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 9.3, Problem 1E
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Given an array A[0 ...n – 1], where each element of the array represents a vote in the
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The asymptotic complexity of this algorithm is O(nlogn). If we change the algorithm so that tin each phase: if the number of rows is more than the number of columns, choose the middle row instead of the middle column, find the max and remove half the rows as we did for columns. Then what is the asymptotic complexity of the new algorithm? How does new algorithm work?(Prove)
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- (Algorithms)Suppose we are given two sorted arrays S and T, each with n items. Describe an O(logn)-time algorithm for finding the kth smallest key in the union of the keys from S and T(assuming no duplicates). Present pseudocode, argue correctness and analyze the running time.arrow_forwardThe SELECT algorithm uses median of sub-medians as the pivot (let us call it s). Show that if n ≥ 140, then at least ⌈n/4⌉ elements are greater than p and at least ⌈n/4⌉ elements are less than p. Note that, in the lecture, we showed that the lower bounds of these two numbers are 3 ∗ (⌈ m/2 ⌉ − 2) with m = n/5arrow_forwardGiven an array A[0…n-1] , where each element of the array represents a vote in the election. Assume that each vote is given as an integer representing the ID of the chosen candidate. Implementan algorithm for determining who wins the election.arrow_forward
- Design a transform-and-conquer algorithm for finding the minimum and the maximum element of n numbers using no more than 3n/2 comparisons. Justify the number of comparisons of your algorithm.arrow_forwardCompare the (a) Linear search and (b) Binary search algorithms on an input array from which you are supposed to find a specific element. Consider three different cases for (a) (Best case, Average case, Worst case) Arrive at the computational complexity of (a) (all three cases) and (b) in terms of Big O(.) notation. (Python)arrow_forwardWrite a algorithm Record in a square matrix where the secondary diagonal must have the value 1 and the remainder value zero in PSEINTarrow_forward
- please add comments for each matrix algorithms below START OF MATRIX ADDITIONInput no. of rows m1 and columns n1 of first matrixFor i = 0 to m1-1 For j=0 to n1-1 Input a[i][j] End forEnd forInput no. of rows m2 and columns n2 of second matrixFor i = 0 to m2-1 For j=0 to n2-1 Input b[i][j] End forEnd forIf (m1 != n1 and m2!=n2) Print "Addition is not possible"Else Initialize sum matrix sum[m1][n1] as 0 matrix For i = 0 to m1-1 For j=0 to n1-1 sum[i][j] =a[i][j]+b[i][j] End for End forEnd IfFor i = 0 to m1-1 For j=0 to n1-1 Print sum[i][j] End forEnd forEND OF MATRIX ADDITION START OF SCALAR MULTIPLICATIONInput no. of rows m and columns n of matrixFor i = 0 to m-1 For j=0 to n-1 Input a[i][j] End forEnd forInput scalar value kInitialize result matrix res[m][n] as 0 matrixFor i = 0 to m-1 For j=0 to n-1 res[i][j] = k *a[i][j] End forEnd forEnd IfFor i = 0 to m-1 For j=0 to n-1…arrow_forwardA magic square of order n is an arrangement of the integers from 1 to n2 in an n × n matrix, with each number occurring exactly once, so that each row, each column, and each main diagonal has the same sum Design and implement an exhaustive-search algorithm for generating all magic squares of order n.arrow_forwardComputer Science for python The SELECT algorithm uses median of sub-medians as the pivot (let us call it s). Show that if n ≥ 140, then at least ⌈n/4⌉ elements are greater than p and at least ⌈n/4⌉ elements are less than parrow_forward
- In the median finding algorithm, suppose in step 1, • we divide the input into blocks of size 3 each and find the median of the median of blocks and proceed, does that result in a linear algorithm? • we divide the input into blocks of size 7 each and find the median of the median of blocks and proceed, does that result in a linear algorithmarrow_forwardMake an algorithm for this below: Construct a 6x6 table and populate the cells with alphabets from your address (68-9th Street, Nchanga South, Chingola) repeatedly. Design an effective algorithm to create and display the patterns "/ (diagonal)" in increasing and decreasing order. Merge and print any two patterns with maximum length from both increasing & decreasing orders and compress and print the same.arrow_forwardDesign an algorithmthat can performa sequence m union and find operations on a Universal set of n elements, consisting of a sequence of unions followed by a sequence of finds, in time O(m + n).arrow_forward
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