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

Recall & Review

beginner

What is the main difference between recursion and dynamic programming?

Recursion solves problems by breaking them into smaller subproblems and calling itself, but may repeat work. Dynamic programming improves recursion by storing results of subproblems to avoid repeated work.

beginner

When is a greedy algorithm the right choice?

A greedy algorithm works well when local choices lead to a global optimum, meaning making the best choice at each step guarantees the best overall solution.

intermediate

What problem characteristic suggests using dynamic programming?

Dynamic programming is suitable when a problem has overlapping subproblems and optimal substructure, meaning solutions to subproblems can be reused and combined for the final answer.

beginner

How does recursion handle problem solving?

Recursion solves a problem by calling itself with smaller inputs until reaching a base case, then combines results to solve the original problem.

intermediate

Why might greedy algorithms fail on some problems?

Greedy algorithms can fail if local optimal choices do not lead to a global optimum, causing wrong or suboptimal solutions.

Which approach stores results of subproblems to avoid repeated work?

A Greedy Algorithm

B Recursion without memoization

C Dynamic Programming

D Brute Force

Dynamic Programming saves results of subproblems to reuse them, avoiding repeated calculations.

When should you choose a greedy algorithm?

A When problem has no optimal substructure

B When local choices guarantee global optimum

C When recursion is too slow

D When subproblems overlap

Greedy algorithms work best when making the best local choice leads to the best overall solution.

What is a key sign that recursion alone might be inefficient?

A Overlapping subproblems causing repeated work

B No base case in recursion

C Problem is too small

D Greedy choice is obvious

If recursion solves the same subproblems multiple times, it becomes inefficient.

Which method breaks problems into smaller parts and solves each independently?

A Recursion

B Greedy Algorithm

C Dynamic Programming

D Sorting

Recursion solves problems by calling itself on smaller inputs until reaching a base case.

Why might dynamic programming be preferred over recursion?

A It only works for sorting problems

B It always runs faster than greedy

C It never uses extra memory

D It avoids repeated calculations by storing results

Dynamic programming stores results of subproblems to avoid repeating work, improving efficiency.

Explain how to decide between using recursion, dynamic programming, or a greedy algorithm for a problem.

Think about problem structure and if repeated work happens.

Describe the main advantages and disadvantages of greedy algorithms compared to dynamic programming.

Consider speed, correctness, and problem requirements.

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 problems.

2. Step 2: Match approach to characteristics

   Dynamic Programming stores results of subproblems to avoid recomputation, 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 memo causing slow code
• Confusing optimal substructure with greedy choice property

2. Which of the following is the correct syntax to implement memoization in C++ recursion?

easy

A. Use a while loop instead of recursion

B. Use a for loop inside the recursive function

C. Call the recursive function twice without storing results

D. Use a global array or vector to store results and check before recursion

Solution

1. Step 1: Understand memoization concept

   Memoization stores results of recursive calls to avoid repeated work.

2. Step 2: Identify correct syntax usage

   Using a global or passed array/vector to save results and checking it before recursion is the correct way.

3. Final Answer:

   Use a global array or vector to store results and check before recursion -> Option D

4. Quick Check:

   Memoization = store results before recursion [OK]

Hint: Memoize by storing results in array before recursive calls [OK]

Common Mistakes:

• Not storing results causing repeated calculations
• Using loops inside recursion incorrectly
• Calling recursion multiple times without memo

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

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

int main() {
  std::cout << fib(4);
  return 0;
}

medium

A. 4

B. 5

C. 3

D. 7

Solution

1. Step 1: Trace fib(4) calls

   fib(4) = fib(3) + fib(2) - fib(3) = fib(2) + fib(1) = (fib(1)+fib(0)) + 1 = (1+0)+1=2 - fib(2) = fib(1) + fib(0) = 1 + 0 = 1 So fib(4) = 2 + 1 = 3

2. Step 2: Confirm output

   The program prints 3 as the result of fib(4).

3. Final Answer:

   3 -> Option C

4. Quick Check:

   fib(4) = 3 [OK]

Hint: Trace small inputs stepwise to find Fibonacci output [OK]

Common Mistakes:

• Confusing fib(4) with fib(5)
• Adding wrong Fibonacci numbers
• Assuming fib(4) equals 4

4. Identify the error in the following code snippet implementing a greedy approach for coin change:

int coinChange(int amount, vector<int>& coins) {
  int count = 0;
  for (int i = 0; i < coins.size(); i++) {
    while (amount >= coins[i]) {
      amount -= coins[i];
      count++;
    }
  }
  return count;
}

medium

A. Coins vector is not sorted in descending order

B. Using while loop inside for loop is incorrect

C. Function should return amount, not count

D. No error, code is correct

Solution

1. Step 1: Analyze greedy coin change logic

   Greedy coin change requires coins sorted descending to pick largest coin first.

2. Step 2: Identify error in code

   The code loops coins in given order; if coins are not sorted descending, greedy fails to minimize count.

3. Final Answer:

   Coins vector is not sorted in descending order -> Option A

4. Quick Check:

   Greedy coin change needs descending sorted coins [OK]

Hint: Sort coins descending before greedy coin change [OK]

Common Mistakes:

• Not sorting coins descending
• Returning wrong variable
• Thinking while loop inside for is wrong

5. You want to find the minimum number of coins to make a given amount using coins of denominations [1, 3, 4]. Which approach is best and why?

hard

A. Greedy approach because picking largest coin first always works

B. Dynamic Programming to store minimum coins needed for sub-amounts

C. Simple recursion without memoization to try all combinations

D. Brute force by checking all subsets of coins

Solution

1. Step 1: Understand problem requirements

   We want minimum coins for amount using coins [1,3,4]. Greedy fails here because picking largest coin first may not give minimum coins.

2. Step 2: Choose best approach

   Dynamic Programming stores minimum coins for all smaller amounts, building up to the target efficiently and correctly.

3. Final Answer:

   Dynamic Programming to store minimum coins needed for sub-amounts -> Option B

4. Quick Check:

   Minimum coins with tricky denominations = DP [OK]

Hint: Use DP when greedy fails to find minimum coins [OK]

Common Mistakes:

• Assuming greedy always works for coin change
• Using recursion without memo causing slow code
• Trying brute force which is inefficient