Add 1 to a number represented as linked list

Number is represented in linked list such that each digit corresponds to a node in linked list. Add 1 to it. For example 1999 is represented as (1-> 9-> 9 -> 9) and adding 1 to it should change it to (2->0->0->0)

Below are the steps :

1. Reverse given linked list. For example, 1-> 9-> 9 -> 9 is converted to 9-> 9 -> 9 ->1.
2. Start traversing linked list from leftmost node and add 1 to it. If there is a carry, move to the next node. Keep moving to the next node while there is a carry.
3. Reverse modified linked list and return head.

Below is C++ implementation of above steps.

// C++ program to add 1 to a linked list
#include<bits/stdc++.h>

/* Linked list node */
struct Node
{
    int data;
    Node* next;
};

/* Function to create a new node with given data */
Node *newNode(int data)
{
    Node *new_node = new Node;
    new_node->data = data;
    new_node->next = NULL;
    return new_node;
}

/* Function to reverse the linked list */
Node *reverse(Node *head)
{
    Node * prev   = NULL;
    Node * current = head;
    Node * next;
    while (current != NULL)
    {
        next  = current->next;
        current->next = prev;
        prev = current;
        current = next;
    }
    return prev;
}

/* Adds one to a linked lists and return the head
   node of resultant list */
Node *addOneUtil(Node *head)
{
    // res is head node of the resultant list
    Node* res = head;
    Node *temp, *prev = NULL;

    int carry = 1, sum;

    while (head != NULL) //while both lists exist
    {
        // Calculate value of next digit in resultant list.
        // The next digit is sum of following things
        // (i) Carry
        // (ii) Next digit of head list (if there is a
        //     next digit)
        sum = carry + head->data;

        // update carry for next calulation
        carry = (sum >= 10)? 1 : 0;

        // update sum if it is greater than 10
        sum = sum % 10;

        // Create a new node with sum as data
        head->data = sum;

        // Move head and second pointers to next nodes
        temp = head;
        head = head->next;
    }

    // if some carry is still there, add a new node to
    // result list.
    if (carry > 0)
        temp->next = newNode(carry);

    // return head of the resultant list
    return res;
}

// This function mainly uses addOneUtil().
Node* addOne(Node *head)
{
    // Reverse linked list
    head = reverse(head);

    // Add one from left to right of reversed
    // list
    head = addOneUtil(head);

    // Reverse the modified list
    return reverse(head);
}

// A utility function to print a linked list
void printList(Node *node)
{
    while (node != NULL)
    {
        printf("%d", node->data);
        node = node->next;
    }
    printf("\n");
}

/* Driver program to test above function */
int main(void)
{
    Node *head = newNode(1);
    head->next = newNode(9);
    head->next->next = newNode(9);
    head->next->next->next = newNode(9);

    printf("List is ");
    printList(head);

    head = addOne(head);

    printf("\nResultant list is ");
    printList(head);

    return 0;
}

Output:

List is 1999

Resultant list is 2000

 
Recursive Implementation:
We can recursively reach the last node and forward carry to previous nodes. Recursive solution doesn’t require reversing of linked list. We can also use a stack in place of recursion to temporarily hold nodes.

Below is C++ implementation of recursive solution.

// Recursive C++ program to add 1 to a linked list
#include<bits/stdc++.h>

/* Linked list node */
struct Node
{
    int data;
    Node* next;
};

/* Function to create a new node with given data */
Node *newNode(int data)
{
    Node *new_node = new Node;
    new_node->data = data;
    new_node->next = NULL;
    return new_node;
}

// Recursively add 1 from end to beginning and returns
// carry after all nodes are processed.
int addWithCarry(Node *head)
{
    // If linked list is empty, then
    // return carry
    if (head == NULL)
        return 1;

    // Add carry returned be next node call
    int res = head->data + addWithCarry(head->next);

    // Update data and return new carry
    head->data = (res) % 10;
    return (res) / 10;
}

// This function mainly uses addWithCarry().
Node* addOne(Node *head)
{
    // Add 1 to linked list from end to beginning
    int carry = addWithCarry(head);

    // If there is carry after processing all nodes,
    // then we need to add a new node to linked list
    if (carry)
    {
        Node *newNode = new Node;
        newNode->data = carry;
        newNode->next = head;
        return newNode; // New node becomes head now
    }

    return head;
}

// A utility function to print a linked list
void printList(Node *node)
{
    while (node != NULL)
    {
        printf("%d", node->data);
        node = node->next;
    }
    printf("\n");
}

/* Driver program to test above function */
int main(void)
{
    Node *head = newNode(1);
    head->next = newNode(9);
    head->next->next = newNode(9);
    head->next->next->next = newNode(9);

    printf("List is ");
    printList(head);

    head = addOne(head);

    printf("\nResultant list is ");
    printList(head);

    return 0;
}

Output:

List is 1999

Resultant list is 2000

This article is contributed by Aditya Goel. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above