() {
  int arr[] = {1, 2, 3, 4};
  int result = sumArray(arr, 4);
  std::cout << result;
  return 0;
}

medium

A. Compilation error

B. 24

C. 0

D. 10

Solution

1. Step 1: Trace recursive calls

   sumArray(arr,4) = arr[3] + sumArray(arr,3) = 4 + sumArray(arr,3) sumArray(arr,3) = arr[2] + sumArray(arr,2) = 3 + sumArray(arr,2) sumArray(arr,2) = arr[1] + sumArray(arr,1) = 2 + sumArray(arr,1) sumArray(arr,1) = arr[0] + sumArray(arr,0) = 1 + 0 = 1

2. Step 2: Calculate total sum

   Total = 4 + 3 + 2 + 1 = 10

3. Final Answer:

   10 -> Option D

4. Quick Check:

   Sum of {1,2,3,4} = 10 [OK]

Hint: Sum recursion adds last element + sum of rest [OK]

Common Mistakes:

• Confusing index n-1 with n
• Forgetting base case returns 0
• Assuming sum is product

4. Find the error in this recursive function that counts occurrences of character c in string s:

int countChar(string s, char c, int index) {
  if (index == s.length()) return 0;
  if (s[index] == c) return 1 + countChar(s, c, index++);
  else return countChar(s, c, index++);
}

medium

A. Missing check for empty string

B. Base case condition is wrong

C. Using post-increment (index++) causes infinite recursion

D. Function should return bool, not int

Solution

1. Step 1: Analyze recursive calls with index++

   Using index++ passes the current index value before increment, so recursive call uses same index repeatedly.

2. Step 2: Identify infinite recursion cause

   Because index does not increase in recursive calls, base case is never reached, causing infinite recursion.

3. Final Answer:

   Using post-increment (index++) causes infinite recursion -> Option C

4. Quick Check:

   Post-increment in recursion argument = infinite loop [OK]

Hint: Use pre-increment (++index) or index+1 in recursion call [OK]

Common Mistakes:

• Using post-increment in recursive call argument
• Ignoring base case correctness
• Confusing return types

5. Given a string s, write a recursive function to check if it is a palindrome (reads same forward and backward). Which approach below correctly implements this?

hard

A. Reverse string using loop and compare with original

B. Check if first and last chars match, then recurse on substring excluding them

C. Count matching characters from start only

D. Use recursion to count characters and compare counts

Solution

1. Step 1: Understand palindrome check recursively

   To check palindrome recursively, compare first and last characters; if they match, recurse on substring excluding them.

2. Step 2: Evaluate options

   Check if first and last chars match, then recurse on substring excluding them matches this logic. Reverse string using loop and compare with original uses loops, not recursion. Options C and D do not correctly check palindrome property.

3. Final Answer:

   Check if first and last chars match, then recurse on substring excluding them -> Option B

4. Quick Check:

   Palindrome recursion = compare ends + recurse inside [OK]

Hint: Compare ends, recurse inside substring [OK]

Common Mistakes:

• Using loops instead of recursion
• Only checking one side of string
• Counting chars instead of comparing