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Summary - Knapsack

Solve knapsack and print the best value in a mini task.

Summary - Knapsack

0/1 knapsack finds the max value with a 2D DP table and take/skip decisions. Used in resource allocation and investment decisions.

In this mini task you will solve knapsack and print the best value; combine all steps.

0/1 knapsack gives Θ(nW) time; if W is large it is called pseudo-polynomial.

Practice Print knapsack

Write knap_print(W, weights, values, n). Print the max value with DP and print(). Output of knap_print(50, [10, 20, 30], [60, 100, 120], 3): 220.

Starter code

solution.py
def knap_print(W, weights, values, n):
    # Print knapsack

Sample solution

solution.py
def knap_print(W, weights, values, n):
    # Print knapsack
    dp = [[0] * (W + 1) for _ in range(n + 1)]
    for i in range(1, n + 1):
        for w in range(1, W + 1):
            if weights[i - 1] <= w:
                dp[i][w] = max(dp[i - 1][w], values[i - 1] + dp[i - 1][w - weights[i - 1]])
            else:
                dp[i][w] = dp[i - 1][w]
    print(dp[n][W])
knap_print(50, [10, 20, 30], [60, 100, 120], 3)

Expected output

220

Questions and answers

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

1 Summary - Knapsack: match the terms

Term Meaning
knapsack Knapsack
DP Table
take Take
skip Skip

2 Weight check

Question 
if weights[i - 1] <= ____:
Answer 
if weights[i - 1] <= w:

Explanation: w is right.

3 Knapsack is an example of which area?

  • Backtracking
  • Greedy
  • Dynamic programming Correct answer
  • Divide and conquer

Explanation: Dynamic programming.

All lessons in Advanced

1 DP - Memoization

  1. What is memoization?
  2. Fibonacci memoization
  3. Dict-based cache
  4. Summary - Memoization

2 DP - Tabulation

  1. What is tabulation?
  2. Building the table
  3. Fibonacci tabulation
  4. Summary - Tabulation

3 LCS

  1. LCS definition
  2. DP table
  3. Backtracking the table
  4. Summary - LCS

4 Knapsack

  1. Knapsack problem
  2. 0/1 knapsack DP
  3. Decision table
  4. Summary - Knapsack

5 DP project

  1. Project: Overview
  2. Cost table
  3. DP solution
  4. Print the result

6 Matrix chain

  1. Multiplication order
  2. DP table
  3. Split point
  4. Summary - Matrix chain

7 Floyd-Warshall

  1. All pairs
  2. Triple loop
  3. Table update
  4. Summary - Floyd-Warshall

8 Dijkstra

  1. Single source
  2. Priority queue
  3. Relaxation
  4. Summary - Dijkstra

9 Bellman-Ford

  1. Negative weights
  2. Edge relaxation loop
  3. Negative cycle
  4. Summary - Bellman-Ford

10 Kruskal

  1. Minimum spanning tree
  2. Edge sorting
  3. Cycle check
  4. Summary - Kruskal

11 Prim

  1. Prim idea
  2. Priority queue
  3. Visited set
  4. Summary - Prim

12 Topological sort

  1. Dependency order
  2. DFS-based sort
  3. Kahn algorithm
  4. Summary - Topological sort

13 Union-find, trie, segment tree

  1. Union-find
  2. Trie
  3. Segment tree
  4. Summary - Advanced structures

14 Advanced final

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