For each of the following functions, determine the running time in terms of O in the variable n. Show your work. We're more interested in the thought process than the final answer. void programA(int n) { long prod = 1; for (int c=n;c>0;c=c/2) = prod %3D prod c; } void programB(int n) { long prod for (int c=1;c

For each of the following functions, determine the running time in terms of O in the variable n. Show your work. We're more interested in the thought process than the final answer. void programA(int n) { long prod = 1; for (int c=n;c>0;c=c/2) = prod %3D prod c; } void programB(int n) { long prod for (int c=1;c

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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Consider the following function and answer the ensuing questions. function pesky(n) 1. r := 0; 2. for i := 1 to n do 3. for j := 1 to i do 4. for k := j to i + j do 5. r := r + 1 6. return(r) a) What is the value of r returned by the following function, when n = 5? b) What is the time complexity of the function?
Write the Fibonacci Function program with: Recursive and Iterative method respectively using the following condition: Fib (1) is 1 Fib (2) is 1 Fib (N) is Fib (N-2) + Fib (N-1), for N > 2 Show the Hand Simulations of activation records for both the programs and display the output
Information is present in the screenshot and below. Based on that need help in solving the code for this problem in python. The time complexity has to be as less as possible (nlogn or n at best, no n^2). Apply dynamic programming. Do not use recursion. Make sure ALL test cases return expected outputs. Output FormatOutput a single line containing the fastest time to get to square N from square 1. Sample Input 05 2 1 4 13 Sample Output 06 Explanation 0The optimal answer is to: RUN to square 2 (+2 seconds). Sonic now has 1 energy. DASH to square 3 (+1 second). Sonic now has 0 energy. RUN to square 4 (+2 seconds). Sonic now has 1 energy. DASH to square 5 (+1 second). Sonic now has 0 energy. Total time is 6 seconds. Sample Input 15 4 2 10 0 Sample Output 112 Explanation 1The optimal answer is to: RUN to square 2 (+4 seconds). Sonic now has 1 energy. RUN to square 3 (+4 seconds). Sonic now has 2 energy. DASH to square 4 (+2 seconds). Sonic now has 1 energy.…
What is the effect in the time required to solve a problem when you increase the size of the input from n ton + 1, assuming that the number of milliseconds the algorithm uses to solve the problem with input size n iseach of these functions? [Express your answer in the simplest form possible, either as a ratio or a difference. Youranswer may be a function of n or a constant.]a) log n b) 100n c) n^2 d) 2^n e) n!
The binomial coefficient C(N,k) can be defined recursively as follows: C(N,0) = 1, C(N,N) = 1, and for 0 < k < N, C(N,k) = C(N-1,k) + C(N - 1,k - 1). Write a function and give an analysis of the running time to compute the binomial coefficients as follows: A. The function is written using dynamic programming.
Let recursive algorithm F be defined as follows: F(int n):if n=1 then return 1else return F(n-1)*n (a) i. Assuming x is a positive integer, what mathematical expression is returned by F(x)?ii. Repeat (i) but assume the line “return 1” is replaced by “return 0”? (b) Which of the following replacements for the last line will yield a function guaranteed to terminate for all valid inputs? i. return F(n-2)+2ii. return F( )*2iii. return F( )*2
Question 4 Consider the following function:function HappyAlgo(n)sum = 0for (i = 1, i <= n, i = i ∗ 4) dofor (j = 0, j < i, j = j + 2) dosum = sum + (i + j)end forend forreturn sumend functionc) Define a runtime expression T (n) for the number of iterations run by HappyAlgo in terms of n.d) Define a tight upper bound (using Big–O notation) for the number of iterations run by HappyAlgoin terms of n. ... .
The function below has the recursive relation T(x,y) = 2T(y/2)+O(1) when x,y>0Knowing these information, find the following: 1) The worst-case time complexity of the function2) The worst-case auxiliary space complexity of the function3) Explanation as to how the time complexity of the function can be improved without using multiplication operations.
Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solutions including original diagram for part a!
Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solution!
This problem exercises the basic concepts of game playing, using tic-tac-toe (noughtsand crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3 = 1 and −1 to any position with O3 = 1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval (s) = 3X2(s)+X1(s)−(3O2(s)+O1(s))."Mark on your tree the evaluations of all the positions at depth 2."
Consider the functionf :: Int -> Intf n = if n==0then 0else 1 + (f(n-1))Use induction to show that the function f returns the value of n for all possible inputs n ≥0.Here are the steps:1. Verify that f 0 returns 0 to show the base case.2. Show that if f(n-1) returns n −1 then f n returns n.3. Since you have shown the base case and the induction step, you can confidentlystate that the function works for all possible nonnegative input values.Hint: To show that ”if f(n-1) returns n −1 then f n returns n” is valid you need toassume that f(n-1) returns n −1 and then argue that it must follow that f n returnsn. Use the definition of the function and just a little bit of algebra.Criteria for Success: You have clearly written down all three steps of the inductive proof. Your proof contains complete sentences which explain all the steps andthe algebra. I don’t want to see just a bunch of symbols on a page!