greedy

Interval merging is a classic that tests the sort-then-sweep insight. The signal is sorting by start, then merging in one pass, O(n log n). Here is the pattern and the family of problems it unlocks.

Gas Station rewards spotting a greedy invariant that turns O(n²) into O(n). Two facts carry the whole solution: total feasibility, and that a failed prefix lets you skip every start inside it.

Jump Game rewards spotting that a greedy reachability scan beats DP. The signal is tracking the farthest reachable index in one pass, and detecting the exact moment you fall behind it.

Merging intervals is the gateway to the whole interval family. The trick is sorting by start so overlaps land next to each other, then collapsing them in one linear sweep. Here is the pattern and the sweep-line generalization behind it.

Kruskal builds a minimum spanning tree by sorting edges and adding the cheapest that does not form a cycle, using union-find for the cycle check. The signal is the greedy cut property and why disjoint-set is the right tool. Here is the answer.