Programming, problem solving, and algorithms

CPSC 203, 2025 W2

March 24, 2026

Announcements

Travelling Salesperson Problem (TSP)

Maps: Running Errands

You’ve got 9 errands to run. What order do you do them in?

Determine the least cost route through a set of given locations, returning to the start.

Travelling Salesperson Problem (TSP)

“Given a list of cities, and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?”

• Classic problem on graphs

• First known mention was in 1930

• ________________________________________

No algorithmic solution that works in all cases, for large graphs. No way to tell if an answer is the best possible one!

Why is the problem so hard?

Suppose you have 6 locations. How many different candidate solutions are there? Generalize to k locations?

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Demo Blog

https://medium.com/data-science/around-the-world-in-90-414-kilometers-ce84c03b8552

Why This Matters

There are lots of applications:

• 📦 UPS/FedEx/Amazon Delivery Millions saved by reducing even 1km per driver per day.
• 🍔 UberEats/DoorDash/Skip Multi-stop pickup/delivery with time windows.
• 🧬 DNA Sequencing & Genome Assembly Ordering fragments relies on TSP-like reconstruction.
• 🚌 School Bus Routing Minimize buses, fuel, and time while meeting constraints.
• 🧪 Medical Lab Sample Pipelines Robotic arms schedule efficient multi-station workflows.
• ❄️ Snowplow & Garbage Truck Routing Efficiently cover every street in a city.
• 🏭 Factory Robots & CNC Machines Optimizing tool paths reduces waste, heat, and wear.
• ✈️ Airline Crew Scheduling Complex daily routing: crews must return to base, meet rest rules.
• 🌍 City Infrastructure Planning Utility inspections, meter reading, streetlight repair routes.
• 🚑 Ambulance & Emergency Routing Minimize response times; life-critical optimization.

Plan for Code

Steps to assemble our solution:

 

1. ________________________________________

2. ________________________________________

3. ________________________________________

4. ________________________________________

5. ________________________________________

1. assemble the graph and errands
2. create pairwise distances
3. create all possible permutations of paths
4. find minimum route and assemble turn-by-turn for that route
5. visualize on map

2. Create pairwise distances

What structure should we use?

dist['Vancouver']['Bellingham'] -> int path['Vancouver']['Bellingham'] -> list

example: dist['Van']['Bel'] = nx.shortest_path(G, 'Van', 'Bel', weight='length')

3. Create all possible orders

tours = list(itertools.permutations(list(dferrands['node'])))

Tour Distance

We assemble each candidate solution as an arrangement of all of the errands:

Ex: A D B E F C

How do we find the total distance if we do the errands in the suggested order?

What Does lambda Do?

dferrands['latlong'] = dferrands.apply(
                lambda row: ox.geocode(row['errand']),
                axis=1
              )

Goal: Create a new column (latlong) and fill it with coordinates for each errand in the dataframe.

How it works:

• df.apply(..., axis=1): Run a function once for each row.

• lambda row: ox.geocode(row['errand']): A tiny inline function. Read it as: “Given a row, look up the place name in row['errand'],geocode it, and return the (lat, lon).”

• The returned value becomes the entry in the new latlong column.

Why lambda? We only need this function once, so we write it right where it’s used.

Demo

PrairieLearn Activity