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Summary - Floyd-Warshall

Run Floyd-Warshall on a small graph in a mini task.

Summary - Floyd-Warshall

In this group you learned Floyd-Warshall, which finds shortest paths for all pairs. Adjacency matrix, triple loop and relaxation formula combine into the solution.

Now you will write a query function that brings all pieces together. This summary unites the group's concepts in a single piece of code.

Practice shortest_distance function

Write shortest_distance(graph, src, dst). Run Floyd-Warshall, return dist[src][dst]. Print 6 with print(shortest_distance(init_graph(), 0, 3)).

Starter code

solution.py
def shortest_distance(graph, src, dst):
    # Solve all pairs and return src→dst

Sample solution

solution.py
def shortest_distance(graph, src, dst):
    # Solve all pairs and return src→dst
    n = len(graph)
    dist = [row[:] for row in graph]
    for k in range(n):
        for i in range(n):
            for j in range(n):
                dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j])
    return dist[src][dst]
print(shortest_distance(init_graph(), 0, 3))

Expected output

6

Questions and answers

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

1 What is the output of Floyd-Warshall?

  • A single distance
  • Edge weights
  • A path list
  • All-pairs distance matrix Correct answer

Explanation: The output is the all-pairs distance matrix.

2 Matrix copy

Question 
dist = [row[:] for row in ____]
Answer 
dist = [row[:] for row in graph]

Explanation: graph is right.

3 Summary - Floyd-Warshall: match the terms

Term Meaning
init_graph Graph
relax_edge Relaxation
floyd_warshall Triple loop
dist Distance

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