(1) Write a function that given an integer n, it finds all binary sequences of length 2n such that the sum of thefirst n bits is same as the sum of last n bits.Example:For n = 2, the sequences are:I,1] [,2] [,3] [,4] L,51 [,6][1,] 0 1 1 0 0 10 0[2,1 01 1 1[3,1 010.1.[4,1 011For n = 3, the sequences are:[1 oI IO o o o o o I II III 0 o 0 1a1 o o 0 I1.0 0 0 0 O I1.110即 0O 0 I O O61 0 0 11.L1 0 0 0 IO OO 0 I 0 II0I(2) Write a function that given an integer n computes all non-increasing partitions of n.Example:For n=3,111213For n=4,111122211314

In this program the if n=3 then the binary sequence first 3 bits and last bit sum should be same.…

non that given an integer n, it finds all binary sequences of length 2n such that the sum of the first n bits is same as the sum of last n bits. Example: For n = 2, the sequences are: 1,1] [,2] [,3] L,4] [,51 (,61 [1,] 0 1 1 0 0 1 0 0 [2,1 0 [3,1 0 1 1 1 [4,1 0 1 0 1 1 For n 3, the sequences are: [] o 11 IO 0 o o 0 1 III IIO O 1 a1 o o 0 o 1. C幻 0 0 0 0 0 的 61 0 0 3. 1. O I 0 0 I 6O G1 0 0 0 IO O (2) Write a function that given an integer n computes all non-increasing partitions of n. Example: For n=3, 111 21 3 For n=4, 1111 22 211 31 4

non that given an integer n, it finds all binary sequences of length 2n such that the sum of the first n bits is same as the sum of last n bits. Example: For n = 2, the sequences are: 1,1] [,2] [,3] L,4] [,51 (,61 [1,] 0 1 1 0 0 1 0 0 [2,1 0 [3,1 0 1 1 1 [4,1 0 1 0 1 1 For n 3, the sequences are: [] o 11 IO 0 o o 0 1 III IIO O 1 a1 o o 0 o 1. C幻 0 0 0 0 0 的 61 0 0 3. 1. O I 0 0 I 6O G1 0 0 0 IO O (2) Write a function that given an integer n computes all non-increasing partitions of n. Example: For n=3, 111 21 3 For n=4, 1111 22 211 31 4

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

The last index numbers of an array of size NxM will be: [N-1][M-1] [N][M] 2NM None of the answers are correct.
Given n arrays, each array contain n positive integers. Write an O (n² log n) algorithm to find the smallest n sums out of nn possible sums that can be obtained by picking one positive integer from each of n arrays. For example, given three arrays as follows: [5, 1, 8], [5, 2,9], and [6,7, 10]. The smallest n sums of the given array is [9, 10, 12].
Legendre's formula finds the exponent of the largest power of some prime p that divides (is a factor of) the factorial of some number n Legendre's formula example (p = 2 and n = 27): €₂ (27!) To illustrate: 27 27 []+[] + 2 p = 5 n = 100 =13 +6+3+1 =23 So 2^23 is the largest power of 2 that divides 27!. The formula returns the sum of many fractions (rounded down) with n as the numerator and a steadily increasing power of p as the denominator, stopping when it exceeds the numerator. 27 23 int(100/5) int(100/25) // No 100/125 because 125 > 100.
Consider the following algorithm that uses a sorted list of n elements (alist). What is the worst case runtime of this algorithm? for each element in alist 1. ask the user for an input, call it value 2. search value in alist using binary search 3. if value exists in alist, print "successful" otherwise print "unsuccessful" Question options: a. O(log n) b. O(n) c. O(n log n) d. O(2^n) e. O(n^2) f. O(1)
Many computer applications involve searching through a set of data and sorting the data. A number of effi cient searching and sorting algorithms have been devised in order to reduce the runtime of these tedious tasks. In this problem we will consider how best to parallelize these tasks.Consider the following binary search algorithm (a classic divide and conquer algorithm) that searches for a value X in a sorted N-element array A and returns the index of matched entry:BinarySearch(A[0..N−1], X) {low = 0high = N −1while (low <= high) {mid = (low + high) / 2if (A[mid] >X)high = mid −1else if (A[mid] <X)low = mid + 1elsereturn mid // found}return −1 // not found}Assume that you have Y cores on a multi-core processor to run BinarySearch. Assuming that Y is much smaller than N, express the speedup factor you might expect to obtain for values of Y and N. Plot these on a graph.Next, assume that Y is equal to N. How would this affect your conclusions in your previous answer? If you…
Given an unsorted array of integers, write a function in Python to find the length of the longest increasing subsequence (LIS) in the array. For example, given the array [10, 9, 2, 5, 3, 7, 101, 18], the LIS is [2, 3, 7, 101], which has a length of 4. Your solution should have a time complexity of O(n log n), where n is the length of the input array. Here's some code to get you started: def longest increasing_subsequence(arr): # TODO: implement function pass # example usage arr = [10, 9, 2, 5, 3, 7, 101, 18] print(longest_increasing_subsequence(arr)) # should print 4
Given an integer array [A], efficiently find a descending sorted triplet such that: A[i]> A[i]> A[k] and 0 <=i<j <k <n, where n is the array size. For example, Input: A[] = {9, 1, 6, 7, 3, 4, 5) Output: Any one of the following triplets: (9, 7,5) (9, 7, 4) (9, 7, 3) (9, 6, 5) (9, 6, 4) (9, 6, 3) a) Design a brute-force algorithm to solve this problem complexity of your solution b) Design a more efficient algorithm to do the same task with less complexity and analyse the complexity of your solution. c) Develop a python code to implement your efficient algorithm. depend on the correctness of the code, indentation, comments, test-case] d) Prepare a brief report (250 words) comparing the two algorithms
Evaluate the performance per line
Let A[0..n − 1] be an array of n real numbers. A pair (A[i], A[j ]) is said to be an inversion if these numbers are out of order, i.e., i < j but A[i]>A[j ]. Design an O(n log n) algorithm for counting the number of inversions. i want code in java ?
Let M(n) be the minimum number of comparisons needed to sort an array A with exactly n ele- ments. For example, M(1) = 0, M(2) = 1, and M(4) = 4. If n is an even number, clearly explain why M(n) = 2M(n/2) + n/2.
Given an integer array A of size N where every element is in the range [0, 9]. When traversing the array, one could move from index į to index (i-1), index (i+1) or index j # į such that A[i]=A[j]. For example, given A = {4, 3, 1, 6, 3, 7, 1}, one can move • From A[0] to A[1] • From A[1] to A[2], A[0] or A[4] (since A[4]=A[1]=3) • From A[2] to A[3], A[1] or A[6] (since A[6]=A[2]=1) From A[3] to A[4], A[2] • And so on. The task is to compute the minimum number of moves to reach to the last index of the array starting from the first index. Examples: Input: A = {1, 2, 3, 4, 1, 5} Output: 2 Explanation: First move from A[0] to A[4] and then from A[4] to A[5]. Input: A = {1, 2, 3, 4, 5, 1} Output: 1 Explanation: Move from A[O] to A[5]. 6. Input: A = {1, 2, 3, 4, 5, 6, 7, 3, 4, 5, 4, 3, 6, 1, 5, 5, 4, 4, 7, 7} Output: 5 Explanation: Move from A[0] to A[13], from A[13] to A[12], from A[12] to A[5], from A[5] to A[6], from A[6] to A[19]. a) Explain how you would represent this problem as a…