Greedy vs DP How to Know Which to Apply in DSA Python - Interactive Comparison Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if a problem has optimal substructure property.

DSA Python

def has_optimal_substructure(problem):
    # If solution can be built from solutions of subproblems
    return problem.can_build_solution_from_subproblems() and problem.has_[1]()

Drag options to blanks, or click blank then click option'

Aoverlapping_subproblems

Boptimal_substructure

Cgreedy_choice_property

Ddivide_and_conquer

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing greedy choice property with optimal substructure.

The optimal substructure property means the optimal solution can be constructed from optimal solutions of its subproblems.

2fill in blank

medium

Complete the code to check if a problem has the greedy choice property.

DSA Python

def has_greedy_choice_property(problem):
    # If local optimal choice leads to global optimum
    return problem.can_make_local_choice() and problem.has_[1]()

Drag options to blanks, or click blank then click option'

Aoptimal_substructure

Boverlapping_subproblems

Cgreedy_choice_property

Dmemoization

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up greedy choice property with overlapping subproblems.

The greedy choice property means making the best local choice at each step leads to a global optimum.

3fill in blank

hard

Fix the error in the function that decides which approach to apply.

DSA Python

def choose_approach(problem):
    if problem.has_optimal_substructure() and problem.has_[1]():
        return 'Dynamic Programming'
    elif problem.has_greedy_choice_property():
        return 'Greedy'
    else:
        return 'Brute Force'

Drag options to blanks, or click blank then click option'

Aoverlapping_subproblems

Bgreedy_choice_property

Cmemoization

Doptimal_substructure

Attempts:

3 left

💡 Hint

Common Mistakes

Using greedy_choice_property instead of overlapping_subproblems for DP.

Dynamic programming requires both optimal substructure and overlapping subproblems.

4fill in blank

hard

Fill both blanks to complete the function that explains why greedy works.

DSA Python

def explain_greedy(problem):
    if problem.has_[1]() and problem.has_[2]():
        return 'Greedy approach is suitable'
    else:
        return 'Greedy approach may fail'

Drag options to blanks, or click blank then click option'

Agreedy_choice_property

Boptimal_substructure

Coverlapping_subproblems

Dmemoization

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing overlapping subproblems as needed for greedy.

Greedy algorithms require greedy choice property and optimal substructure to guarantee correct solutions.

5fill in blank

hard

Fill all three blanks to complete the function that decides approach based on problem properties.

DSA Python

def decide_approach(problem):
    if problem.has_[1]() and problem.has_[2]():
        return 'Dynamic Programming'
    elif problem.has_[3]():
        return 'Greedy'
    else:
        return 'Brute Force'

Drag options to blanks, or click blank then click option'

Aoptimal_substructure

Boverlapping_subproblems

Cgreedy_choice_property

Dmemoization

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing greedy_choice_property with overlapping_subproblems for DP.

Dynamic programming needs optimal substructure and overlapping subproblems; greedy needs greedy choice property.

Practice

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

easy

A. When the problem has optimal substructure and no overlapping subproblems

B. When the problem has overlapping subproblems and requires memoization

C. When the problem requires checking all possible combinations

D. When the problem involves sorting large datasets

Solution

1. Step 1: Understand greedy algorithm conditions

   Greedy algorithms work when choosing the best option at each step leads to a global optimum, which means the problem has optimal substructure and no overlapping subproblems.

2. Step 2: Compare with dynamic programming conditions

   Dynamic programming is used when problems have overlapping subproblems and require storing intermediate results (memoization) to avoid repeated work.

3. Final Answer:

   When the problem has optimal substructure and no overlapping subproblems -> Option A

4. Quick Check:

   Greedy = optimal substructure + no overlap [OK]

Hint: Use greedy if no overlapping subproblems exist [OK]

Common Mistakes:

• Confusing overlapping subproblems as a greedy condition
• Thinking greedy always finds the best solution
• Using dynamic programming when greedy suffices

2. Which of the following Python code snippets correctly initializes a memoization dictionary for dynamic programming?

easy

A. memo = []

B. memo = {}

C. memo = set()

D. memo = 0

Solution

1. Step 1: Identify the correct data structure for memoization

   Memoization requires storing key-value pairs of subproblem results, so a dictionary (hash map) is appropriate.

2. Step 2: Check the options

   memo = {} initializes an empty dictionary, which is correct. Lists or sets do not store key-value pairs, and an integer cannot store multiple results.

3. Final Answer:

   memo = {} -> Option B

4. Quick Check:

   Memoization uses dictionary = {} [OK]

Hint: Use {} to store subproblem results in DP [OK]

Common Mistakes:

• Using list or set instead of dictionary for memo
• Initializing memo as a number
• Confusing data structures for memoization

3. What is the output of the following Python code that uses a greedy approach to select intervals?

intervals = [(1, 3), (2, 5), (4, 7)]
intervals.sort(key=lambda x: x[1])
selected = []
end = 0
for start, finish in intervals:
    if start >= end:
        selected.append((start, finish))
        end = finish
print(selected)

medium

A. [(1, 3), (2, 5)]

B. [(2, 5), (4, 7)]

C. [(1, 3), (4, 7)]

D. [(1, 3), (2, 5), (4, 7)]

Solution

1. Step 1: Sort intervals by finish time

   Sorted intervals: [(1, 3), (2, 5), (4, 7)]

2. Step 2: Select intervals greedily

   Start with end=0. (1,3) start=1 >=0, select it, end=3. Next (2,5) start=2 <3 skip. Next (4,7) start=4 >=3 select it.

3. Final Answer:

   [(1, 3), (4, 7)] -> Option C

4. Quick Check:

   Greedy interval selection = [(1, 3), (4, 7)] [OK]

Hint: Sort by finish time, pick earliest finishing intervals [OK]

Common Mistakes:

• Not sorting intervals by finish time
• Selecting overlapping intervals
• Appending intervals without condition

4. The following code attempts to solve the Fibonacci sequence using dynamic programming but has a bug. What is the error?

def fib(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 1:
        return n
    memo[n] = fib(n-1) + fib(n-2)
    return memo[n]

print(fib(5))

medium

A. Mutable default argument causes incorrect memoization across calls

B. Missing base case for n=0

C. Incorrect recursive calls fib(n-1) and fib(n-2)

D. Memo dictionary is not updated

Solution

1. Step 1: Identify the use of mutable default argument

   The function uses memo={} as a default argument, which is mutable and shared across calls, causing unexpected behavior if fib is called multiple times.

2. Step 2: Explain why this is a bug

   This can cause memo to retain values from previous calls, leading to incorrect results or memory issues.

3. Final Answer:

   Mutable default argument causes incorrect memoization across calls -> Option A

4. Quick Check:

   Mutable default dict in function = bug [OK]

Hint: Avoid mutable defaults like dict in function args [OK]

Common Mistakes:

• Ignoring mutable default argument issue
• Thinking base cases are missing
• Assuming memo is not updated

5. You want to find the minimum number of coins to make a target amount using coin denominations [1, 3, 4]. Which approach is best and why? A greedy approach picks the largest coin first. Dynamic programming tries all combinations. Which is correct?

hard

A. Neither approach works for coin change problems

B. Greedy always works because picking largest coin reduces count

C. Greedy and dynamic programming give the same result here

D. Dynamic programming is needed because greedy fails for some amounts

Solution

1. Step 1: Understand greedy approach limitation

   Greedy picks largest coin first, but for amount 6, greedy picks 4+1+1=3 coins, but optimal is 3+3=2 coins.

2. Step 2: Recognize dynamic programming advantage

   Dynamic programming tries all combinations and finds minimum coins, handling cases where greedy fails.

3. Final Answer:

   Dynamic programming is needed because greedy fails for some amounts -> Option D

4. Quick Check:

   Coin change needs DP, greedy can fail [OK]

Hint: Use DP for coin change; greedy can fail [OK]

Common Mistakes:

• Assuming greedy always finds minimum coins
• Ignoring counterexamples where greedy fails
• Thinking coin change is always greedy