Greedy vs DP How to Know Which to Apply in DSA Go - 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 than 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 choose a greedy algorithm over DP?

Choose greedy when the problem has the greedy-choice property and optimal substructure, meaning local best choices lead to a 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 test if a greedy approach works for a problem?

Try to prove that making local optimal choices leads to a global optimum, or test with examples to see if greedy fails on any case.

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

A Greedy-choice property

B No overlapping subproblems

C Exponential time complexity

D Randomized input

The greedy-choice property means local optimal choices lead to a global optimum, which is essential for greedy algorithms.

What does Dynamic Programming store to avoid repeated work?

A Random guesses

B Intermediate results of subproblems

C All possible solutions

D Only the final answer

DP stores intermediate results (memoization or tabulation) to avoid solving the same subproblems multiple times.

If a problem has overlapping subproblems but no greedy-choice property, which approach is better?

A Divide and Conquer

B Greedy

C Brute Force

D Dynamic Programming

DP handles overlapping subproblems well, especially when greedy choices don't guarantee optimal solutions.

Which of these is a sign that greedy might fail?

A Problem is very large

B Problem has optimal substructure

C Local choices do not lead to global optimum

D Subproblems do not overlap

If local best choices don't lead to the global best, greedy algorithms can fail.

What is a common example of a problem solved by greedy algorithms?

A Shortest path in a graph with non-negative edges (Dijkstra's algorithm)

B Coin change with unlimited coins

C Fibonacci sequence

D Matrix chain multiplication

Dijkstra's algorithm uses a greedy approach to find shortest paths in graphs with non-negative edges.

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

Think about problem properties and how solutions build up.

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

Focus on how each approach 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 requires exploring all possible solutions

B. When the problem is unsolvable by any algorithm

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: Check 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 Go code snippet correctly declares a memoization map for dynamic programming?

easy

A. memo := new(map[int]int)

B. memo := make(map[int]int)

C. memo := map[]int{}

D. memo := []int{}

Solution

1. Step 1: Understand Go map declaration

   In Go, maps are declared with make(map[keyType]valueType) to initialize properly.

2. Step 2: Check each option

   memo := make(map[int]int) uses make with correct syntax. memo := []int{} is a slice, not a map. memo := map[]int{} has invalid syntax. memo := new(map[int]int) uses new which returns pointer, not initialized map.

3. Final Answer:

   memo := make(map[int]int) -> Option B

4. Quick Check:

   Use make(map[key]value) for maps [OK]

Hint: Use make(map[key]value) to create maps in Go [OK]

Common Mistakes:

• Using new(map[int]int) which returns nil map pointer
• Confusing slices with maps
• Incorrect map syntax like map[]int{}

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

func max(a, b int) int {
    if a > b {
        return a
    }
    return b
}

func main() {
    weights := []int{1, 3, 4, 5}
    values := []int{1, 4, 5, 7}
    capacity := 7
    dp := make([]int, capacity+1)

    for i := 0; i < len(weights); i++ {
        for w := capacity; w >= weights[i]; w-- {
            dp[w] = max(dp[w], dp[w-weights[i]] + values[i])
        }
    }
    fmt.Println(dp[capacity])
}

medium

A. 12

B. 10

C. 11

D. 9

Solution

1. Step 1: Understand the code - 0/1 Knapsack DP

   The code uses bottom-up DP to find max value for capacity 7 with given weights and values.

2. Step 2: Trace DP array updates

   Items: (1,1), (3,4), (4,5), (5,7). DP updates from capacity down to weight. Final dp[7] = max value achievable is 11.

3. Final Answer:

   11 -> Option C

4. Quick Check:

   DP knapsack max value = 11 [OK]

Hint: Trace DP from largest capacity down to weight [OK]

Common Mistakes:

• Iterating w from low to high causing wrong results
• Confusing weights and values arrays
• Forgetting to update dp[w] with max

4. Identify the bug in this greedy approach for coin change problem in Go:

func coinChange(coins []int, amount int) int {
    count := 0
    for _, coin := range coins {
        count += amount / coin
        amount %= coin
    }
    if amount != 0 {
        return -1
    }
    return count
}

func main() {
    coins := []int{1, 3, 4}
    amount := 6
    fmt.Println(coinChange(coins, amount))
}

medium

A. Coins slice is not sorted descending

B. Using integer division causes wrong count

C. No base case for amount zero

D. Returns -1 even if solution exists

Solution

1. Step 1: Analyze greedy coin change logic

   The greedy approach works only if coins are sorted descending to pick largest coin first.

2. Step 2: Check coins order

   Coins are {1,3,4} ascending, so greedy picks 1 first, leading to wrong minimal count.

3. Final Answer:

   Coins slice is not sorted descending -> Option A

4. Quick Check:

   Sort coins descending for greedy coin change [OK]

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

Common Mistakes:

• Not sorting coins descending
• Assuming greedy always works for coin change
• Ignoring leftover amount check

5. You want to find the minimum number of coins to make amount 11 using coins {1, 5, 6}. Which approach is best and why?

hard

A. Dynamic Programming, because greedy fails due to no greedy choice property

B. Greedy, because coins are sorted ascending

C. Greedy, because picking largest coin first always works

D. Neither, because problem is unsolvable

Solution

1. Step 1: Check greedy choice property for coin set

   For coins {1,5,6}, greedy picks 6 then 5, total 2 coins for 11, which is minimal. However, greedy does not always work for all amounts with these coins.

2. Step 2: Consider counterexamples and DP suitability

   In some cases greedy fails (e.g., amount 7 with coins {1,5,6} greedy picks 6+1=2 coins but better is 1+1+5=3 coins, so greedy works here but not always. DP always finds minimal coins by exploring all subproblems.

3. Final Answer:

   Dynamic Programming, because greedy fails due to no greedy choice property -> Option A

4. Quick Check:

   Use DP if greedy choice property missing [OK]

Hint: Use DP if greedy choice property is missing [OK]

Common Mistakes:

• Assuming greedy always works for coin change
• Ignoring overlapping subproblems in coin change
• Choosing greedy because coins are sorted ascending