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Capacity to Ship Packages Within D Days — BS on Answer
Find the minimum ship capacity to ship all packages within d days using binary search on capacity.
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Find Peak Element — Binary Search on Slope
Find any peak element in O(log n) by always moving toward the uphill neighbor, which guarantees finding a peak.
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Find K Closest Elements — BS on Left Window Boundary
Find the k closest elements to x in a sorted array by binary searching for the optimal left window boundary.
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Single Element in a Sorted Array — Parity Index Binary Search
Find the single non-duplicate element in O(log n) by observing that pairs shift the parity of indices after the singleton.
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Longest Increasing Subsequence — Patience Sort Binary Search
Find the length of LIS in O(n log n) using patience sorting: binary search to maintain a sorted tails array.
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