设计一个数据结构，以支持在Θ(1)时间内进行以下操作。
insert(x)：将x插入数据结构(如果尚不存在)。
remove(x)：从数据结构中删除项x(如果存在)。
search(x)：在数据结构中搜索项目x。
getRandom()：从当前元素集中返回一个随机元素
我们可以使用散列来支持Θ(1)时间中的前3个运算。怎么做第四次手术?这个想法是将可调整大小的数组( JavaArrayList，C中为vector)与哈希一起使用。可调整大小的数组支持以Θ(1)摊销的时间复杂度进行插入。要实现getRandom()，我们可以简单地选择一个从0到size-1的随机数(size是当前元素的数量)并在该索引处返回该元素。哈希图将数组值存储为键，并将数组索引存储为值。
以下是详细的操作。
插入(x)
1)通过执行哈希映射查找来检查x是否已经存在。
2)如果不存在，则将其插入数组的末尾。
3)还要在哈希表中添加x，作为键，最后一个数组索引作为索引。
删除(x)
1)通过进行哈希映射查找来检查x是否存在。
2)如果存在，则找到其索引并将其从哈希映射中删除。
3)将最后一个元素与此数组中的元素交换，然后删除最后一个元素。
进行交换是因为可以在O(1)时间内删除最后一个元素。
4)更新哈希图中最后一个元素的索引。
getRandom()
1)生成一个从0到最后一个索引的随机数。
2)将数组元素返回到随机生成的索引处。
搜索(x)
在哈希图中查找x。
下面是数据结构的实现。
C++
/* C++ program to design a DS that supports folloiwng operations
in Theta(n) time
a) Insert
b) Delete
c) Search
d) getRandom */
#include
using namespace std;
// class to represent the required data structure
class myStructure
{
// A resizable array
vector arr;
// A hash where keys are array elements and vlaues are
// indexes in arr[]
map Map;
public:
// A Theta(1) function to add an element to MyDS
// data structure
void add(int x)
{
// If ekement is already present, then noting to do
if(Map.find(x) != Map.end())
return;
// Else put element at the end of arr[]
int index = arr.size();
arr.push_back(x);
// and hashmap also
Map.insert(std::pair(x, index));
}
// function to remove a number to DS in O(1)
void remove(int x)
{
// element not found then return
if(Map.find(x) == Map.end())
return;
// remove element from map
int index = Map.at(x);
Map.erase(x);
// swap with last element in arr
// then remove element at back
int last = arr.size() - 1;
swap(arr[index], arr[last]);
arr.pop_back();
// Update hash table for new index of last element
Map.at(arr[index]) = index;
}
// Returns index of element if element is present, otherwise null
int search(int x)
{
if(Map.find(x) != Map.end())
return Map.at(x);
return -1;
}
// Returns a random element from myStructure
int getRandom()
{
// Find a random index from 0 to size - 1
srand (time(NULL));
int random_index = rand() % arr.size();
// Return element at randomly picked index
return arr.at(random_index);
}
};
// Driver main
int main()
{
myStructure ds;
ds.add(10);
ds.add(20);
ds.add(30);
ds.add(40);
cout << ds.search(30) << endl;
ds.remove(20);
ds.add(50);
cout << ds.search(50) << endl;
cout << ds.getRandom() << endl;
}
// This code is contributed by Aditi Sharma Java
/* Java program to design a data structure that support folloiwng operations
in Theta(n) time
a) Insert
b) Delete
c) Search
d) getRandom */
import java.util.*;
// class to represent the required data structure
class MyDS
{
ArrayList arr; // A resizable array
// A hash where keys are array elements and vlaues are
// indexes in arr[]
HashMap hash;
// Constructor (creates arr[] and hash)
public MyDS()
{
arr = new ArrayList();
hash = new HashMap();
}
// A Theta(1) function to add an element to MyDS
// data structure
void add(int x)
{
// If ekement is already present, then noting to do
if (hash.get(x) != null)
return;
// Else put element at the end of arr[]
int s = arr.size();
arr.add(x);
// And put in hash also
hash.put(x, s);
}
// A Theta(1) function to remove an element from MyDS
// data structure
void remove(int x)
{
// Check if element is present
Integer index = hash.get(x);
if (index == null)
return;
// If present, then remove element from hash
hash.remove(x);
// Swap element with last element so that remove from
// arr[] can be done in O(1) time
int size = arr.size();
Integer last = arr.get(size-1);
Collections.swap(arr, index, size-1);
// Remove last element (This is O(1))
arr.remove(size-1);
// Update hash table for new index of last element
hash.put(last, index);
}
// Returns a random element from MyDS
int getRandom()
{
// Find a random index from 0 to size - 1
Random rand = new Random(); // Choose a different seed
int index = rand.nextInt(arr.size());
// Return element at randomly picked index
return arr.get(index);
}
// Returns index of element if element is present, otherwise null
Integer search(int x)
{
return hash.get(x);
}
}
// Driver class
class Main
{
public static void main (String[] args)
{
MyDS ds = new MyDS();
ds.add(10);
ds.add(20);
ds.add(30);
ds.add(40);
System.out.println(ds.search(30));
ds.remove(20);
ds.add(50);
System.out.println(ds.search(50));
System.out.println(ds.getRandom());
}
} Python3
'''
Python program to design a DS that
supports following operations
in Theta(n) time:
a) Insert
b) Delete
c) Search
d) getRandom
'''
import random
# Class to represent the required
# data structure
class MyDS:
# Constructor (creates a list and a hash)
def __init__(self):
# A resizable array
self.arr = []
# A hash where keys are lists elements
# and values are indexes of the list
self.hashd = {}
# A Theta(1) function to add an element
# to MyDS data structure
def add(self, x):
# If element is already present,
# then nothing has to be done
if x in self.hashd:
return
# Else put element at
# the end of the list
s = len(self.arr)
self.arr.append(x)
# Also put it into hash
self.hashd[x] = s
# A Theta(1) function to remove an element
# from MyDS data structure
def remove(self, x):
# Check if element is present
index = self.hashd.get(x, None)
if index == None:
return
# If present, then remove
# element from hash
del self.hashd[x]
# Swap element with last element
# so that removal from the list
# can be done in O(1) time
size = len(self.arr)
last = self.arr[size - 1]
self.arr[index], \
self.arr[size - 1] = self.arr[size - 1], \
self.arr[index]
# Remove last element (This is O(1))
del self.arr[-1]
# Update hash table for
# new index of last element
self.hashd[last] = index
# Returns a random element from MyDS
def getRandom(self):
# Find a random index from 0 to size - 1
index = random.randrange(0, len(self.arr))
# Return element at randomly picked index
return self.arr[index]
# Returns index of element
# if element is present,
# otherwise none
def search(self, x):
return self.hashd.get(x, None)
# Driver Code
if __name__=="__main__":
ds = MyDS()
ds.add(10)
ds.add(20)
ds.add(30)
ds.add(40)
print(ds.search(30))
ds.remove(20)
ds.add(50)
print(ds.search(50))
print(ds.getRandom())
# This code is contributed
# by Saurabh Singh输出：
2
3
40