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

Recall & Review

beginner

What is the main idea behind the Greedy approach?

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 use Greedy over DP?

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

beginner

What is the optimal substructure property?

A problem has optimal substructure if an optimal solution can be built from optimal solutions of its subproblems.

intermediate

How can you tell if a problem needs DP instead of Greedy?

If the problem has overlapping subproblems and no greedy-choice property, DP is needed to explore all options and store results.

Which property must a problem have for Greedy to work correctly?

A Memoization

B Overlapping subproblems

C Greedy-choice property

D Backtracking

Greedy-choice property means local best choices lead to global best solution, essential for Greedy to work.

What does Dynamic Programming use to avoid repeated work?

A Memoization or tabulation

B Greedy choices

C Random guessing

D Divide and conquer without storage

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

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

A Backtracking

B Greedy

C Brute force

D Dynamic Programming

Greedy is preferred if greedy-choice property holds, even if subproblems overlap.

Which of these problems is typically solved by Dynamic Programming?

A Fibonacci sequence calculation

B Finding minimum spanning tree

C Sorting an array

D Binary search

Fibonacci has overlapping subproblems and optimal substructure, ideal for DP.

What is NOT a sign that Greedy might fail?

A Local choices don't lead to global optimum

B Overlapping subproblems

C No greedy-choice property

D Optimal substructure

Optimal substructure alone does not mean Greedy fails; it is necessary but not sufficient.

Explain how to decide between using Greedy or Dynamic Programming for a problem.

Think about whether making the best choice now guarantees the best overall solution.

Describe the key differences between Greedy and Dynamic Programming approaches.

Consider how each approach handles problem parts and solution building.

Practice

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

easy

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

B. When the problem requires checking all possible combinations

C. When the problem has overlapping subproblems but no greedy choice

D. When the problem is about sorting large datasets

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: Compare with dynamic programming conditions

   Dynamic programming is used when subproblems overlap and greedy choice property does not hold.

3. Final Answer:

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

4. Quick Check:

   Greedy choice property = Use greedy [OK]

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

Common Mistakes:

• Confusing overlapping subproblems with greedy choice
• Using greedy when problem needs full exploration
• Assuming sorting problems always need greedy

2. Which of the following is the correct syntax to declare a memoization array for dynamic programming in C?

easy

A. int memo[1000] = {0};

B. int memo[] = 0;

C. int memo(1000) = {0};

D. int memo = new int[1000];

Solution

1. Step 1: Recall C array declaration syntax

   In C, arrays are declared with fixed size and optional initialization using braces.

2. Step 2: Check each option

   int memo[1000] = {0}; correctly declares an int array of size 1000 initialized to zero. Others are invalid C syntax.

3. Final Answer:

   int memo[1000] = {0}; -> Option A

4. Quick Check:

   C arrays use [] with size [OK]

Hint: Use int arr[size] = {0} for zero-initialized arrays [OK]

Common Mistakes:

• Using parentheses instead of brackets for arrays
• Trying to assign 0 directly to array
• Using new keyword in C (it's C++ syntax)

3. What is the output of the following C code snippet that uses a greedy approach to select coins?

int coins[] = {1, 5, 10, 25};
int amount = 30;
int count = 0;
for (int i = 3; i >= 0; i--) {
    while (amount >= coins[i]) {
        amount -= coins[i];
        count++;
    }
}
printf("%d\n", count);

medium

A. 3

B. 4

C. 2

D. 5

Solution

1. Step 1: Trace the greedy coin selection

   Start with coin 25: amount=30, 30>=25, subtract 25, amount=5, count=1.

2. Step 2: Continue with smaller coins

   Next coin 10: amount=5<10, skip. Next coin 5: amount=5>=5, subtract 5, amount=0, count=2.

3. Step 3: No more coins needed

   Loop ends, total coins used = 2.

4. Final Answer:

   2 -> Option C

5. Quick Check:

   25 + 5 = 30 using 2 coins [OK]

Hint: Subtract largest coin repeatedly until amount zero [OK]

Common Mistakes:

• Counting coins incorrectly in loops
• Not updating amount after subtraction
• Confusing coin order in loop

4. The following code attempts to solve the Fibonacci sequence using a greedy approach. What is the error?

int fib(int n) {
    if (n <= 1) return n;
    int a = 0, b = 1, c = 0;
    for (int i = 2; i <= n; i++) {
        c = a + b;
        a = b;
        b = c;
    }
    return c;
}

medium

A. Loop should start from i = 1 instead of 2

B. No error, code correctly computes Fibonacci

C. Variable c is not initialized properly

D. Greedy approach is incorrect for Fibonacci calculation

Solution

1. Step 1: Understand Fibonacci calculation

   Fibonacci requires summing previous two numbers, which is a classic dynamic programming problem.

2. Step 2: Identify greedy approach misuse

   The code uses iteration correctly but calling it greedy is wrong because Fibonacci does not have greedy choice property.

3. Final Answer:

   Greedy approach is incorrect for Fibonacci calculation -> Option D

4. Quick Check:

   Fibonacci needs DP, not greedy [OK]

Hint: Fibonacci needs DP, greedy won't work [OK]

Common Mistakes:

• Thinking iterative is greedy
• Ignoring problem properties
• Confusing initialization with error

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

hard

A. Greedy, because always picking the largest coin works here

B. Dynamic Programming, because greedy fails for some amounts

C. Brute force, because both greedy and DP are too complex

D. Sorting coins and picking smallest first

Solution

1. Step 1: Test greedy approach on example

   For amount 6, greedy picks 4 + 1 + 1 = 3 coins, but optimal is 3 + 3 = 2 coins.

2. Step 2: Recognize overlapping subproblems

   Dynamic programming stores solutions for smaller amounts to build up answer correctly.

3. Step 3: Conclude best approach

   Greedy fails due to lack of greedy choice property; DP handles all cases optimally.

4. Final Answer:

   Dynamic Programming, because greedy fails for some amounts -> Option B

5. Quick Check:

   Greedy fails, DP works [OK]

Hint: Test greedy on small cases; if fails, use DP [OK]

Common Mistakes:

• Assuming greedy always works for coin change
• Ignoring counterexamples
• Choosing brute force unnecessarily