Write Algorithm for Constructing initial ranking in rank adjustment tournaments. Initial-Rank-Adjustment(P,S) in: set P of n unranked players in the tournament; sequence S of m non-negative integers in which Si defines the number of players that have the same rank i (m−1i=0 Si = n) out: set R of ranked players having the ranking structure S local: match sequences M and M of players

Write Algorithm for Constructing initial ranking in rank adjustment tournaments. Initial-Rank-Adjustment(P,S) in: set P of n unranked players in the tournament; sequence S of m non-negative integers in which Si defines the number of players that have the same rank i (m−1i=0 Si = n) out: set R of ranked players having the ranking structure S local: match sequences M and M of players

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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Create a ranking construction algorithm for tournaments with rank adjustment.Initial-Rank-Adjustment(P,S) in: sequence S of m non-negative integers in which Si determines the number of players who have the same rank as I (m1i=0 Si = n); set P of n unranked participants in the competition.out: set R of players with rankings according to the ranking scheme S local: M and M player match sequences
Create an algorithm for determining the initial ranking in rank adjustment tournaments.Initial-Rank-Adjustment(P,S) in: set P of n unranked tournament participants; sequence S of m non-negative integers in which Si determines the number of players with the same rank I (m1i=0 Si = n)out: R rated players with the ranking structure S local: M and M player match sequences
Write Algorithm for Round robin tournament including a scoring for the match results.Round-Robin-Tournament(P)in: sequence P of n players (1 ≤ n)out: sequence R of n players with attribute score(i)constant: score points for a winner w, for a loser , for a tie tlocal: number of rounds t
Given the following code snippet, find the following:1) Recurrence relation of func (x,y) when x>0 and length of y is n.T(x,n) = T(_) + O(_) (Just fill in the blanks)For 2-3, consider worst-case scenario and initial value of y as [1]2) Time complexity of func (x,y)3) Auxiliary Space Complexity of func (x,y)
Write Algorithm for Straightforward pairings for a round robin tournament.in: round index r (0 ≤ r ≤ 2 · (n − 1)/2); number of players n (1 ≤ n)out: sequence R of n player indices indicating the match pairings between players R2i and R2i+1, when i = 0,..., n/2 − 1; if n is odd, Rn−1 indicates the restingplayer
Algorithm for Normalized pairings for a round robin tournament.Normalized-Round-Robin-Pairings(r, n)in: round index r (0 ≤ r ≤ 2 · (n − 1)/2); number of players n (1 ≤ n)out: sequence R of n player indices indicating the match pairings between players R2iand R2i+1, when i = 0,..., n/2 − 1; if n is odd, Rn−1 indicates the restingplayer.
Given the following code snippet, find the following:1) Recurrence relation of func (x,y) when x>0 and length of y is n. Express in the form below:T(x,n) = T(?) + O(?)For 2-3, consider worst-case scenario and initial value of y as [1]2) Time complexity of func (x,y)3) Space Complexity and Auxiliary Space Complexity of func (x,y)
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!
Implement the algorithm for an optimal parenthesization of a matrix chain product as dis-cussed in the class.Use the following recursive function as part of your program to print the outcome, assumethe matrixes are namedA1, A2, ..., An.PRINT-OPTIMAL-PARENS(s, i, j){if (i=j) thenprint “A”i else{print “(”PRINT-OPTIMAL-PARENS(s,i,s[i, j])PRINT-OPTIMAL-PARENS(s, s[i, j] + 1, j)print “)”} }a- Test your algorithm for the following cases:1. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<5,10,3, X,12,5,50, Y,6>.2. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<5,10,50,6, X,15,40,18, Y,30,15, Z,3,12,5>. 3. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<50,6, X,15,40,18, Y,5,10,3,12,5, Z,40,10,30,5>. X=10 Y=20 Z=30
Algorithm for Match in a pyramid tournament.in: set P of players in the pyramid structure; players p and q (p, q ∈ P ∧((rank(p) = rank(q) ∧ ¬peerWinner(q)) ∨ (rank(p) = rank(q) − 1 ∧peerWinner(q))))out: set R of players after p and q have had a matchlocal: match outcome m
Given a set of n positive integers, C = {c1,c2, ..., cn} and a positive integer K, is there a subset of C whose elements sum to K? A dynamic program for solving this problem uses a 2-dimensional Boolean table T, with n rows and k + 1 columns. T[i,j] 1≤ i ≤ n, 0 ≤ j ≤ K, is TRUE if and only if there is a subset of C = {c1,c2, ..., ci} whose elements sum to j. Which of the following is valid for 2 ≤ i ≤ n, ci ≤ j ≤ K? a) T[i, j] = ( T[i − 1, j] or T[i, j − ci]) b) T[i, j] = ( T[i − 1, j] and T[i, j − ci ]) c) T[i, j] = ( T[i − 1, j] or T[i − 1, j − ci ]) d) T[i, j] = ( T[i − 1, j] and T[i − 1, j − cj ]) In the above problem, which entry of the table T, if TRUE, implies that there is a subset whose elements sum to K? a) T[1, K + 1] b) T[n, K] c) T[n, 0] d) T[n, K + 1]