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 8.4, Problem 1E
Program Plan Intro
To illustrate the operation of BUCKET-SORT on the array
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Given an 8-element array: A = {x1, X2, X3, X4, X5, X6, 7, x8}, we would like to find
its 3rd smallest element. It is known that x₁ and 8 are the two extreme elements:
max and min, but we do not know which one is the max and which one is the min.
It is also known that x4 and x5 are the two medians: left-median and right-median.
What is the minimum number of comparisons you need to find the 3rd smallest
element of the original array?
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Please Help me with this Problem
Given an unsorted array of size n. Array elements are in the range from 1 to n. One number from set {1, 2,..., n} is missing and one number occurs twice in the array. Find these two numbers.
For the following array A=[1,-3,2;-3,3,-1;2,-1,0]
find the values of the second column after applying the
initial operations
H12(-1), H23(1), H21, K23(-1), H13, H1(-1)
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- Write an algorithm that applies right shift on one dimensional array (trace your algorithm on example array A:[0,9,2,10,3] and show the result of your trace steps as a table). (Do not use extra array while solving this problem)arrow_forwardConsider the array L = 387, 690, 234 435 567 123 441 as an example. The number of components in this case is 7, the number of numbers is 3, and the radix is 10. This suggests that radix sort would require 10 bins and 3 cycles to complete the sorting. shows how the radix order is followed by the list. Each key is probably thrown into the garbage bin facing down. Each bin is turned into a key when the output to the is to be attached to the phrase: at the end of the bin.arrow_forwardGiven an array arg[] below, use the incremental approach to sort it in assending order 11 42 35 38 22 45 18 39 3arrow_forward
- Array x is [a, b, c, . . . , y] has 25 integers. To find median of medians we form five sub-arrays: [d, c, b, e, a], [i, f, h, j, g], [1, m, k, n, o], [p, s, q, r, t], [w, x, v, u, y]. We find median from these sub-arrays and generate new sorted array [k, h, q, b, v]. Median of new sorted array is q, so median of medians is q. List all elements guaranteed to be greater or equal to q.arrow_forwardIn an array-based implementation of a List, why does the add operation take O(n) time in the average case? Select one: a. The time it takes to shift entries over to make room in the array depends on the number of entries in the List b. The time to copy the current entries into a newly allocated, larger array depends on the number of entries in the List c. The time to access the position in the array to add the new entry depends on the number of entries in the List d. The time to access the position in the array to add the new entry depends on the capacity of the arrayarrow_forwardIllustrate (step by step) the operation of COUNTING-SORT on the array A = {6, 2, 0, 1, 3, 4, 6, 3, 2}.arrow_forward
- there is array [4,3,4,3,3], each player hac has 10 points. Player takes out a number from their array and he substracts that number from his points and then computer plays with same rules . Game finishes when there is one element in array. In the end, whoever has more points , he wins.How to code it with MIN-MAX algorithm for computer to play?You can code it in Java, JavaScript, Python, C++arrow_forwardCodeGiven an unsorted array A of size N that contains only positive integers, find a continuous sub-array that adds to a given number S and return the left and right index(1-based indexing) of that subarray. In case of multiple subarrays, return the subarray indexes which come first on moving from left to right. Note:- You have to return an ArrayList consisting of two elements left and right. In case no such subarray exists return an array consisting of element -1.arrow_forwardGive example to sort an array in dscending orderarrow_forward
- For the given array, simulate the working operation of Bubble Sort. Show your work at each step.Make sure to show the status of the array after every insertion.[ 28, 13, 22, 7, 34, 2, 15, 18 ]arrow_forwardGiven an array of integers, return the largest gap between the sorted elements of the array. For example, consider the array: [9, 4, 26, 26, 0, 0, 5, 20, 6, 25, 5] ... in which, after sorting, the array becomes: [0, 0, 4, 5, 5, 6, 9, 20, 25, 26, 26] so that we now see that the largest gap in the array is between 9 and 20 which is *** 11. Examples largestGap ([9, 4, 26, 26, 0, 0, 5, 20, 6, 25, 5]) → 11 // After sorting: [0, 0, 4, 5, 5, 6, 9, 20, 25, 26, 26] // Largest gap between 9 and 20 is 11arrow_forwardYou have been given an array A of size N and an integer K. This array consists of N integers ranging from 1 to 10^7. Each element in this array is said to have a Special Weight. The special weight of an element a[i] is a[i]%K. You now need to sort this array in Non-Increasing order of the weight of each element, i.e the element with the highest weight should appear first, then the element with the second highest weight and so on. In case two elements have the same weight, the one with the lower value should appear in the output first. Input Format: The first line consists of two space separated integers N and K. The next line consists of N space separated integers denoting the elements of array A. Output Format: Print N space separated integers denoting the elements of the array in the order in which they are required. Constraints: 1≤N≤10^5 1≤A[i]≤10^7 1≤K≤10^7 Note: You need to print the value of each element and not their weight. SAMPLE INPUT 5 21 2 3 4 5 SAMPLE OUTPUT 1 3 5 2 4…arrow_forward
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