DP vs Recursion vs Greedy Choosing the Right Tool in DSA Go - Key Differences

Recall & Review

beginner

What is recursion in problem solving?

Recursion is a method where a function calls itself to solve smaller parts of a problem until it reaches a simple case that can be solved directly.

beginner

What does DP (Dynamic Programming) do differently from simple recursion?

DP stores results of solved subproblems to avoid repeating work, making the solution faster by reusing these stored answers.

beginner

When is a greedy algorithm the right choice?

A greedy algorithm works well when choosing the best option at each step leads to the overall best solution, without needing to reconsider previous choices.

intermediate

Why might recursion be inefficient for some problems?

Recursion can be inefficient because it may solve the same subproblems multiple times, causing extra work and slower performance.

intermediate

How do you decide between DP and greedy approaches?

Use DP when subproblems overlap and you need to remember past results. Use greedy when local best choices lead to a global best solution without overlap.

Which approach stores answers to subproblems to avoid repeated work?

A Dynamic Programming

B Greedy Algorithm

C Simple Recursion

D Brute Force

Dynamic Programming saves results of subproblems to reuse them, improving efficiency.

When is a greedy algorithm most suitable?

A When local choices lead to global optimum

B When subproblems overlap

C When recursion depth is too large

D When all solutions must be checked

Greedy algorithms work best when picking the best local option leads to the best overall solution.

What is a main drawback of simple recursion without optimization?

A Uses too much memory

B Always slower than greedy

C Cannot solve problems with base cases

D May repeat solving the same subproblems

Simple recursion can solve the same subproblems multiple times, causing inefficiency.

Which technique is best when subproblems do NOT overlap?

A Dynamic Programming

B Greedy Algorithm

C Recursion with memoization

D Backtracking

Greedy algorithms are suitable when subproblems are independent and local choices lead to global optimum.

What does memoization help with in recursion?

A Simplifies code

B Makes recursion iterative

C Avoids repeated calculations

D Increases recursion depth

Memoization stores results of subproblems to avoid recalculating them.

Explain how to choose between recursion, dynamic programming, and greedy algorithms for solving a problem.

Think about problem structure and if subproblems repeat or if local choices are enough.

Describe a real-life example where a greedy algorithm works well and why dynamic programming would be unnecessary.

Think about simple step-by-step choices that lead to best result.

Practice

1. Which approach is best suited when a problem has overlapping subproblems and optimal substructure?

easy

A. Dynamic Programming

B. Greedy Algorithm

C. Simple Recursion without memoization

D. Brute Force

Solution

1. Step 1: Understand problem characteristics

   Overlapping subproblems means the same smaller problems repeat. Optimal substructure means the best solution can be built from best solutions of smaller parts.

2. Step 2: Match approach to characteristics

   Dynamic Programming stores results of subproblems to avoid repeated work, ideal for overlapping subproblems and optimal substructure.

3. Final Answer:

   Dynamic Programming -> Option A

4. Quick Check:

   Overlapping subproblems + optimal substructure = Dynamic Programming [OK]

Hint: Use DP when subproblems repeat and build optimal solutions [OK]

Common Mistakes:

• Choosing greedy when subproblems overlap
• Using simple recursion without memoization
• Confusing brute force with DP

2. Which of the following Go function signatures correctly represents a recursive function to compute factorial?

easy

A. func factorial(n int) { if n == 0 { return 1 } return n * factorial(n-1) }

B. func factorial(n int) int { if n == 0 { return 1 } return n * factorial(n-1) }

C. func factorial(n int) int { if n == 0 { return 0 } return n * factorial(n-1) }

D. func factorial(n int) int { if n == 1 { return 0 } return n * factorial(n-1) }

Solution

1. Step 1: Check function return type and base case

   Factorial returns int, so function must return int. Base case for factorial is n == 0 returning 1.

2. Step 2: Verify recursive call and return statement

   Recursive call multiplies n by factorial(n-1). func factorial(n int) int { if n == 0 { return 1 } return n * factorial(n-1) } matches correct signature and logic.

3. Final Answer:

   func factorial(n int) int { if n == 0 { return 1 } return n * factorial(n-1) } -> Option B

4. Quick Check:

   Correct return type and base case = func factorial(n int) int { if n == 0 { return 1 } return n * factorial(n-1) } [OK]

Hint: Check base case and return type carefully in recursion [OK]

Common Mistakes:

• Missing return type in function signature
• Incorrect base case value
• Returning wrong type or no return

3. What is the output of this Go code using recursion to compute Fibonacci numbers?

func fib(n int) int {
  if n <= 1 {
    return n
  }
  return fib(n-1) + fib(n-2)
}

func main() {
  fmt.Println(fib(5))
}

medium

A. 3

B. 8

C. 5

D. 13

Solution

1. Step 1: Trace fib(5) calls

   fib(5) = fib(4) + fib(3); fib(4) = fib(3) + fib(2); fib(3) = fib(2) + fib(1); fib(2) = fib(1) + fib(0)

2. Step 2: Calculate values bottom-up

   fib(0)=0, fib(1)=1; fib(2)=1; fib(3)=2; fib(4)=3; fib(5)=5

3. Final Answer:

   5 -> Option C

4. Quick Check:

   Fibonacci(5) = 5 [OK]

Hint: Remember Fibonacci sequence: 0,1,1,2,3,5,8... [OK]

Common Mistakes:

• Confusing index starting point
• Miscomputing recursive calls
• Assuming fib(1) = 0

4. Identify the error in this greedy algorithm code snippet for coin change in Go:

func coinChange(coins []int, amount int) int {
  count := 0
  for i := len(coins) - 1; i >= 0; i-- {
    for amount >= coins[i] {
      amount -= coins[i]
      count++
    }
  }
  if amount != 0 {
    return -1
  }
  return count
}

medium

A. Greedy may fail if coins are not canonical denominations

B. The inner loop should increment amount instead of decrement

C. Coins array must be sorted in ascending order

D. Return value should be amount instead of count

Solution

1. Step 1: Understand greedy coin change logic

   The code tries largest coins first, subtracting from amount until no longer possible.

2. Step 2: Identify limitation of greedy approach

   Greedy works only if coin denominations are canonical (like US coins). Otherwise, it may not find minimum coins or any solution.

3. Final Answer:

   Greedy may fail if coins are not canonical denominations -> Option A

4. Quick Check:

   Greedy correctness depends on coin set [OK]

Hint: Greedy coin change fails on non-standard coin sets [OK]

Common Mistakes:

• Assuming greedy always finds minimum coins
• Ignoring coin order importance
• Misunderstanding return values

5. You want to find the longest increasing subsequence (LIS) in an array. Which approach is best and why? A) Simple recursion tries all subsequences but is slow. B) Greedy picks local best but may miss global LIS. C) Dynamic Programming stores LIS lengths to avoid recomputation. D) Brute force enumerates all subsequences without optimization.

hard

A. Simple recursion is best for LIS

B. Greedy approach always finds LIS

C. Brute force is efficient for LIS

D. Dynamic Programming is best for LIS

Solution

1. Step 1: Analyze LIS problem nature

   LIS requires checking subsequences and their lengths. Simple recursion tries all but is exponential time.

2. Step 2: Compare approaches

   Greedy fails because local choices don't guarantee global LIS. DP stores LIS lengths for subproblems, improving efficiency.

3. Final Answer:

   Dynamic Programming is best for LIS -> Option D

4. Quick Check:

   LIS problem = DP best approach [OK]

Hint: Use DP for LIS to avoid exponential recursion [OK]

Common Mistakes:

• Choosing greedy for LIS
• Ignoring exponential time of recursion
• Thinking brute force is efficient