mediumLeetCode#bellman-ford#bounded-relaxation

Cheapest Flights Within K Stops

Find the cheapest route using at most k intermediate stops, or return -1.

The Runtime Theory TeamSeptember 25, 202625 min read

Solve it

Solving happens on the judge — come back and mark it done

Sample cases

inn=4, flights=[[0,1,100],[1,2,100],[2,0,100],[1,3,600],[2,3,200]], src=0, dst=3, k=1

out700

inn=3, flights=[[0,1,100],[1,2,100],[0,2,500]], src=0, dst=2, k=1

out200

inn=3, flights=[[0,1,100],[1,2,100]], src=0, dst=2, k=0

out-1

Find the cheapest route using at most k intermediate stops, or return -1.

A good solution should

State the invariant or decision rule that makes the approach correct.
Explain time and space costs in terms of input size and required output.
Handle empty, minimal, duplicate, and boundary-shaped inputs.

Reasoning prompt

Bound relaxations by edge count or track stops in the state. An unconstrained shortest-path algorithm can use too many edges.

Use the linked judge for the canonical challenge. The examples above are compact TRT checks; create additional tests around the boundary most likely to break your invariant.

One dispatch a week

The trace behind each problem, the tradeoff that explains it, and one technical dispatch per week — no noise.

One technical dispatch per week. No noise.

Not started

A good solution should

Reasoning prompt

More practice in this topic

One dispatch a week