What is the time and space complexity of Cheapest Flights Within K Stops?

Time complexity: O(K * E). Space complexity: O(V).

Cheapest Flights Within K Stops

Hard

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Solution Guide: Cheapest Flights Within K Stops

Approach

Relax all edges exactly k+1 times, representing paths with up to k intermediate stops. Copy previous distances each round to avoid using newly updated values in same round.

Complexity Analysis

Time: O(K * E)
Space: O(V)

Pattern

DP by Edge Count (Bellman-Ford)

Why It Works

Any path with at most K stops has at most K+1 edges. Each iteration allows one extra edge, and relaxation accumulates best costs constrained by edge count.

Updated Feb 2026