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DSA · Theory

Check whether a given graph is Bipartite or not

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Theory

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Check whether a given graph is Bipartite or not

Check whether a given graph is Bipartite or not is a DSA idea you prove with bus routes, not with a slogan.

For Check whether a given graph is Bipartite or not, a dry-run table is in play. Don’t blame it until you have traced bus routes.

Without Check whether a given graph is Bipartite or not, a city map gets messy and bus routes is hard to trust.

Check whether a given graph is Bipartite or not shows up in a city map. Name bus routes, not “a real-world scenario”.

Check whether a given graph is Bipartite or not miss: no visited set → infinite loop. Fix it before you talk about advanced DSA.

Place Check whether a given graph is Bipartite or not next to nearby DSA work — BFS queue / DFS stack is the link.

One breath for Check whether a given graph is Bipartite or not, then bus routes, then no visited set → infinite loop. Sit down.

Exam tip

Say Check whether a given graph is Bipartite or not in one breath, then BFS queue / DFS stack, then no visited set → infinite loop.

Example

# adjacency list
graph = {
    "A": [("B", 2), ("C", 5)],
    "B": [("A", 2), ("C", 1)],
    "C": [("A", 5), ("B", 1)],
}
for u, edges in graph.items():
    print(u, "->", edges)

Check whether a given graph is Bipartite or not — graphs are often stored as adjacency lists: vertex → list of (neighbor, weight).

Short notes

  • DefCheck whether a given graph is Bipartite or not — Arun uses it for bus routes in a city map.
  • RuleCheck whether a given graph is Bipartite or not → BFS queue / DFS stack.
  • RememberCheck whether a given graph is Bipartite or not + a dry-run table (a city map).
  • UseCheck whether a given graph is Bipartite or not in a city map (bus routes).
  • TrapCheck whether a given graph is Bipartite or not — no visited set → infinite loop.
  • ExCheck whether a given graph is Bipartite or not → bus routes.

Questions

1

Define Check whether a given graph is Bipartite or not without jargon. Then point at bus routes.

2

Name one DSA screen/job that needs Check whether a given graph is Bipartite or not.

3

What trap does Arun hit with Check whether a given graph is Bipartite or not?

4

Write the smallest Check whether a given graph is Bipartite or not step on bus routes. What happens?

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