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Greedy limits

Greedy is not always optimal.

Greedy limits

Greedy is not always optimal. Example: [1, 3, 4] for amount 6. Greedy gives [4, 1, 1] (3 coins); the optimum is [3, 3] (2 coins).

In such cases dynamic programming is better; greedy makes a wrong choice.

So verify the problem structure before applying greedy; otherwise a wrong result arises.

Counter-example

An input showing an algorithm is wrong is a counter-example. It is used to test greedy's limits.

The [1, 3, 4] and 6 example above is one; greedy gives 3 coins, optimum is 2.

Counter-examples decide algorithm choice; they reveal a wrong approach early.

Practice Greedy's worst case

Write greedy_bad(coins, amount). Return the greedy coin count. Print 3 with print(greedy_bad([1, 3, 4], 6)).

Starter code

solution.py
def greedy_bad(coins, amount):
    # Greedy worst case

Sample solution

solution.py
def greedy_bad(coins, amount):
    # Greedy worst case
    coins.sort(reverse=True)
    count = 0
    for coin in coins:
        count += amount // coin
        amount = amount % coin
    return count
print(greedy_bad([1, 3, 4], 6))

Expected output

3

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Greedy limits: match the terms

Term Meaning
counter-example Shows flaw
greedy Local best
DP Global best
optimum Best

2 How many coins does greedy give for [1, 3, 4] and 6?

  • 1
  • 2
  • 4
  • 3 Correct answer

Explanation: 3 (4 + 1 + 1).

3 Optimum solution

Question 
Fewest coins for 6: ____ result
Answer 
Fewest coins for 6: 3, 3 result

Explanation: 3, 3 is right.

All lessons in Intermediate

1 Merge sort

  1. Divide and conquer
  2. Merge operation
  3. Full merge sort
  4. Summary - Merge sort

2 Quick sort

  1. Pivot selection
  2. Partitioning
  3. Recursive quick sort
  4. Summary - Quick sort

3 Heap sort

  1. What is a heap?
  2. Heapify
  3. Build heap and sort
  4. Summary - Heap sort

4 Counting sort

  1. Counting idea
  2. Count array
  3. Output array
  4. Summary - Counting sort

5 Radix sort

  1. Radix idea
  2. Digit pass
  3. Stable sub-sort
  4. Summary - Radix sort

6 Sorting project

  1. Project: Overview
  2. Score array
  3. Apply merge sort
  4. Print statistics

7 Tree

  1. What is a tree?
  2. Node and edge
  3. Binary tree
  4. Summary - Trees

8 Binary search tree

  1. BST rule
  2. BST insert
  3. BST search
  4. Summary - BST

9 AVL tree

  1. Balanced tree
  2. Rotation
  3. Balance after insert
  4. Summary - AVL tree

10 Heap

  1. Min and max heap
  2. Insert
  3. Extract
  4. Summary - Heap

11 Priority queue

  1. What is a priority queue?
  2. Heap-based implementation
  3. Push and pop
  4. Summary - Priority queue

12 Data structures project

  1. Project: Overview
  2. Undo stack
  3. Pending queue
  4. Print the state

13 Graph basics

  1. What is a graph?
  2. Adjacency list
  3. Adjacency matrix
  4. Summary - Graph

14 Breadth-first search

  1. BFS idea
  2. Using a queue
  3. Marking visited
  4. Summary - BFS

15 Depth-first search

  1. DFS idea
  2. Stack or recursion
  3. Backtracking
  4. Summary - DFS

16 Greedy algorithms

  1. Greedy approach
  2. Coin change
  3. Greedy limits
  4. Summary - Greedy

17 Divide and conquer

  1. Three steps
  2. Recursive structure
  3. Master theorem
  4. Summary - Divide and conquer

18 Backtracking

  1. What is backtracking?
  2. State tree
  3. Pruning
  4. Summary - Backtracking

19 Graph project

  1. Project: Overview
  2. City graph
  3. BFS for reachability
  4. Print the result

20 Intermediate final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4