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138. 随机链表的复制

题目描述

给你一个长度为 n 的链表，每个节点包含一个额外增加的随机指针 random ，该指针可以指向链表中的任何节点或空节点。

构造这个链表的 深拷贝。 深拷贝应该正好由 n 个 全新 节点组成，其中每个新节点的值都设为其对应的原节点的值。新节点的 next 指针和 random 指针也都应指向复制链表中的新节点，并使原链表和复制链表中的这些指针能够表示相同的链表状态。复制链表中的指针都不应指向原链表中的节点 。

例如，如果原链表中有 X 和 Y 两个节点，其中 X.random --> Y 。那么在复制链表中对应的两个节点 x 和 y ，同样有 x.random --> y 。

返回复制链表的头节点。

用一个由 n 个节点组成的链表来表示输入/输出中的链表。每个节点用一个 [val, random_index] 表示：

  • val：一个表示 Node.val 的整数。
  • random_index：随机指针指向的节点索引（范围从 0 到 n-1）；如果不指向任何节点，则为  null 。

你的代码 只 接受原链表的头节点 head 作为传入参数。

 

示例 1：

输入：head = [[7,null],[13,0],[11,4],[10,2],[1,0]]
输出：[[7,null],[13,0],[11,4],[10,2],[1,0]]

示例 2：

输入：head = [[1,1],[2,1]]
输出：[[1,1],[2,1]]

示例 3：

输入：head = [[3,null],[3,0],[3,null]]
输出：[[3,null],[3,0],[3,null]]

 

提示：

  • 0 <= n <= 1000
  • -104 <= Node.val <= 104
  • Node.random 为 null 或指向链表中的节点。

 

解法

方法一：哈希表 + 模拟

我们可以定义一个虚拟头节点 $\textit{dummy}$，用一个指针 $\textit{tail}$ 指向虚拟头节点，然后遍历链表，将链表中的每个节点都复制一份，并将每个节点及其复制节点的对应关系存储在哈希表 $\textit{d}$ 中，同时连接好复制节点的 $\textit{next}$ 指针。

接下来再遍历链表，根据哈希表中存储的对应关系，将复制节点的 $\textit{random}$ 指针连接好。

时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为链表的长度。

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"""
# Definition for a Node.
class Node:
    def __init__(self, x: int, next: 'Node' = None, random: 'Node' = None):
        self.val = int(x)
        self.next = next
        self.random = random
"""


class Solution:
    def copyRandomList(self, head: "Optional[Node]") -> "Optional[Node]":
        d = {}
        dummy = tail = Node(0)
        cur = head
        while cur:
            node = Node(cur.val)
            tail.next = node
            tail = tail.next
            d[cur] = node
            cur = cur.next
        cur = head
        while cur:
            d[cur].random = d[cur.random] if cur.random else None
            cur = cur.next
        return dummy.next

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/*
// Definition for a Node.
class Node {
    int val;
    Node next;
    Node random;

    public Node(int val) {
        this.val = val;
        this.next = null;
        this.random = null;
    }
}
*/

class Solution {
    public Node copyRandomList(Node head) {
        Map<Node, Node> d = new HashMap<>();
        Node dummy = new Node(0);
        Node tail = dummy;
        for (Node cur = head; cur != null; cur = cur.next) {
            Node node = new Node(cur.val);
            tail.next = node;
            tail = node;
            d.put(cur, node);
        }
        for (Node cur = head; cur != null; cur = cur.next) {
            d.get(cur).random = cur.random == null ? null : d.get(cur.random);
        }
        return dummy.next;
    }
}

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/*
// Definition for a Node.
class Node {
public:
    int val;
    Node* next;
    Node* random;

    Node(int _val) {
        val = _val;
        next = NULL;
        random = NULL;
    }
};
*/

class Solution {
public:
    Node* copyRandomList(Node* head) {
        Node* dummy = new Node(0);
        Node* tail = dummy;
        unordered_map<Node*, Node*> d;
        for (Node* cur = head; cur; cur = cur->next) {
            Node* node = new Node(cur->val);
            tail->next = node;
            tail = node;
            d[cur] = node;
        }
        for (Node* cur = head; cur; cur = cur->next) {
            d[cur]->random = cur->random ? d[cur->random] : nullptr;
        }
        return dummy->next;
    }
};

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/**
 * Definition for a Node.
 * type Node struct {
 *     Val int
 *     Next *Node
 *     Random *Node
 * }
 */

func copyRandomList(head *Node) *Node {
    dummy := &Node{}
    tail := dummy
    d := map[*Node]*Node{}
    for cur := head; cur != nil; cur = cur.Next {
        node := &Node{Val: cur.Val}
        d[cur] = node
        tail.Next = node
        tail = node
    }
    for cur := head; cur != nil; cur = cur.Next {
        if cur.Random != nil {
            d[cur].Random = d[cur.Random]
        }
    }
    return dummy.Next
}

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/**
 * Definition for _Node.
 * class _Node {
 *     val: number
 *     next: _Node | null
 *     random: _Node | null
 *
 *     constructor(val?: number, next?: _Node, random?: _Node) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.next = (next===undefined ? null : next)
 *         this.random = (random===undefined ? null : random)
 *     }
 * }
 */

function copyRandomList(head: _Node | null): _Node | null {
    const d: Map<_Node, _Node> = new Map();
    const dummy = new _Node();
    let tail = dummy;
    for (let cur = head; cur; cur = cur.next) {
        const node = new _Node(cur.val);
        tail.next = node;
        tail = node;
        d.set(cur, node);
    }
    for (let cur = head; cur; cur = cur.next) {
        d.get(cur)!.random = cur.random ? d.get(cur.random)! : null;
    }
    return dummy.next;
}

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/**
 * // Definition for a _Node.
 * function _Node(val, next, random) {
 *    this.val = val;
 *    this.next = next;
 *    this.random = random;
 * };
 */

/**
 * @param {_Node} head
 * @return {_Node}
 */
var copyRandomList = function (head) {
    const d = new Map();
    const dummy = new _Node();
    let tail = dummy;
    for (let cur = head; cur; cur = cur.next) {
        const node = new _Node(cur.val);
        tail.next = node;
        tail = node;
        d.set(cur, node);
    }
    for (let cur = head; cur; cur = cur.next) {
        d.get(cur).random = cur.random ? d.get(cur.random) : null;
    }
    return dummy.next;
};

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/*
// Definition for a Node.
public class Node {
    public int val;
    public Node next;
    public Node random;

    public Node(int _val) {
        val = _val;
        next = null;
        random = null;
    }
}
*/

public class Solution {
    public Node CopyRandomList(Node head) {
        Dictionary<Node, Node> d = new Dictionary<Node, Node>();
        Node dummy = new Node(0);
        Node tail = dummy;

        for (Node cur = head; cur != null; cur = cur.next) {
            Node node = new Node(cur.val);
            tail.next = node;
            tail = node;
            d[cur] = node;
        }

        for (Node cur = head; cur != null; cur = cur.next) {
            if (cur.random != null) {
                d[cur].random = d[cur.random];
            }
        }

        return dummy.next;
    }
}

方法二：模拟（空间优化）

在方法一中，我们使用了额外的哈希表来存储原节点和复制节点的对应关系，我们也可以不使用额外的空间，具体做法如下：

  1. 遍历原链表，对于每个节点，复制一个新节点并将其插入到原节点和原节点的下一个节点之间。
  2. 再次遍历链表，根据原节点的 $\textit{random}$ 指针，设置新节点的 $\textit{random}$ 指针。
  3. 最后将链表拆分为原链表和复制链表。

时间复杂度 $O(n)$，其中 $n$ 为链表的长度。忽略答案链表的空间占用，空间复杂度 $O(1)$。

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"""
# Definition for a Node.
class Node:
    def __init__(self, x: int, next: 'Node' = None, random: 'Node' = None):
        self.val = int(x)
        self.next = next
        self.random = random
"""


class Solution:
    def copyRandomList(self, head: "Optional[Node]") -> "Optional[Node]":
        if head is None:
            return None
        cur = head
        while cur:
            node = Node(cur.val, cur.next)
            cur.next = node
            cur = node.next
        cur = head
        while cur:
            cur.next.random = cur.random.next if cur.random else None
            cur = cur.next.next
        cur = head
        ans = head.next
        while cur.next:
            node = cur.next
            cur.next = node.next
            cur = node
        return ans

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/*
// Definition for a Node.
class Node {
    int val;
    Node next;
    Node random;

    public Node(int val) {
        this.val = val;
        this.next = null;
        this.random = null;
    }
}
*/

public class Solution {
    public Node copyRandomList(Node head) {
        if (head == null) {
            return null;
        }
        Node cur = head;
        while (cur != null) {
            Node node = new Node(cur.val);
            node.next = cur.next;
            cur.next = node;
            cur = node.next;
        }
        cur = head;
        while (cur != null) {
            cur.next.random = cur.random == null ? null : cur.random.next;
            cur = cur.next.next;
        }
        cur = head;
        Node ans = head.next;
        while (cur.next != null) {
            Node node = cur.next;
            cur.next = node.next;
            cur = node;
        }
        return ans;
    }
}

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/*
// Definition for a Node.
class Node {
public:
    int val;
    Node* next;
    Node* random;

    Node(int _val) {
        val = _val;
        next = NULL;
        random = NULL;
    }
};
*/

class Solution {
public:
    Node* copyRandomList(Node* head) {
        if (!head) {
            return nullptr;
        }
        Node* cur = head;
        while (cur != nullptr) {
            Node* node = new Node(cur->val);
            node->next = cur->next;
            cur->next = node;
            cur = node->next;
        }
        cur = head;
        while (cur != nullptr) {
            cur->next->random = cur->random == nullptr ? nullptr : cur->random->next;
            cur = cur->next->next;
        }
        cur = head;
        Node* ans = head->next;
        while (cur->next != nullptr) {
            Node* node = cur->next;
            cur->next = node->next;
            cur = node;
        }
        return ans;
    }
};

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/**
 * Definition for a Node.
 * type Node struct {
 *     Val int
 *     Next *Node
 *     Random *Node
 * }
 */

func copyRandomList(head *Node) *Node {
    if head == nil {
        return nil
    }
    for cur := head; cur != nil; {
        node := &Node{cur.Val, cur.Next, nil}
        cur.Next = node
        cur = node.Next
    }
    for cur := head; cur != nil; cur = cur.Next.Next {
        if cur.Random != nil {
            cur.Next.Random = cur.Random.Next
        }
    }
    ans := head.Next
    for cur := head; cur.Next != nil; {
        node := cur.Next
        cur.Next = node.Next
        cur = node
    }
    return ans
}

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/**
 * Definition for _Node.
 * class _Node {
 *     val: number
 *     next: _Node | null
 *     random: _Node | null
 *
 *     constructor(val?: number, next?: _Node, random?: _Node) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.next = (next===undefined ? null : next)
 *         this.random = (random===undefined ? null : random)
 *     }
 * }
 */

function copyRandomList(head: _Node | null): _Node | null {
    if (head === null) {
        return null;
    }
    let cur = head;
    while (cur !== null) {
        const node = new _Node(cur.val);
        node.next = cur.next;
        cur.next = node;
        cur = node.next;
    }
    cur = head;
    while (cur !== null) {
        cur.next.random = cur.random === null ? null : cur.random.next;
        cur = cur.next.next;
    }
    cur = head;
    const ans = head.next;
    while (cur.next !== null) {
        const node = cur.next;
        cur.next = node.next;
        cur = node;
    }
    return ans;
}

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/**
 * // Definition for a _Node.
 * function _Node(val, next, random) {
 *    this.val = val;
 *    this.next = next;
 *    this.random = random;
 * };
 */

/**
 * @param {_Node} head
 * @return {_Node}
 */
var copyRandomList = function (head) {
    if (head === null) {
        return null;
    }
    let cur = head;
    while (cur !== null) {
        const node = new _Node(cur.val);
        node.next = cur.next;
        cur.next = node;
        cur = node.next;
    }
    cur = head;
    while (cur !== null) {
        cur.next.random = cur.random === null ? null : cur.random.next;
        cur = cur.next.next;
    }
    cur = head;
    const ans = head.next;
    while (cur.next !== null) {
        const node = cur.next;
        cur.next = node.next;
        cur = node;
    }
    return ans;
};

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/*
// Definition for a Node.
public class Node {
    public int val;
    public Node next;
    public Node random;

    public Node(int _val) {
        val = _val;
        next = null;
        random = null;
    }
}
*/

public class Solution {
    public Node CopyRandomList(Node head) {
        if (head == null) {
            return null;
        }
        Node cur = head;
        while (cur != null) {
            Node node = new Node(cur.val);
            node.next = cur.next;
            cur.next = node;
            cur = node.next;
        }
        cur = head;
        while (cur != null) {
            cur.next.random = cur.random == null ? null : cur.random.next;
            cur = cur.next.next;
        }
        cur = head;
        Node ans = head.next;
        while (cur.next != null) {
            Node node = cur.next;
            cur.next = node.next;
            cur = node;
        }
        return ans;
    }
}

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