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Lecture 5 |Master Theorem
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Proof in the general case [see image] Statement of Master Theorem [see statement on image] Closest pair of points: naive method Compute all O(n^2) pairwise distances, return pair with smallest Closest pair DAC method split points into left and write, then solve both subproblems and recombine Closest pair: Sorting by x-coordinate and cutting in the middle - complexity (time) O(n log n) Closest pair: naive recombination O(n^2) pairs (left, right) Closest pair, recombination: 1st observation - If d is minimal distance on both sides, then it is sufficient to.. focus on a strip of width 2d around the middle Closest pair, recombination: 2nd observation - at most ... 4 points at dist = d from one another can lie in a dxd square
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