Consider the following problem: Input: a set of N positive integers A = {a1, a2,..., an} and a positive integer t Output: the total number of ways to add numbers in A to add up to t. Numbers may be repeated. Example: A = {1, 2} and t = 6; There are 4 ways: (a) 1+1+1+1+1+1 (b) 1+1+1+1+2 (c) 1+1+2+2 (d) 2+2+2 (a) Give a recurrence to solve the problem. (b) Compute the time and space complexity when your recurrence is implemented (c) Given A = {1, 2, 3, 5} and t = 7, how many ways can you add up to 7 if numbers can be repeated?

Consider the following problem: Input: a set of N positive integers A = {a1, a2,..., an} and a positive integer t Output: the total number of ways to add numbers in A to add up to t. Numbers may be repeated. Example: A = {1, 2} and t = 6; There are 4 ways: (a) 1+1+1+1+1+1 (b) 1+1+1+1+2 (c) 1+1+2+2 (d) 2+2+2 (a) Give a recurrence to solve the problem. (b) Compute the time and space complexity when your recurrence is implemented (c) Given A = {1, 2, 3, 5} and t = 7, how many ways can you add up to 7 if numbers can be repeated?

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

Consider a real estate company that owns homes on a very long street. Each home on that street is for sale and each home has a, potentially, different integer price in dollars from any other home on the street. What is the largest number of homes a potential buyer can buy, provided that the buyer cannot purchase (immediately) neighboring homes? Using standard pseudo-code notation (it can be similar to Python, for example), write a dynamic programming algorithm (bottom-up) that solves this problem for any n number of homes on such a street.
Create a program in Python that takes a user's inputted set of data points, x and y values, until the user enters q to quit. The program should then ask the user for any x value and then have a y value returned, where the y value is the best estimate, using linear interpolation/extrapolation, from the nearest x value. The user should be able to repeatedly interpolate or extrapolate until they enter q.
Implement the vacuum cleaning agent function in Python/Java for the scenario described below: Consider two-dimensional Boolean array of size m x n (m and n can each be equal to 4) where m is the number of rows, and n is the number of columns. Obtain numerical positive integer values for m and n as inputs from the user. Generate random numbers and scale them down to either a “0” or a “1” according to whether they represent “Clean” or “Dirty”, respectively. After filling the array with 0s or 1s, start at some random array position indicating the initial position of the vacuum cleaner. First check if at that current position, there is the presence of a “Dirt” or not determined by whether 0 or 1 is filled in at that initial position of the vacuum cleaner. If there is a “Dirt”, clean it, and if there is no “Dirt” do a No-operation. After this is done, generate random numbers modulo 4 to obtain random numbers 0, 1, 2, 3 indicating whether to take a left, right, up or down correspondingly. If…
Write a program that takes an integer N and uses the function “np.random.randint(low = 0, high = N)” to generate a random sequence of integers between 0 and N-1. Run experiments to validate the hypothesis that the number of integers generated before the first repeated value is found is “~sqrt(pi * N / 2)”. please help with last part Show that as n increases (e.g. with a doubling experiment), from n = 2 to n = 1,000, the value of “day_sim(n)” approaches “sqrt(pi * n / 2)”.
Write a function triple_riffle_repeat(mylist,n) which takes as input a list (again with length a multiple of 3) and outputs the result of doing a 3-way riffle shufffle n times Write a function period(m) which takes as input a number m (which we will always take as a multiple of 3) and outputs the smallest positive integer n so that triple_riffle_repeat(list(range(m)),n) == list(range(m)) Discuss, with evidence, the outputs of your function period for different values of m, writing your answer as a comment.
3. Write a program to evaluate a polynomial \[ p(x)=c_{n} x^{n}+c_{n-1} x^{n-1}+\cdots+c_{2} x^{2}+c_{1} x+c_{0} \] and its derivative at a given pointt. The input is the row vectorcof coefficients of the polynomial arranged from highest to lowest power, and the numbert, and the two outputs arep(t)andp′(t). Computep(t)by first computing the row véctor \[ \left[t^{n}, t^{n-1}, \ldots, t^{2}, t, 1\right] \] and combine that with the vectorcto get the result. Computep′(t)by computing the coefficients of the derivative polynomial from the vectorc, and then evaluating that polynomial in the same way. Include some tests that provide evidence that your code produces the correct results. Please give proper explanation and typed answer only.
Write a program that reads from stdin and filters out duplicate lines of input. It should read lines from stdin, and then print each unique line along with a count of how many times it appeared. Input is case-sensitive, so “hello” and “Hello” are not duplicates. There can be an arbitrary number of strings, of arbitrary length. Note that only adjacent duplicates count, so if the input were the lines “hello”, “world”, and “hello” again, all three would be treated as unique. ./uniqhellohellohelloworldworld^D # close stdin3 hello2 world ./uniqhelloworldhello^D # close stdin1 hello1 world1 hello
Given a positive integer, N, the ’3N+1’ sequence starting from N is defined as follows:If N is an even number, then divide N by two to get a new value for NIf N is an odd number, then multiply N by 3 and add 1 to get a new value for N.Continue to generate numbers in this way until N becomes equal to 1For example, starting from N = 3 the complete ’3N+1’ sequence would be:3, 10, 5, 16, 8, 4, 2, 1Write code to ask the user to enter a positive integer (N) in the main() function. Write a function sequence()that receives the integer value N and display the ‘3N+1’ sequence starting from the integer value that wasreceived (entered by the user). The function must also count and return the numbers that the sequenceconsists of. The returned value must be displayed from the main() function.
consider a jewler who shows a collection of diamonds to a person. all diamonds have different integer ounce weights and are laid out in a single row on the table. what is the largest weight amount of diamonds that the person can take, provided that the person cannot select adjacent diamonds? use standard pseudocode notation similar to python to write a dynamic programming bottom up algorithm that solves this problem for any n number of diamonds.
a) Implement a function start( ) that takes as input a positive number a, rounds its logarithm base 4 to the nearest integer n, and returns the value of 1.0 x 2^n.
I need to write a recursive Java program to count the number of muck-free regions in a lagoon. The Lagoon is represented by a rectangle of N x M squares. Each square contains either muck ('M') or sand ('.'). A region is defined as a connected set of one of more squares with sand in it, where a square is considered to connect to all eight of its adjacent squares. Sample input/output is shown in picture attached
I need to write a Java program to count the number of muck-free regions in a lagoon. The Lagoon is represented by a rectangle of N x M squares. Each square contains either muck ('M') or sand ('.'). A region is defined as a connected set of one of more squares with sand in it, where a square is considered to connect to all eight of its adjacent squares. Sample input/output is shown in picture attached