Minimum Cover - Algorithm

Sort by start time. Greedily extend coverage as far as possible.

$1.$ Sort intervals by start.

$2.$ Track current coverage end.

$3.$ Among intervals starting at or before current end, pick the one extending furthest.

$4.$ Update coverage end and increment count.

$5.$ Repeat until coverage >= T or no progress possible. Time: $O(n \log n)$. Space: $O(1)$. Common bug: picking the first usable interval instead of the one that extends furthest.