Recursion on Arrays and Strings in DSA C++ - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Recursive Sum on Array

What is the output of the following C++ code that recursively sums elements of an array?

DSA C++

#include <iostream>

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

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

A 24

B 10

C 0

D Compilation error

💡 Hint

Think about how the function adds the last element and calls itself with one less element.

The function adds the last element arr[n-1] to the sum of the previous elements recursively. For arr = {1,2,3,4}, sum is 1+2+3+4 = 10.

❓ Predict Output

intermediate

Output of Recursive String Reverse

What is the output of this C++ code that recursively reverses a string?

DSA C++

#include <iostream>
#include <string>

std::string reverseString(const std::string& s) {
    if (s.empty()) return "";
    return reverseString(s.substr(1)) + s[0];
}

int main() {
    std::string input = "code";
    std::cout << reverseString(input) << std::endl;
    return 0;
}

A edoc

B code

C Compilation error

D edocd

💡 Hint

The function calls itself on the substring excluding the first character, then adds the first character at the end.

The function reverses the string by moving the first character to the end after reversing the rest recursively. "code" reversed is "edoc".

🧠 Conceptual

advanced

Recursion Base Case Importance

Why is a base case necessary in a recursive function that processes arrays or strings?

A To convert recursion into iteration

B To allocate memory dynamically

C To stop the recursion and prevent infinite calls

D To make the function run faster

💡 Hint

Think about what happens if recursion never stops.

The base case stops recursion by providing a condition where the function returns without further calls, preventing infinite recursion.

🔧 Debug

advanced

Identify the Error in Recursive Palindrome Check

What error does this C++ code produce when checking if a string is a palindrome recursively?

DSA C++

#include <iostream>
#include <string>

bool isPalindrome(const std::string& s, int start, int end) {
    if (start >= end) return true;
    if (s[start] != s[end]) return false;
    return isPalindrome(s, start + 1, end - 1);
}

int main() {
    std::string test = "level";
    std::cout << isPalindrome(test, 0, test.size() - 1) << std::endl;
    return 0;
}

A Outputs 1 (true) correctly

B Compilation error due to missing header

C Runtime error due to out-of-range index

D Outputs 0 (false) incorrectly

💡 Hint

Check the value of 'end' passed to the function and how it is used as an index.

The function uses 'end' as an index, but main originally passed test.size() which is out of bounds (indexing from 0 to size()-1). Passing test.size() - 1 fixes this and outputs true correctly.

🚀 Application

expert

Number of Recursive Calls in Fibonacci

How many times is the function called (including the first call) when computing fibonacci(4) using this naive recursive code?

DSA C++

#include <iostream>

int fibonacci(int n) {
    if (n <= 1) return n;
    return fibonacci(n-1) + fibonacci(n-2);
}

int main() {
    int calls = fibonacci(4);
    std::cout << calls << std::endl;
    return 0;
}

A 15

B 7

C 5

D 9

💡 Hint

Draw the call tree for fibonacci(4) and count all calls.

The call tree for fibonacci(4) has 9 calls total: fibonacci(4), fibonacci(3), fibonacci(2), fibonacci(1), fibonacci(0), fibonacci(1), fibonacci(2), fibonacci(1), fibonacci(0).

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