Searching: Linear Probing And Insertion

Algorithm L

Algorithm L (Linear probing and insertion). This algorithm searches an M-
node table, looking for a given key K. If K is not in the table and the table is
not full, K is inserted.
The nodes of the table are denoted by TABLE[i], for 0 <= i < M, and they
are of two distinguishable types, empty and occupied. An occupied node contains
a key, called KEY[i], and possibly other fields. An auxiliary variable N is used
to keep track of how many nodes are occupied; this variable is considered to be
part of the table, and it is increased by 1 whenever a new key is inserted.
This algorithm makes use of a hash function h(K), and it uses the linear
probing sequence (20) to address the table. Modifications of that sequence are
discussed below.
L1. [Hash.] Set i <– h(K). (Now 0 <= i < M.)
L2. [Compare.] If TABLE[i] is empty, go to step L4. Otherwise if KEY[i] = K,
the algorithm terminates successfully.
L3. [Advance to next.] Set i <– i-1; if now i < 0, set i <– i+M. Go back to
step L2.
L4. [Insert.] (The search was unsuccessful.) If N = M-1, the algorithm
terminates with overflow. (This algorithm considers the table to be full
when N = M - 1, not when N = M; see exercise 15.) Otherwise set
N <– N + 1, mark TABLE[i] occupied, and set KEY[i] <– K. |

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Linear open addressing

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Java program

In this program, R1,…,RN were simplified to K1,…,KN.

package com.algorithms.searching;/** * Created with IntelliJ IDEA. * User: 1O1O * Date: 12/13/13 * Time: 6:52 PM * :)~ * Linear Probing And Insertion:Searching */public class Main {    public static int[] TABLE = new int[19];    public static int M = 19;    public static int N = 0;    public static void searchAndInsertNode(int key){        int hash = key%19;                           /*Hash function:h(K)*/        if(TABLE[hash] == 0){            TABLE[hash] = key;            N++;            System.out.println(String.format("%4s",key+":")+" not found in the hash table, then insert it in TABLE["+hash+"]");        }else {            if(key == TABLE[hash]){                System.out.println(key+" found in the hash table: TABLE["+hash+"]");            }else {                do{                    hash--;                    if(hash < 0){                        hash+=M;                    }                    if(TABLE[hash] == 0){                        if(N == M-1){                            System.out.println("Error: Hash Table Overflow!"+", Key:"+key+" can not be inserted!");                            break;                        }else {                            TABLE[hash] = key;                            N++;                            System.out.println(String.format("%4s",key+":")+" not found in the hash table, then insert it in TABLE["+hash+"]");                            break;                        }                    }                }while (true);            }        }    }    public static void main(String[] args) {        /*Prepare the Hash Table: suppose all the numbers are not zero!!!*/        System.out.println("Prepare the Hash Table:");        searchAndInsertNode(503);        searchAndInsertNode(87);        searchAndInsertNode(512);        searchAndInsertNode(61);        searchAndInsertNode(908);        searchAndInsertNode(170);        searchAndInsertNode(897);        searchAndInsertNode(275);        searchAndInsertNode(653);        searchAndInsertNode(426);        searchAndInsertNode(154);        searchAndInsertNode(509);        searchAndInsertNode(612);        searchAndInsertNode(677);        searchAndInsertNode(765);        searchAndInsertNode(703);        System.out.println();        /*Print the current Hash Table with 16 nodes*/        System.out.println("Print the current Hash Table with 16 nodes:");        for(int j=0; j<19; j++){            if(TABLE[j] != 0){                System.out.println(String.format("%3s", j+":")+TABLE[j]);            }        }        System.out.println();        /*Search Node 765 in current Hash Table*/        System.out.println("Search Node 765 in current Hash Table:");        searchAndInsertNode(765);        System.out.println();        searchAndInsertNode(1);        searchAndInsertNode(2);        searchAndInsertNode(3);        searchAndInsertNode(4);        searchAndInsertNode(5);    }}

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Outputs

Prepare the Hash Table:503: not found in the hash table, then insert it in TABLE[9] 87: not found in the hash table, then insert it in TABLE[11]512: not found in the hash table, then insert it in TABLE[18] 61: not found in the hash table, then insert it in TABLE[4]908: not found in the hash table, then insert it in TABLE[15]170: not found in the hash table, then insert it in TABLE[17]897: not found in the hash table, then insert it in TABLE[3]275: not found in the hash table, then insert it in TABLE[8]653: not found in the hash table, then insert it in TABLE[7]426: not found in the hash table, then insert it in TABLE[6]154: not found in the hash table, then insert it in TABLE[2]509: not found in the hash table, then insert it in TABLE[14]612: not found in the hash table, then insert it in TABLE[1]677: not found in the hash table, then insert it in TABLE[12]765: not found in the hash table, then insert it in TABLE[5]703: not found in the hash table, then insert it in TABLE[0]Print the current Hash Table with 16 nodes: 0:703 1:612 2:154 3:897 4:61 5:765 6:426 7:653 8:275 9:50311:8712:67714:50915:90817:17018:512Search Node 765 in current Hash Table:765 found in the hash table: TABLE[5]  1: not found in the hash table, then insert it in TABLE[16]  2: not found in the hash table, then insert it in TABLE[13]Error: Hash Table Overflow!, Key:3 can not be inserted!Error: Hash Table Overflow!, Key:4 can not be inserted!Error: Hash Table Overflow!, Key:5 can not be inserted!

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Reference

<< The art of computer programming: Sorting and Searching >> VOLUME 3, DONALD E. KNUTH