# Design a structure which supports insertion and first non-repeating element in O(1) time

Design a Data structure which supports insertion and first non-repeating element in O(1) time. Operations that are supported by the data structure:

**Insertion**: Insert a element into the data structure.**First non-repeating Element**: First non-repeating element into the array.

**Note:** If there is no non-repeating element in the array then print -1.

Consider the following custom Data structure:

Insert(4):[4]Insert(1):[4, 1]Insert(4):[4, 1, 4]First_Non_Repeating Element:1

The idea is to use Doubly Linked List and a Hash-map to maintain the frequency of the elements of the array. Below is the use-cases of the Hash-map and Doubly-Linked List in this Data-structure:

**Doubly Linked-List:**to keep track of the non-repeating elements in the array.**Hash-map:**To keep track of the occurrence of the elements and the address of non-repeating elements in the Doubly Linked-List

Below is the illustration of the operations:

**Insertion:**Insert an element into the array and check the frequency of the element into the map. If it is previously occurred then remove the element from the Doubly Linked List with the help of the addresses stored in the hash-map. Finally, increase the occurrence of the element into the hash-map.**First Non-repeating element:**First Non-repeating element of the array will be the first element of the Doubly Linked List.

**Advantages of this Data-structure:**

- Insertion and First Non-repeating element in O(1) time.

**Disadvantages of this Data-structure:**

- Cannot Keep track of the order of the elements.
- Custom Data-structures will need custom Hasp-map to store the elements into the map.
- Memory Inefficient

Below is the implementation of the above approach:

## C++

`// C++ implementation of a structure` `// which supports insertion, deletion` `// and first non-repeating element` `// in constant time` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Node for doubly` `// linked list` `struct` `node {` ` ` ` ` `// Next pointer` ` ` `struct` `node* next;` ` ` ` ` `// Previous pointer` ` ` `struct` `node* prev;` ` ` ` ` `// Value of node` ` ` `int` `data;` `};` `// Head and tail pointer` `// for doubly linked list` `struct` `node *head = NULL, *tail = NULL;` `// Occurrences map container` `// to count for occurrence` `// of the element` `map<` `int` `, ` `int` `> occurrences;` `// Address map container` `// to store nodes of the` `// list which are unique` `map<` `int` `, node*> address;` `// Function to insert the element` `// into the given data-structure` `void` `insert(` `int` `value)` `{` ` ` `// Increasing count of` ` ` `// value to be inserted` ` ` `occurrences[value]++;` ` ` `// If count of element is` ` ` `// exactly 1 and is yet` ` ` `// not inserted in the list,` ` ` `// we insert value in list` ` ` `if` `(occurrences[value] == 1 &&` ` ` `address.find(value) == address.end()) {` ` ` `struct` `node* temp =` ` ` `(` `struct` `node*)` `malloc` `(` `sizeof` `(` `struct` `node));` ` ` `temp->next = NULL;` ` ` `temp->prev = NULL;` ` ` `temp->data = value;` ` ` ` ` `// Storing node mapped` ` ` `// to its value in` ` ` `// address map container` ` ` `address[value] = temp;` ` ` ` ` `// Inserting first element` ` ` `if` `(head == NULL)` ` ` `{` ` ` `head = temp;` ` ` `tail = temp;` ` ` `}` ` ` `else` ` ` `{` ` ` `// Appending` ` ` `// element at last` ` ` `tail->next = temp;` ` ` `temp->prev = tail;` ` ` `tail = temp;` ` ` `}` ` ` `}` ` ` `// if occurrence of particular` ` ` `// value becomes >1 and,` ` ` `// it is present in address` ` ` `// container(which means` ` ` `// it is not yet deleted)` ` ` `else` `if` `(occurrences[value] > 1 &&` ` ` `address.find(value) != address.end()) {` ` ` ` ` `// Taking node to be deleted` ` ` `struct` `node* temp = address[value];` ` ` ` ` `// Erasing its value from` ` ` `// map to keep track that` ` ` `// this element is deleted` ` ` `address.erase(value);` ` ` `// Deleting node in` ` ` `// doubly linked list` ` ` `if` `(temp == head) {` ` ` `temp = head;` ` ` `head = head->next;` ` ` `free` `(temp);` ` ` `}` ` ` `else` `if` `(temp == tail) {` ` ` `temp = tail;` ` ` `tail->prev->next = NULL;` ` ` `free` `(temp);` ` ` `}` ` ` `else` `{` ` ` `temp->next->prev = temp->prev;` ` ` `temp->prev->next = temp->next;` ` ` `free` `(temp);` ` ` `}` ` ` `}` `}` `// Function to find the first` `// unique element from list` `void` `findUniqueNumber()` `{` ` ` `// No element in list` ` ` `if` `(head == NULL)` ` ` `cout << ` `"-1\n"` `;` ` ` ` ` `// Head node contains` ` ` `// unique number` ` ` `else` ` ` `cout << head->data << ` `"\n"` `;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Inserting element in list` ` ` `insert(4);` ` ` `insert(1);` ` ` `insert(4);` ` ` `// Finding the first` ` ` `// unique number` ` ` `findUniqueNumber();` ` ` `cout << ` `"\n"` `;` ` ` `return` `0;` `}` |

## Python3

`# Python3 implementation of a structure` `# which supports insertion, deletion` `# and first non-repeating element` `# in constant time` ` ` `# Node for doubly` `# linked list` `class` `node:` ` ` ` ` `def` `__init__(` `self` `):` ` ` ` ` `# Next pointer` ` ` `self` `.` `next` `=` `None` ` ` ` ` `# Previous pointer` ` ` `self` `.prev ` `=` `None` ` ` ` ` `# Value of node` ` ` `self` `.data ` `=` `0` ` ` `# Head and tail pointer` `# for doubly linked list` `head ` `=` `None` `tail ` `=` `None` ` ` `# Occurrences map container` `# to count for occurrence` `# of the element` `occurrences ` `=` `dict` `()` ` ` `# Address map container` `# to store nodes of the` `# list which are unique` `address ` `=` `dict` `()` ` ` `# Function to insert the element` `# into the given data-structure` `def` `insert(value):` ` ` ` ` `global` `head, tail` ` ` ` ` `# Increasing count of` ` ` `# value to be inserted` ` ` `if` `value ` `not` `in` `occurrences:` ` ` `occurrences[value] ` `=` `0` ` ` ` ` `occurrences[value] ` `+` `=` `1` ` ` ` ` `# If count of element is` ` ` `# exactly 1 and is yet` ` ` `# not inserted in the list,` ` ` `# we insert value in list` ` ` `if` `(value ` `in` `occurrences ` `and` ` ` `occurrences[value] ` `=` `=` `1` `and` ` ` `value ` `not` `in` `address):` ` ` `temp ` `=` `node()` ` ` `temp.` `next` `=` `None` ` ` `temp.prev ` `=` `None` ` ` `temp.data ` `=` `value` ` ` ` ` `# Storing node mapped` ` ` `# to its value in` ` ` `# address map container` ` ` `address[value] ` `=` `temp` ` ` ` ` `# Inserting first element` ` ` `if` `(head ` `=` `=` `None` `):` ` ` `head ` `=` `temp` ` ` `tail ` `=` `temp` ` ` `else` `:` ` ` ` ` `# Appending` ` ` `# element at last` ` ` `tail.` `next` `=` `temp` ` ` `temp.prev ` `=` `tail` ` ` `tail ` `=` `temp` ` ` `# If occurrence of particular` ` ` `# value becomes >1 and,` ` ` `# it is present in address` ` ` `# container(which means` ` ` `# it is not yet deleted)` ` ` `elif` `(value ` `in` `occurrences ` `and` ` ` `occurrences[value] > ` `1` `and` ` ` `value ` `in` `address):` ` ` ` ` `# Taking node to be deleted` ` ` `temp ` `=` `address[value]` ` ` ` ` `# Erasing its value from` ` ` `# map to keep track that` ` ` `# this element is deleted` ` ` `address.pop(value)` ` ` ` ` `# Deleting node in` ` ` `# doubly linked list` ` ` `if` `(temp ` `=` `=` `head):` ` ` `temp ` `=` `head` ` ` `head ` `=` `head.` `next` ` ` `del` `(temp)` ` ` ` ` `elif` `(temp ` `=` `=` `tail):` ` ` `temp ` `=` `tail` ` ` `tail.prev.` `next` `=` `None` ` ` `del` `(temp)` ` ` ` ` `else` `: ` ` ` `temp.` `next` `.prev ` `=` `temp.prev` ` ` `temp.prev.` `next` `=` `temp.` `next` ` ` `del` `(temp)` ` ` `# Function to find the first` `# unique element from list` `def` `findUniqueNumber():` ` ` ` ` `global` `head` ` ` ` ` `# No element in list` ` ` `if` `(head ` `=` `=` `None` `):` ` ` `print` `(` `-` `1` `)` ` ` ` ` `# Head node contains` ` ` `# unique number` ` ` `else` `:` ` ` `print` `(head.data)` ` ` `# Driver Code` `if` `__name__` `=` `=` `'__main__'` `:` ` ` ` ` `# Inserting element in list` ` ` `insert(` `4` `)` ` ` `insert(` `1` `)` ` ` `insert(` `4` `)` ` ` ` ` `# Finding the first` ` ` `# unique number` ` ` `findUniqueNumber()` ` ` `# This code is contributed by rutvik_56` |

**Output:**

1