1, You don't know hash tables
1. What is a hash table?
- We already know a data item, keyword mapping storage location.
- In fact, our search process is to compare and constantly compare keywords, so that we can find the storage location.
- Now you should find that they are like functions, X = keyword and Y = storage location.
- The difficulty of hash table is to find the mapping relationship: f(x) = y
- Call the function: hash function.
- The table established according to this idea is a hash table.
- The advantage of hash table is that it does not need to be compared continuously, but can be found directly, just once.
- Bold is the key
2. Conflict
- The mathematical definition of a function has one thing: one X is not allowed to correspond to multiple Y.
- The hash function is also a function, so there is one case left: multiple X corresponds to a Y.
- Therefore, the conflict to be solved by hash table: different keywords may get the same storage address.
- Mistakes can be resolved, but conflicts cannot be completely avoided. We usually need to set up a method to deal with conflicts.
3. Key terms
- Hash table: a table formed by a keyword corresponding to a storage location.
- Storage location = hash address = hash address
- Function relation = mapping relation = correspondence relation = hash construction = hash
- H(x) = y
2, You already know the hash table
(1) Construction method of hash function
-Objective: to construct a hash function.
-Good hash function: the keyword gets a "random address" through the hash function, so that the hash addresses of a group of keywords are evenly distributed in the whole address interval, so as to reduce conflicts.
1. Direct addressing method
H ( k e y ) = k e y or H ( k e y ) = a ∗ k e y + b H(key) = key or H(key) = a*key + b H(key)=key or H(key)=a * key+b
2. Digital analysis
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3. Square middle method - important
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Take the middle digits after the square of the keyword as the hash address
Take the middle digits after the square of the keyword as the hash address
- For example:
4. Folding method
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- Folding hair is suitable for a large number of keywords, and the numbers on each bit are roughly evenly distributed.
- For example:
5. Division and remainder method - important
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m is the table length of the hash table
m is the table length of the hash table
- It can be used with other methods.
- The choice of p is very important.
(2) . methods of handling conflicts
1. Open addressing - important
H i = ( H ( k e y ) + d i ) M O D m Hi = (H(key) + di) MOD m Hi=(H(key)+di)MODm
- H(key) is a hash function.
- m is the length of the hash table.
- di is an incremental sequence.
- The formula di = 1, 2, 3,..., m-1 is called linear detection re hashing.
- The formula di = 1^2, -1^2, 2^2, -2^2,..., K ^ 2, - K ^ 2 (k < = m / 2) is called quadratic detection hashing.
- The formula di = pseudo-random sequence is called random detection re hashing.
- For example:
2. In hash method
3. Chain address method
4. Establish a public overflow area
3, Hash table lookup code
(1) Data structure of hash table
// Storage structure of open addressing hash table
int hashsize[] = {997, ... }; // Hash table capacity increment table, an appropriate prime sequence
typedef struct {
ElemType * elem; // Dynamically allocate arrays
int count; // Number of current elements
int sizeindex; // hashsize[sizeindex] is the current capacity
}HashTable;
(2) Java code of hash table
- Construction of hash table:
/**
* Divide and remainder method to construct hash table
*
* @param keys
* @param values
* @param hashTableLength Hash table, table length, prime
*/
public Search(int[] keys, String[] values, int hashTableLength) {
length = hashTableLength;
searchTable = new DataItem[length];
for (int i = 0; i < length; i++) {
searchTable[i] = null;
}
int tempPosition;
for (int i = 0; i < keys.length; i++) {
tempPosition = keys[i] % hashTableLength;
while (searchTable[tempPosition] != null) {
tempPosition = (tempPosition + 1) % hashTableLength;
System.out.println("conflict, Move keywords forward" + keys[i]);
}
searchTable[tempPosition] = new DataItem(keys[i], values[i]);
}
}
- Hash lookup:
/**
* hash search
*
* @param key
* @return
*/
public String hashSearch(int key) {
int tempPosition = key % length;
while (searchTable[tempPosition] != null) {
if (searchTable[tempPosition].key == key) {
return searchTable[tempPosition].value;
}
tempPosition = (tempPosition + 1) % length;
}
return null;
} // hashSearch
- Test function:
public static void main(String[] args) {
int[] key = { 1, 3, 5, 6, 7, 9, 10 };
String[] values = { "if", "then", "else", "switch", "case", "for", "while" };
Search search = new Search(key, values, 13);
System.out.println(search.toString());
System.out.println("Search result of 10 is: " + search.hashSearch(10));
}
(3) . output sample
- Source code of Search class:
package search;
public class Search {
/** Lookup table */
DataItem[] searchTable;
/** Table length */
int length;
class DataItem {
/** Keyword domain */
int key;
/** Other domains */
String value;
DataItem(int key, String value) {
this.key = key;
this.value = value;
}
public String toString() {
return "[" + key + ", " + value + "]";
}
} // data item
/**
* Construct lookup table
*
* @param keys
* @param values
*/
public Search(int[] keys, String[] values) {
// TODO
if (keys.length != values.length) {
throw new RuntimeException("Key does not correspond to value!");
}
length = keys.length;
searchTable = new DataItem[length];
for (int i = 0; i < length; i++) {
searchTable[i] = new DataItem(keys[i], values[i]);
}
} // structure
/**
* Divide and remainder method to construct hash table
*
* @param keys
* @param values
* @param hashTableLength Hash table, table length, prime
*/
public Search(int[] keys, String[] values, int hashTableLength) {
length = hashTableLength;
searchTable = new DataItem[length];
for (int i = 0; i < length; i++) {
searchTable[i] = null;
}
int tempPosition;
for (int i = 0; i < keys.length; i++) {
tempPosition = keys[i] % hashTableLength;
while (searchTable[tempPosition] != null) {
tempPosition = (tempPosition + 1) % hashTableLength;
System.out.println("conflict, Move keywords forward" + keys[i]);
}
searchTable[tempPosition] = new DataItem(keys[i], values[i]);
}
}
/**
* Print lookup table
*/
public String toString() {
String resultString = "I am a search table with " + length + " data items.\r\n";
for (int i = 0; i < length; i++) {
resultString += searchTable[i] + " ";
}
return resultString;
}// toString
/**
* Sequential search
*
* @param key
* @return key Corresponding value
*/
public String sequentialSearch(int key) {
// TODO
searchTable[0].key = key; // "Sentry"
int i;
for (i = length - 1; searchTable[i].key != key; i--)
;
return searchTable[i].value;
} // sequentialSearch
/**
* Half search
*
* @param key
* @return
*/
public String binarySearch(int key) {
// TODO
int low = 0;
int high = length - 1;
int mid = (low + high) / 2;
while (low <= high) {
mid = (low + high) / 2;
if (searchTable[mid].key == key) {
return searchTable[mid].value;
} else if (searchTable[mid].key < key) {
low = mid + 1;
} else {
high = mid - 1;
}
} // Of while
return null;
}// binarySearch
/**
* hash search
*
* @param key
* @return
*/
public String hashSearch(int key) {
int tempPosition = key % length;
while (searchTable[tempPosition] != null) {
if (searchTable[tempPosition].key == key) {
return searchTable[tempPosition].value;
}
tempPosition = (tempPosition + 1) % length;
}
return null;
} // hashSearch
public static void main(String[] args) {
// TODO
System.out.println("\r\n-------sequentialSearchTest-------");
// 1 declaration
int[] keys1 = { -1, 5, 3, 6, 10, 7, 1, 9 };
String[] values1 = { "null", "if", "then", "else", "switch", "case", "for", "while" };
// Object 2
Search search1 = new Search(keys1, values1);
// 3 printing
System.out.println(search1.toString());
// 4 test
long startTime1 = System.nanoTime(); // Get start time
System.out.println("Search result of 10 is: " + search1.sequentialSearch(10));
long endTime1 = System.nanoTime(); // Get end time
System.out.println("Find time (nanoseconds): " + (endTime1 - startTime1));
System.out.println("\r\n-------binarySearchTest-------");
// 1 declaration
int[] keys2 = { 1, 3, 5, 6, 7, 9, 10 };
String[] values2 = { "if", "then", "else", "switch", "case", "for", "while" };
// 2 object
Search search2 = new Search(keys2, values2);
// 3 printing
System.out.println(search2.toString());
// 4 test
long startTime2 = System.nanoTime(); // Get start time
System.out.println("Search result of 10 is: " + search2.binarySearch(10));
long end2Time2 = System.nanoTime(); // Get end time
System.out.println("Find time (nanoseconds): " + (end2Time2 - startTime2));
System.out.println("\r\n-------hashSearchTest-------");
// 1 declaration
int[] key3 = { 1, 3, 5, 6, 7, 9, 10 };
String[] values3 = { "if", "then", "else", "switch", "case", "for", "while" };
// 2 object
Search search3 = new Search(key3, values3, 13);
// 3 printing
System.out.println(search3.toString());
// 4 test
long startTime3 = System.nanoTime(); // Get start time
System.out.println("Search result of 10 is: " + search3.hashSearch(10));
long endTime3 = System.nanoTime(); // Get end time
System.out.println("Find time (nanoseconds): " + (endTime3 - startTime3));
}
} // Search
- Output:
