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$ curl repovive.com/roadmaps/graph-theory/mixed-practice-advanced-graphs/hamiltonian-flights-analysis

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$ curl repovive.com/roadmaps/graph-theory/mixed-practice-advanced-graphs/hamiltonian-flights-analysis

Repovive

Hamiltonian Flights - Analysis - Mixed Practice: Advanced Graphs | Graph Theory | Repovive

Repovive.

Graph Theory37 sections · 1633 units81h total

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Hamiltonian Flights - Analysis

Recognizing the bitmask DP pattern.

Pattern recognition:

Visit every vertex exactly once = Hamiltonian path
Count paths, not just existence
$n \leq 20$ = bitmask DP is feasible

State: dp[mask][i] = number of paths visiting exactly the cities in $mask$ , ending at city $i$ .

Transition: For each edge $(i, j)$ :

if mask has i and not j:
 dp[mask | (1 << j)][j] += dp[mask][i]

Answer: dp[2^n - 1][n-1] (all cities visited, ending at city $n$ ).