Recursion on Arrays and Strings in DSA Java

Mental Model

Recursion breaks a big problem into smaller similar problems until it becomes simple enough to solve directly.

Analogy: Imagine peeling an onion layer by layer until you reach the center; each peel is like a smaller problem solved by recursion.

Array: [a, b, c, d, e]
String: "hello"
Recursion call stack:
call5 ↑
call4 -> call5
call3 -> call4
call2 -> call3
call1 -> call2

Dry Run Walkthrough

Input: array: [1, 2, 3], find sum using recursion

Goal: Calculate the sum of all elements in the array using recursion

Step 1: call sum on array starting at index 0

sum([1,2,3], index=0) waiting for sum([1,2,3], index=1)

Why: We start from the first element and reduce the problem by moving to the next index

Step 2: call sum on array starting at index 1

sum([1,2,3], index=1) waiting for sum([1,2,3], index=2)

Why: We keep moving forward to reach the base case

Step 3: call sum on array starting at index 2

sum([1,2,3], index=2) waiting for sum([1,2,3], index=3)

Why: Continue until index reaches array length

Step 4: call sum on array starting at index 3 (base case)

sum([1,2,3], index=3) returns 0

Why: Index 3 is beyond last element, so return 0 to stop recursion

Step 5: return sum at index 2: array[2] + 0 = 3 + 0 = 3

sum([1,2,3], index=2) returns 3

Why: Add current element to sum of rest

Step 6: return sum at index 1: array[1] + 3 = 2 + 3 = 5

sum([1,2,3], index=1) returns 5

Why: Add current element to sum of rest

Step 7: return sum at index 0: array[0] + 5 = 1 + 5 = 6

sum([1,2,3], index=0) returns 6

Why: Add current element to sum of rest

Result:

Final sum = 6

Annotated Code

DSA Java

public class RecursionArray {

    // Recursive function to sum elements from index to end
    public static int sumArray(int[] arr, int index) {
        if (index == arr.length) {
            return 0; // base case: no elements left
        }
        return arr[index] + sumArray(arr, index + 1); // add current and recurse
    }

    public static void main(String[] args) {
        int[] array = {1, 2, 3};
        int result = sumArray(array, 0);
        System.out.println("Sum of array elements: " + result);
    }
}

if (index == arr.length) {

check base case to stop recursion when index reaches array length

return 0;

return 0 as sum of empty part of array

return arr[index] + sumArray(arr, index + 1);

add current element to sum of rest of array recursively

Output

Sum of array elements: 6

Complexity Analysis

Time: O(n) because the function calls itself once per element until the end

Space: O(n) due to the recursion call stack growing with each element

vs Alternative: Iterative sum uses O(1) space and same O(n) time, recursion is simpler to write but uses more memory

Edge Cases

empty array

returns 0 immediately as base case triggers at index 0

DSA Java

if (index == arr.length) {

single element array

returns that element as sum after one recursive call

DSA Java

return arr[index] + sumArray(arr, index + 1);

When to Use This Pattern

When you see a problem that can be broken down into smaller similar problems on arrays or strings, use recursion to simplify the solution.

Common Mistakes

Mistake: Forgetting the base case causing infinite recursion
Fix: Add a clear base case that stops recursion when index reaches array length

Mistake: Not moving the index forward in recursive call
Fix: Increment the index in the recursive call to progress towards base case

Summary

Recursion on arrays and strings solves problems by breaking them into smaller parts until simple cases.

Use recursion when a problem can be naturally divided into similar subproblems on smaller slices.

The key is to define a base case and reduce the problem size each recursive call.

Practice

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

easy

A. It calls itself with a smaller part of the array until a base case is reached

B. It uses loops to iterate over the array elements

C. It modifies the array without calling itself

D. It sorts the array before processing

Solution

1. Step 1: Understand recursion on arrays

   Recursive functions reduce the problem size by calling themselves with smaller parts of the array.

2. Step 2: Identify base case and recursive call

   The function stops when the array part is empty or has one element (base case), otherwise it calls itself with a smaller array.

3. Final Answer:

   It calls itself with a smaller part of the array until a base case is reached -> Option A

4. Quick Check:

   Recursion = smaller problem calls [OK]

Hint: Recursion breaks problem into smaller parts until simple case [OK]

Common Mistakes:

• Thinking recursion uses loops instead of self-calls
• Ignoring the base case in recursion
• Assuming recursion sorts the array automatically

2. Which of the following is the correct syntax to define a recursive method in Java that takes an integer array and an index as parameters?

easy

A. void recurse(int arr[], index int) { ... }

B. public void recurse(int[] arr, int index) { ... }

C. public int recurse(int arr, int index) { ... }

D. public void recurse(int[] arr; int index) { ... }

Solution

1. Step 1: Check Java method syntax

   Java methods require return type, method name, and parameters with types and commas.

2. Step 2: Validate parameter types and order

   public void recurse(int[] arr, int index) { ... } correctly uses 'int[] arr' and 'int index' separated by a comma and proper method signature.

3. Final Answer:

   public void recurse(int[] arr, int index) { ... } -> Option B

4. Quick Check:

   Java method syntax = returnType name(type1 param1, type2 param2) [OK]

Hint: Remember Java method parameters need types and commas [OK]

Common Mistakes:

• Using wrong parameter order or missing commas
• Incorrect array parameter syntax
• Missing return type in method definition

3. What will be the output of the following Java code?

public class Test {
  public static void printArray(int[] arr, int index) {
    if (index == arr.length) return;
    System.out.print(arr[index] + " ");
    printArray(arr, index + 1);
  }
  public static void main(String[] args) {
    int[] nums = {1, 2, 3};
    printArray(nums, 0);
  }
}

medium

A. Compilation error

B. 3 2 1

C. 1 2 3 0

D. 1 2 3

Solution

1. Step 1: Trace the recursive calls

   printArray prints arr[index] then calls itself with index+1 until index equals arr.length (3).

2. Step 2: Output elements in order

   It prints 1, then 2, then 3, then stops without extra output.

3. Final Answer:

   1 2 3 -> Option D

4. Quick Check:

   Recursion prints array elements in order [OK]

Hint: Recursion prints then calls next index until end [OK]

Common Mistakes:

• Expecting reverse order output
• Thinking extra elements print after recursion ends
• Confusing base case condition

4. Identify the error in this recursive method that tries to sum elements of an integer array:

public int sumArray(int[] arr, int index) {
  if (index > arr.length) return 0;
  return arr[index] + sumArray(arr, index + 1);
}

medium

A. Array parameter should be List<Integer>

B. Method should return void instead of int

C. Base case condition should be index >= arr.length

D. Recursive call should use index - 1

Solution

1. Step 1: Check base case condition

   Index should stop recursion when it reaches arr.length, so condition must be index >= arr.length.

2. Step 2: Understand array bounds

   Using index > arr.length allows index == arr.length, which causes ArrayIndexOutOfBoundsException.

3. Final Answer:

   Base case condition should be index >= arr.length -> Option C

4. Quick Check:

   Base case must prevent out-of-bounds access [OK]

Hint: Base case index must not exceed array length [OK]

Common Mistakes:

• Using wrong base case condition causing runtime error
• Changing return type incorrectly
• Incorrect recursive index update

5. Given a string, write a recursive method to check if it is a palindrome (reads the same forwards and backwards). Which approach correctly describes the recursion?

hard

A. Compare first and last characters, then recurse on substring excluding them

B. Reverse the string using recursion and compare with original

C. Count characters recursively and check if count is even

D. Use recursion to sort characters and check equality

Solution

1. Step 1: Understand palindrome check logic

   Check if first and last characters match, then check the substring inside recursively.

2. Step 2: Identify correct recursive approach

   Compare first and last characters, then recurse on substring excluding them matches this logic, reducing problem size each call until base case (empty or one char string).

3. Final Answer:

   Compare first and last characters, then recurse on substring excluding them -> Option A

4. Quick Check:

   Palindrome recursion = compare ends, recurse inside substring [OK]

Hint: Check ends match, then recurse inside substring [OK]

Common Mistakes:

• Trying to reverse string recursively instead of comparing ends
• Counting characters instead of comparing
• Sorting characters which changes original order