Implementation

function activitySelection(activities)
 sort activities by end time ascending
 count := 1
 lastEnd := activities[0].end
 for i from 1 to length of activities - 1
 if activities[i].start >= lastEnd then
 count := count + 1
 lastEnd := activities[i].end
 return count

Time: $O(n \log n)$ for sorting, $O(n)$ for scanning. Total: $O(n \log n)$. Space: $O(1)$ extra (assuming in-place sort).