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LC 287 has n+1 integers in [1,n] with exactly one duplicate. The binary search approach counts elements <= mid: if count > mid, the duplicate is in [1,mid]. O(n log n) time, O(1) space. Also understand the O(n) Floyd cycle detection approach.
LC 786 asks for the kth smallest fraction a[i]/a[j] from a sorted prime array. Binary search on the fraction value [0.0, 1.0] and count fractions below mid using two pointers. O(n log(1/epsilon)) total. A hard binary search on value problem.
LC 1346 asks if any element and its double both appear in an array. The optimal O(n) hash set approach processes elements one by one. An O(n log n) sort-and-binary-search alternative demonstrates the binary search pattern. A good warm-up for two-sum variants.
LC 981 implements a key-value store where each key can have values at different timestamps. set() in O(1), get(key, timestamp) in O(log n) using right-boundary binary search on the sorted timestamp list. A classic design + binary search interview problem.
LC 1353 asks for the maximum number of events you can attend given start and end days. Greedy approach: each day, attend the event with the earliest end date using a min-heap. Sort events by start day and use a pointer to add available events. O(n log n).