Memoization to Optimize Recursion in DSA Java - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Fibonacci with Memoization

What is the output of the following Java code that calculates Fibonacci numbers using memoization?

DSA Java

import java.util.HashMap;
public class FibMemo {
    private static HashMap<Integer, Integer> memo = new HashMap<>();
    public static int fib(int n) {
        if (n <= 1) return n;
        if (memo.containsKey(n)) return memo.get(n);
        int result = fib(n - 1) + fib(n - 2);
        memo.put(n, result);
        return result;
    }
    public static void main(String[] args) {
        System.out.println(fib(6));
    }
}

A 13

B 34

C 8

D 21

💡 Hint

Remember that Fibonacci sequence starts with 0, 1, 1, 2, 3, 5, 8, 13...

fib(6) = fib(5) + fib(4) = 5 + 3 = 8.

❓ Predict Output

intermediate

Memoization Cache State After Calls

After running fib(5) using the memoized Fibonacci function below, what is the content of the memo cache?

DSA Java

import java.util.HashMap;
public class FibMemo {
    private static HashMap<Integer, Integer> memo = new HashMap<>();
    public static int fib(int n) {
        if (n <= 1) return n;
        if (memo.containsKey(n)) return memo.get(n);
        int result = fib(n - 1) + fib(n - 2);
        memo.put(n, result);
        return result;
    }
    public static void main(String[] args) {
        fib(5);
        System.out.println(memo);
    }
}

A {2=1, 3=2, 4=3, 5=5}

B {1=1, 2=1, 3=2, 4=3, 5=5}

C {0=0, 1=1, 2=1, 3=2, 4=3, 5=5}

D {3=2, 4=3, 5=5}

💡 Hint

Base cases are not stored in memo, only computed results for n > 1 are cached.

The memo cache stores results for n > 1 only. fib(0) and fib(1) return directly without caching.

🔧 Debug

advanced

Identify the Error in Memoized Factorial

What error will the following Java code produce when calling factorial(5)?

DSA Java

import java.util.HashMap;
public class FactorialMemo {
    private static HashMap<Integer, Integer> memo = new HashMap<>();
    public static int factorial(int n) {
        if (n == 0) return 1;
        if (memo.containsKey(n)) return memo.get(n);
        int result = n * factorial(n - 1);
        memo.put(n, result);
        return result;
    }
    public static void main(String[] args) {
        System.out.println(factorial(5));
    }
}

A Prints 120

B StackOverflowError

C NullPointerException

D ArithmeticException

💡 Hint

Check base case and recursive calls carefully.

The code correctly implements memoized factorial and prints 120 for factorial(5).

❓ Predict Output

advanced

Output of Memoized Climbing Stairs Problem

What is the output of the following Java code that uses memoization to count ways to climb stairs?

DSA Java

import java.util.HashMap;
public class ClimbStairs {
    private static HashMap<Integer, Integer> memo = new HashMap<>();
    public static int climb(int n) {
        if (n <= 1) return 1;
        if (memo.containsKey(n)) return memo.get(n);
        int ways = climb(n - 1) + climb(n - 2);
        memo.put(n, ways);
        return ways;
    }
    public static void main(String[] args) {
        System.out.println(climb(4));
    }
}

A 7

B 5

C 8

D 3

💡 Hint

Number of ways to climb 4 stairs with 1 or 2 steps at a time is Fibonacci-like.

climb(4) = climb(3) + climb(2) = 3 + 2 = 5 ways.

🧠 Conceptual

expert

Memoization Impact on Time Complexity

Which statement best describes how memoization affects the time complexity of a naive recursive Fibonacci function?

A It increases time complexity because of extra memory usage for caching.

B It changes time complexity from linear to logarithmic by pruning recursion.

C It does not affect time complexity but reduces space complexity.

D It reduces time complexity from exponential to linear by storing intermediate results.

💡 Hint

Think about how many times each Fibonacci number is computed with and without memoization.

Memoization stores results to avoid repeated calculations, reducing exponential calls to linear.

Practice

1. What is the main purpose of using memoization in recursive functions?

easy

A. To store results of expensive function calls and reuse them

B. To make the code shorter and simpler

C. To avoid using loops in recursion

D. To increase the number of recursive calls

Solution

1. Step 1: Understand recursion inefficiency

   Recursive functions often repeat the same calculations multiple times, which wastes time.

2. Step 2: Role of memoization

   Memoization saves the results of these repeated calculations so they can be reused instead of recalculated.

3. Final Answer:

   To store results of expensive function calls and reuse them -> Option A

4. Quick Check:

   Memoization = Store and reuse results [OK]

Hint: Memoization saves repeated results to speed recursion [OK]

Common Mistakes:

• Thinking memoization makes code shorter
• Confusing memoization with iteration
• Believing memoization increases recursion calls

2. Which of the following Java code snippets correctly declares a memoization cache for storing integer results by input integer keys?

easy

A. Map memo = new HashMap<>();

B. List<Integer> memo = new ArrayList<>();

C. int[] memo = new int();

D. HashSet<Integer> memo = new HashSet<>();

Solution

1. Step 1: Identify suitable data structure for key-value pairs

   Memoization requires storing results by input keys, so a Map is ideal.

2. Step 2: Check Java syntax correctness

   Map memo = new HashMap<>(); uses Map with HashMap, which is correct syntax for memoization cache.

3. Final Answer:

   Map memo = new HashMap<>(); -> Option A

4. Quick Check:

   Memo cache = Map for key-value pairs [OK]

Hint: Use Map for key-value memo cache in Java [OK]

Common Mistakes:

• Using List instead of Map for memoization
• Incorrect array declaration syntax
• Using Set which stores only keys, no values

3. What will be the output of the following Java code using memoization for Fibonacci numbers?

import java.util.*;
public class FibMemo {
  static Map memo = new HashMap<>();
  public static int fib(int n) {
    if (n <= 1) return n;
    if (memo.containsKey(n)) return memo.get(n);
    int result = fib(n-1) + fib(n-2);
    memo.put(n, result);
    return result;
  }
  public static void main(String[] args) {
    System.out.println(fib(5));
  }
}

medium

A. Error at runtime

B. 8

C. 5

D. 13

Solution

1. Step 1: Understand Fibonacci sequence calculation

   fib(5) = fib(4) + fib(3), and so on, with base cases fib(0)=0, fib(1)=1.

2. Step 2: Calculate fib(5) with memoization

   fib(2)=1, fib(3)=2, fib(4)=3, fib(5)=5. Memoization avoids repeated calls but result is same.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   fib(5) = 5 [OK]

Hint: Recall Fibonacci(5) = 5, memoization doesn't change result [OK]

Common Mistakes:

• Confusing Fibonacci values for wrong n
• Assuming memoization changes output
• Thinking code causes runtime error

4. Identify the error in this Java memoized factorial function:

import java.util.*;
public class FactorialMemo {
  static Map memo = new HashMap<>();
  public static int fact(int n) {
    if (n == 0) return 1;
    if (memo.containsKey(n)) return memo.get(n);
    int result = n * fact(n - 1);
    memo.put(n, result);
    return result;
  }
  public static void main(String[] args) {
    System.out.println(fact(-1));
  }
}

medium

A. Memo map is not initialized properly

B. fact method should return long instead of int

C. Incorrect multiplication order in recursion

D. No base case for negative input causes infinite recursion

Solution

1. Step 1: Analyze base cases and input handling

   Base case handles n == 0 only, but negative n causes no stop condition.

2. Step 2: Effect of negative input

   Calling fact(-1) leads to infinite recursion because n never reaches 0 or memoized value.

3. Final Answer:

   No base case for negative input causes infinite recursion -> Option D

4. Quick Check:

   Missing negative base case = infinite recursion [OK]

Hint: Check base cases cover all input ranges [OK]

Common Mistakes:

• Ignoring negative input handling
• Assuming memo initialization error
• Thinking multiplication order causes error

5. You want to optimize a recursive function that calculates the number of ways to climb n stairs taking 1 or 2 steps at a time. Which memoization approach below correctly implements this in Java?

hard

A. Use a List<Integer> to store results; always calculate recursively without checking cache.

B. Use a Map to store results; check cache before recursive calls; store results after calculation.

C. Use an int array without initializing values; store results only after all recursion ends.

D. Use a Set<Integer> to store visited stairs; return size of set as result.

Solution

1. Step 1: Understand problem and memoization needs

   We must store number of ways for each stair number to avoid repeated calculations.

2. Step 2: Evaluate memoization approaches

   Use a Map to store results; check cache before recursive calls; store results after calculation. uses Map to store and check results before recursion, which is correct memoization practice.

3. Final Answer:

   Use a Map to store results; check cache before recursive calls; store results after calculation. -> Option B

4. Quick Check:

   Memo = Map with cache check and store [OK]

Hint: Check cache before recursion, store after calculation [OK]

Common Mistakes:

• Not checking cache before recursive calls
• Using List or Set incorrectly for memoization
• Storing results too late or not at all