Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 11.1, Problem 2E
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To describe the application of bit
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- In C program A set of integers 0..MAX may be implemented using an array of boolean values. This particular implementation is called a bit-vector implementation of a Set. Since C doesn’t have the Boolean data type, then substitute TRUE with 1 and FALSE with 0, or define 1 and 0 as TRUE and FALSE, respectively. For example, if the integer 3 is an element of the set, then the array element indexed by 3 is TRUE. On the other hand, if 3 is not an element, then the array element indexed by 3 is FALSE. Implement a programmer-defined data type called BitSet to represent a set as follows: typedef int BitSet[MAX]; Implement the following functions: void initialize(BitSet s); - set all array elements to FALSE void add(int elem,BitSet s); - set the item indexed by elem to TRUE void display(BitSet s); - display the set on the screen using set notation, e.g. {3,4,5,6} - this means that you will print the index value if the content of that cell is TRUE void getUnion(BitSet result,BitSet s1,BitSet…arrow_forwardA common implementation of sequential files on disk has each block point to its successor, which may be any block on the disk. This method requires a constant amount of time to write a block (as the file is originally written), to read the first block in the file, and to read the ith block, once you have read the 1 - 1” block. Reading the lth block therefore requires time proportional to 1. Show how by adding just one additional pointer per node, you can keep all the other properties, but allow the lth block to be read in time proportional to log I. [Hint: heaps have implicit pointers from node I to what other nodes?] Explain what the algorithm for reading the th block has in common with an algorithm for raising a number to the ith power in time proportional to log 1.arrow_forwardCreate a bottom-up mergesort that takes advantage of array order by doing the following each time it has to identify two arrays to merge: locate a sorted subarray (by incrementing a pointer until it finds an entry in the array that is smaller than its predecessor), then locate the next, and finally merge them. Examine the algorithm's running time in terms of array size and the number of maximal rising sequences in the array.arrow_forward
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