A Hash Table with Chaining

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Presentation transcript:

A Hash Table with Chaining A hash table with size m = 13, h(k) = k mod 13, Store keys: 18, 41, 90, 12, 36, 28, 54, 38, 25, 10 A 1 2 3 4 5 6 7 8 9 10 11 12 54 28 41 18 10 36 25 38 12 90

A Hash Table with Chaining A hash table with size m = 11, Key Values: A S E R C H I N G X M P L Hash value: 1 8 5 7 3 9 2 A 1 2 3 4 5 6 7 8 9 10 L A A A M X N C E P E E G R H S I

Linear Probing m = 11, h(k) = k mod 11, Keys stored in the hash table: 21, 26, 5, 13, 37, 16, 15 37 1 2 3 4 5 6 7 8 9 10 13 26 5 37 21 A

Linear Probing m = 11, h(k) = k mod 11, Keys stored in the hash table: 21, 26, 5, 13, 37, 16, 15 16 1 2 3 4 5 6 7 8 9 10 13 26 5 37 16 21 A

Linear Probing m = 11, h(k) = k mod 11, Keys stored in the hash table: 21, 26, 5, 13, 37, 16, 15 15 1 2 3 4 5 6 7 8 9 10 13 26 5 37 16 15 21 A

Linear Probing m = 19, Key values: Hash values: 1 5 18 3 8 9 14 7 13 C H I N G X M P L Hash values: 1 5 18 3 8 9 14 7 13 16 12 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A E A

Linear Probing m = 19, key hash 1 5 18 3 8 9 14 7 13 16 12 1 2 3 4 5 6 C H I N G X M P L hash 1 5 18 3 8 9 14 7 13 16 12 E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A A C E G H I N R A

Linear Probing m = 19, key hash 1 5 18 3 8 9 14 7 13 16 12 1 2 3 4 5 6 C H I N G X M P L hash 1 5 18 3 8 9 14 7 13 16 12 X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A A C E E G H I N R A

Linear Probing m = 19, key hash 1 5 18 3 8 9 14 7 13 16 12 1 2 3 4 5 6 C H I N G X M P L hash 1 5 18 3 8 9 14 7 13 16 12 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A A C E E G H I X N R A

Linear Probing m = 19, key hash 1 5 18 3 8 9 14 7 13 16 12 1 2 3 4 5 6 C H I N G X M P L hash 1 5 18 3 8 9 14 7 13 16 12 E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A A C A E E G H I X L M N P R A

Linear Probing m = 19, key hash 1 5 18 3 8 9 14 7 13 16 12 1 2 3 4 5 6 C H I N G E X A M P L E hash 1 5 18 3 8 9 14 7 13 16 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A A C A E E G H I X E L M N P R A

Linear Probing Inserting the element (k,x) Insert at T[h(k)] if empty else probe until space found Searching for the element (k,x) Look in T[h(k)] and all succeeding elements until there is a space or element is found Removing the element (k,x) Difficult!

Linear Probing Insert E then X; h(E) = 5, E -> 10 1 2 3 4 5 6 7 8 9 10 A 11 12 13 14 15 16 17 18 S E R C H I N G M P L Insert E then X; h(E) = 5, E -> 10 h(X) = 5, X -> 11 Now remove the E and search for X

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G X M P L hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A E A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A C E A R A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A C E G A I N H R A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A C E G A I E N H R A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A C E G A I E X N H R A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A C E G A I E X N H R A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A C E G A I E X N A H R A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 P 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A C E M G A I E X N A H R A

Double Hashing m = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A P C E M G A I E L X N A H R A

Double Hashing N = 19, key hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 R C H I N G E X A M P L E hash1 1 5 18 3 8 9 14 7 13 16 12 hash2 7 3 6 5 8 2 1 4 h(k,i)=[(h1(k)+ixh2(k)] mod 19 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 S A P C E M G A I E L X N A H E R A