Algorithm: Multiply permutations in cycle form-2

Algorithm B

Algorithm B (Multiply permutations in cycle form). This algorithm accom-
plishes essentially the same result as Algorithm A. Assume that the elements per-
muted are named X1,X2, … ,Xn. We use an auxiliary table T[1],T[2],…,T[n];
upon termination of this algorithm, Xi goes to Xj under the input permutation
if and only if T[i] = j.
B1. [Initialize.] Set T[k] <– k for 1 <= k <= n. Also, prepare to scan the input
from right to left.
B2. [Next element.] Examine the next element of the input (right to left). If
the input has been exhausted, the algorithm terminates. If the element is a
“)”, set Z <– 0 and repeat step B2; if it is a “(“, go to B4. Otherwise the
element is xi for some i; go on to B3.
B3. [Change T[i].] Exchange Z <–> T[i]. If this makes T[i] = 0, set j <– i. Return
to step B2.
B4. [Change T[j].] Set T[j] <– Z. (At this point, j is the row that shows a “)”
entry in the notation of Table 2, corresponding to the right parenthesis that
matches the left parenthesis just scanned.) Return to step B2. |

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Flow diagram

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Data table

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Java program

import java.io.BufferedReader;import java.io.IOException;import java.io.InputStreamReader;/** * Created with IntelliJ IDEA. * User: 1O1O * Date: 12/18/13 * Time: 6:52 PM * :)~ * Multiply permutations in cycle form-2:ALGORITHMS */public class Main {    public static void main(String[] args) throws IOException {        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));        String input;        System.out.println("Please input the permutations:");        input = br.readLine();        char max = input.charAt(1);        for(int i=2; i<input.length(); i++){            if(input.charAt(i) > max){                max = input.charAt(i);            }        }        /*We know the value of n here*/        int n=(int)max-96;        int[] T = new int[n+1];        for(int i=1; i<=n; i++){          /*B1*/            T[i]=i;        }        int Z=0;        int j=0;        /*Kernel of the Algorithm*/        for(int i=input.length()-1; i>=0; i--){    /*B2*/            if(input.charAt(i) == ')'){                Z=0;            }else if(input.charAt(i) == '('){                T[j] = Z;                           /*B4*/            }else {                int temp = Z;                          /*B3*/                Z = T[(int)input.charAt(i)-96];                T[(int)input.charAt(i)-96] = temp;                if(T[(int)input.charAt(i)-96] == 0){                    j=(int)input.charAt(i)-96;                }            }        }        /*Print values of T[i], 1<=i<=n*/        System.out.println();        System.out.println("Print values of T[i] (1<=i<=n):");        for(int k=1; k<=n; k++){            System.out.println("T["+k+"]="+T[k]);        }        /*Print the final results*/        System.out.println();        System.out.println("The final results is:");        int[] tag = new int[n+1];        for(int k=1; k<=n; k++){            if(tag[k] == 0){                System.out.print('(');                System.out.print((char)(k+96));                tag[k] = 1;                int index=k;                while (T[index] != k){                    index = T[index];                    System.out.print((char)(index+96));                    tag[index] = 1;                }                System.out.print(')');            }        }    }}

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Inputs & Outputs

Please input the permutations:(acfg)(bcd)(aed)(fade)(bgfae)Print values of T[i] (1<=i<=n):T[1]=4T[2]=3T[3]=5T[4]=7T[5]=2T[6]=6T[7]=1The final results is:(adg)(bce)(f)

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Reference

<< The Art of Computer Programming: Fundamental Algorithms >> VOLUME 1, DONALD E. KNUTH