Greedy vs DP How to Know Which to Apply in DSA Java - Key Differences

Recall & Review

beginner

What is the main idea behind the greedy approach?

The greedy approach makes the best choice at each step, hoping to find the overall best solution without reconsidering previous choices.

beginner

What does Dynamic Programming (DP) do differently from greedy?

DP solves problems by breaking them into smaller overlapping subproblems, solving each once, and storing results to avoid repeated work.

intermediate

When should you consider using a greedy algorithm?

Use greedy when the problem has the 'greedy choice property' and 'optimal substructure', meaning local best choices lead to a global best solution.

intermediate

What is 'optimal substructure' in the context of DP and greedy?

Optimal substructure means the optimal solution to a problem contains optimal solutions to its subproblems.

intermediate

How can you tell if a problem requires DP instead of greedy?

If the problem has overlapping subproblems and no greedy choice property, meaning local best choices don't guarantee global best, use DP.

Which property must a problem have for a greedy algorithm to work correctly?

A Overlapping subproblems

B Backtracking

C Memoization

D Greedy choice property

The greedy choice property ensures that making the best local choice leads to the global optimum.

What does Dynamic Programming use to avoid repeated work?

A Memoization or tabulation

B Greedy choices

C Random guessing

D Divide and conquer without overlap

DP stores results of subproblems using memoization or tabulation to avoid recalculating them.

If a problem has overlapping subproblems but also a greedy choice property, which approach is better?

A Backtracking

B Dynamic Programming

C Greedy

D Brute force

If greedy choice property holds, greedy is simpler and efficient even if subproblems overlap.

Which of these problems is typically solved by Dynamic Programming?

A Coin change with unlimited coins

B Finding minimum spanning tree

C Sorting an array

D Finding maximum in an array

Coin change with unlimited coins has overlapping subproblems and no greedy choice property, so DP is used.

What is a sign that greedy might fail for a problem?

A Problem size is small

B Local best choices do not lead to global best

C Problem has optimal substructure

D Problem has no subproblems

If local best choices don't guarantee global best, greedy approach can fail.

Explain how to decide between using a greedy algorithm and dynamic programming for a problem.

Think about problem properties and how solutions build up.

Describe the key differences in approach between greedy algorithms and dynamic programming.

Focus on how each method builds the solution.

Practice

1. Which of the following best describes when to use a greedy algorithm instead of dynamic programming?

easy

A. When the problem needs to store all intermediate results

B. When the problem requires checking all possible combinations

C. When the problem has overlapping subproblems but no optimal substructure

D. When the problem has the greedy choice property and optimal substructure

Solution

1. Step 1: Understand greedy choice property

   A greedy algorithm works when choosing the best option at each step leads to a global optimum.

2. Step 2: Recognize optimal substructure

   Optimal substructure means the optimal solution can be built from optimal solutions of subproblems.

3. Final Answer:

   When the problem has the greedy choice property and optimal substructure -> Option D

4. Quick Check:

   Greedy = greedy choice + optimal substructure [OK]

Hint: Use greedy if local best leads to global best [OK]

Common Mistakes:

• Confusing overlapping subproblems with greedy applicability
• Using greedy when problem needs full exploration
• Ignoring optimal substructure requirement

2. Which Java syntax correctly declares a 2D array for dynamic programming table initialization?

easy

A. int[][] dp = new int[5];

B. int dp[][] = new int(5,5);

C. int[][] dp = new int[5][5];

D. int dp[5][5] = new int[][];

Solution

1. Step 1: Recall Java 2D array syntax

   Java uses new int[rows][columns] to declare 2D arrays.

2. Step 2: Check each option

   int[][] dp = new int[5][5]; uses correct syntax. Options A, B, C have syntax errors or incomplete declarations.

3. Final Answer:

   int[][] dp = new int[5][5]; -> Option C

4. Quick Check:

   Correct 2D array declaration = int[][] dp = new int[5][5]; [OK]

Hint: Use new int[rows][cols] for 2D arrays in Java [OK]

Common Mistakes:

• Using parentheses instead of brackets
• Missing size in second dimension
• Incorrect array initialization syntax

3. What is the output of the following Java code snippet?

int[] coins = {1, 2, 5};
int amount = 11;
int count = 0;
for (int i = coins.length - 1; i >= 0; i--) {
    count += amount / coins[i];
    amount %= coins[i];
}
System.out.println(count);

medium

A. 3

B. 5

C. 4

D. 6

Solution

1. Step 1: Trace the loop from largest coin to smallest

   Start with amount=11, coins = [1,2,5]. i=2 (coin=5): count += 11/5=2, amount=11%5=1.

2. Step 2: Continue with next coins

   i=1 (coin=2): count += 1/2=0, amount=1%2=1; i=0 (coin=1): count += 1/1=1, amount=1%1=0.

3. Step 3: Calculate total count

   Total count = 2 + 0 + 1 = 3.

4. Final Answer:

   3 -> Option A

5. Quick Check:

   Greedy coin count = 3 [OK]

Hint: Divide and mod with largest coin first [OK]

Common Mistakes:

• Adding counts incorrectly
• Mixing up division and modulo
• Ignoring order of coins

4. The following code attempts to solve the coin change problem using greedy approach. What is the bug?

int[] coins = {1, 3, 4};
int amount = 6;
int count = 0;
for (int i = coins.length - 1; i >= 0; i--) {
    count += amount / coins[i];
    amount %= coins[i];
}
System.out.println(count);

medium

A. Division by zero error

B. Greedy fails because coin set lacks greedy choice property

C. Array index out of bounds error

D. Incorrect initialization of count variable

Solution

1. Step 1: Understand greedy choice property failure

   Coins {1,3,4} do not guarantee greedy choice property for amount 6.

2. Step 2: Trace greedy approach output

   Greedy picks 4 once (count=1), remainder 2; then picks two 1s (count=3). But optimal is two 3s (count=2).

3. Final Answer:

   Greedy fails because coin set lacks greedy choice property -> Option B

4. Quick Check:

   Greedy fails if no greedy choice property [OK]

Hint: Check if greedy choice property holds before using greedy [OK]

Common Mistakes:

• Assuming greedy always works for coin change
• Ignoring optimal substructure requirement
• Confusing runtime errors with logic errors

5. Given a set of tasks with start and end times, which approach is best to find the maximum number of non-overlapping tasks?

class Task {
    int start, end;
    Task(int s, int e) { start = s; end = e; }
}

Choose the correct approach and why.

hard

A. Use greedy by sorting tasks by earliest finish time to select tasks

B. Use dynamic programming to check all subsets of tasks

C. Use greedy by sorting tasks by longest duration first

D. Use dynamic programming to store maximum tasks ending at each time

Solution

1. Step 1: Identify problem type

   This is the activity selection problem, classic greedy example.

2. Step 2: Choose greedy approach

   Sorting by earliest finish time ensures maximum tasks without overlap.

3. Step 3: Compare options

   Use greedy by sorting tasks by earliest finish time to select tasks matches known greedy solution; DP is possible but less efficient here.

4. Final Answer:

   Use greedy by sorting tasks by earliest finish time to select tasks -> Option A

5. Quick Check:

   Activity selection = greedy by finish time [OK]

Hint: Sort tasks by finish time for max non-overlapping tasks [OK]

Common Mistakes:

• Sorting by start time or duration instead of finish time
• Using DP unnecessarily increasing complexity
• Ignoring greedy choice property in scheduling