A sequence (bn)neN is called strictly increasing if b, < bn+1 for all n € No. Such a strictly increasing sequence is divergent if, for any threshold M E R, we can findan index k such that bk > M.We can represent a sequence (bn) by a Python function that takes n as its argument (of type int) and returns bn (of type float).Write a function threshold_index that takes two arguments: The first one is a Python function representing a strictly increasing, divergent sequence. The second oneis a threshold value M. The function threshold_index should return the smallest index n for which the sequence passes the threshold (i.e., bn ≥ M).

def threshold_index (sequence, M): n = 0while sequence(n) < M: n += 1 return ndef…

Answered: A sequence (bn)neN is called strictly…

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

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code required for python: For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0 For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43 Constraints Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function. my code below , however as…
A sequence (bn)neNo is called strictly increasing if b₁ M. We can represent a sequence (bn) by a Python function that takes n as its argument (of type int) and returns bn (of type float). Write a function threshold_index that takes two arguments: The first one is a Python function representing a strictly increasing, divergent sequence. The second one is a threshold value M. The function threshold_index should return the smallest index n for which the sequence passes the threshold (i.e., bn ≥ M).
Write a function lis_rec(arr) that outputs the length of the longest increasing sequence and the actual longest increasing sequence. This function should use divide and conquer strategy to the solve the problem, by using an auxiliary function that is recursive. For example, one possibility is to define a recursive function, lis_rec(arr, i, prev), that takes the array arr, an index i, and the previous element index prev of LIS (which is part of the array arr before index i), and returns the length of the LIS that can be obtained by considering the subarray arr[i:]. Write a dynamic programming version ofthe function, lis_dp(arr), that outputs the length of the longest increasing sequence and the actual longest increasing sequence by using a table to store the results of subproblems in a bottom-up manner. Test the performance of the two functions on arrays of length n = 100, 500, 1000, 5000, 10000. Compare the running times and memory usage of the two functions.
Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. Sierpinski.java When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle with the specified side length. public static double height(double length) // Draws a filled equilateral triangle with the specified side length // whose bottom vertex is (x, y). public static void filledTriangle(double x, double y, double length) // Draws a Sierpinski triangle of order n, such that the largest filled //…
Write a Python function that takes in three parameters - an adjacency matrix of a simple directed graph, a start node, and an end node; and returns "True" if there is a way to get from the start node to the end node using the provided edges. You can use this file as a starter code: path.py ↓ For example: Using the same graph given above. Consider your function with the same adjacency matrix given above as input and: If the start node is 1 and the end node is 4 then your function should return True. If the start node is 2 and the end node is 4 then your function should return False. Input: This function will have three parameters. First is an adjacency matrix in the form of a list of lists (as given above). Then the start_node and the end_node will be integers. Note that python indexing starts from 0 and not from 1, so the naming of the nodes will also follow the python convention and start from 0 instead of 1. Output: Boolean value: True or False.
Plot the following function for -5 ≤ x ≤ 5: y = 1 1+x² The x-values can be generated with x = np.linspace (-5, 5, n), where n refers to the number of x-values generated (you pick a n-value).
Given the functions G(a,b,c) = ∏M ( 1,2,3,5) and F(a,b,c) = ∑m (0,2,4,5 ), express F'+G as Product of Maxterms by filling in the single blank below:F'+G= ∏M (__?)
Below is a Python function definition for a linear search of a list Ist for element. It returns the first index at which element can be found in the list (or None) if element is not in the list. def linearSearch(1st, element): i = 0 for item in 1st: if element == item: return i else: i += 1 return None Write a similar MATLAB function linearSearch.m. Your MATLAB function should take as parameters an unsorted list of non-negative integers, and an integer value, and returns the index where that value is first located in the list. (No argument testing is required.) Unlike the Python code which returns None if the value is not in the array, your MATLAB function should return the value -1 if the value is not found.
Describe an efficient way of putting a VECTOR representing a deck of n cards into random order in C++. You may use the function randomlnt(n), which returns a random number between 0 and n-1, inclusive. Your method should guarantee that every possible ordering is equally likely. What is the running time of your function?
Below is a Python function definition for a linear search of a list lst for element. It returns the first index at which element can be found in the list (or None) if element is not in the list. def linearSearch(lst, element): i = 0 for item in lst: if element == item: return i else: i += 1 return None Write a similar MATLAB function linearSearch.m. Your MATLAB function should take as parameters an unsorted list of non-negative integers, and an integer value, and returns the index where that value is first located in the list. (No argument testing is required.) Unlike the Python code which returns None if the value is not in the array, your MATLAB function should return the value -1 if the value is not found.
You are given a list of integers nums and a positive integer k. Your task is to implement a function find_subsequence(nums, k) that returns the length of the longest increasing subsequence of nums such that the difference between the maximum and minimum element in the subsequence is at most k. For example, given the list [1, 3, 2, 4] and k = 2, the longest increasing subsequence satisfying the condition has length 2 and is [1, 2]. You may assume that the list nums has at least one element and that k is at least 1. Constraints: The list nums has at most length $10^6$. Examples: find_subsequence([1, 3, 2, 4], 2) => 2 find_subsequence([1, 2, 3, 4, 5], 1) => 5 find_subsequence([5, 4, 3, 2, 1], 3) => 1 find_subsequence([1, 2, 3, 2, 3, 4, 5, 4, 5, 6], 2) => 4
A matrix M with i rows, j columns can be transposed into a matrix N having j rows and i columns by simply setting the value of N a,b equal to the value of M b,a for all relevant values of a and b. a. Write a function trasposeMatrix() that takes as an argument a 4 x 5 matrix and a 5 x 4 matrix. Have the function transpose the 4 x 5 matrix and store the results in the 5 x 4 matrix. Also write a main() to test the function. b. Using variable-length arrays, rewrite the transportMatrix() function developed in a. to take the number of rows and columns as arguments, and to transpose the matrix of the specified dimension

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