530 words
3 min read
Visual companion
Python
Type and operator map
Python Week 1: the first filter for runtime behavior
View
Revision summary
What this note is really saying
Short form
# Computational Thinking · Week 8 — Labelled adjacency graphs Deep study for Quiz 2 week 8. Labels on edges carry weights, costs, or names — adjacency structures must store values, not just 0/1.
Computational Thinking · Week 8 — Labelled adjacency graphs
Deep study for Quiz 2 week 8. Labels on edges carry weights, costs, or names — adjacency structures must store values, not just 0/1.
Week map
Unweighted vs labelled → weight matrix → multi-graph caution → shortest-path intuition → reading labelled diagrams.
Labelled edge notation
- Label → data on edge → weight, distance, time, capacity.
- Weighted graph → each edge has numeric label → often non-negative in intro problems.
- → edge from to has weight .
- or → no edge (convention varies — read problem statement).
Mini-example: three cities 0, 1, 2. Direct roads: 0→1 weight 4, 1→2 weight 2, 0→2 weight 10.
text1 --4-- 2 \ | 10 2 \ | ---- 3
(Adjust to matrix form in examples below.)
Weight matrix
textW = [ 0 4 10] [ ∞ 0 2] [ ∞ ∞ 0]
Use ∞ or blank for missing edge. , . Path 0→1→2 has total weight , better than direct 0→2 weight 10.
Adjacency list with labels
Alternative to matrix:
text0 → [(1, 4), (2, 10)] 1 → [(2, 2)] 2 → []
Each entry (neighbor, weight). Space-efficient for sparse graphs.
Directed vs undirected weights
Undirected road length on → typically .
Directed → only one direction gets weight unless both stated.
Pattern families
Easy — Read label from diagram
Identify weight on edge between two named vertices. List all neighbors with weights from one vertex.
Medium — Build weight matrix
From edge list fill . Handle missing edges with 0 or ∞ per convention.
Hard — Compare path totals
Sum weights along path. Compare two routes. Greedy “pick lightest edge next” may fail globally — but Quiz 2 often asks direct sum comparison only.
Worked mini-examples
Example 1 — Matrix fill.
Edges: (0,1,3), (1,2,5). Directed:
textW[0][1]=3, W[1][2]=5, others missing
Example 2 — Path sum.
Path 0→1→2: weights 3 + 5 = 8.
Example 3 — Undirected symmetry.
Edge A—B weight 7 → .
Example 4 — No edge.
missing → no direct 2→0 edge in directed sense.
Example 5 — List form lookup.
From vertex 1 list [(0, 2), (2, 4)]: edge to 0 weight 2, to 2 weight 4.
Traps
- Confusing “no edge” 0 with “zero weight” edge — problem defines convention.
- Forgetting directed orientation when summing path.
- Double-counting undirected edge in degree/weight tally.
- Picking edge with min label locally vs min total path.
- Vertex label mismatch with matrix index.
Diagnostic (try yourself)
-
Weighted edge from X to Y is 6. In matrix with X=1, Y=2, what is ?
-
Path A→B→C with weights 3 and 5. Total weight?
-
Undirected edge weight 4 between vertices 0 and 2. What are and ?
-
Adjacency list for vertex 1 is [(2, 7), (3, 1)]. What is weight of edge 1→3?
-
Direct path weight 12 vs two-hop path 4+5. Which route is cheaper?