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Balanced search tree: A search-tree data structure for which a height of O(lg n) is guaranteed when implementing a dynamic set of n items
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The depth of a node = the number of comparisons made during TREE-INSERT. Assuming all input permutations are equally likely, we have
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Algorithms Day 12 L8.2 A weakness of hashing Problem: For any hash function h, a set of keys exists that can cause the average access time of a hash table to skyrocket. IDEA: Choose the hash function at random, independently of the keys
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Symbol-table problem Symbol table T holding n records: key key[x] [x]
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Order statistics Select the ith smallest of n elements (the element with rank i)
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All the sorting algorithms we have seen so far are comparison sorts: only use comparisons to determine the relative order of elements
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Proposed by C.A.R. Hoare in 1962. Divide-and-conquer algorithm. Sorts “in place” (like insertion sort, but notlike merge sort). Very practical (with tuning)
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1. Divide the problem (instance) into subproblems. 2. Conquer the subproblems by solving them recursively. 3. Combine subproblem solutions
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The analysis of merge sort fromLecture 1 required us to solve arecurrence. Recurrences are like solving integrals,differential equations, etc.o Learn a few tricks
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1. Course Information 2. Calendar 3. Registration (MIT students only) 4. References 5. Objectives and Outcomes 6. Diagnostic Survey
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