Question

138. 随机链表的复制

English Version

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

遍历链表，将链表中的每个节点都复制一份，然后将原节点和复制节点的对应关系存储在哈希表中，同时连接好复制节点的 $next$ 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 $random$ 指针连接好。

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

"""
# 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: "Node") -> "Node":
    d = {}
    dummy = tail = Node(0)
    cur = head
    while cur:
      tail.next = Node(cur.val)
      tail = tail.next
      d[cur] = tail
      cur = cur.next
    tail = dummy.next
    cur = head
    while cur:
      tail.random = d.get(cur.random)
      tail = tail.next
      cur = cur.next
    return dummy.next

/*
// 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) {
      tail.next = new Node(cur.val);
      tail = tail.next;
      d.put(cur, tail);
    }
    tail = dummy.next;
    for (Node cur = head; cur != null; cur = cur.next) {
      tail.random = d.get(cur.random);
      tail = tail.next;
    }
    return dummy.next;
  }
}

/*
// 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) {
    unordered_map<Node*, Node*> d;
    Node* dummy = new Node(0);
    Node* tail = dummy;
    for (auto cur = head; cur; cur = cur->next) {
      tail->next = new Node(cur->val);
      tail = tail->next;
      d[cur] = tail;
    }
    tail = dummy->next;
    for (auto cur = head; cur; cur = cur->next) {
      tail->random = d[cur->random];
      tail = tail->next;
    }
    return dummy->next;
  }
};

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

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

/**
 * 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 map = new Map<Node, Node>();
  let cur = head;
  while (cur != null) {
    map.set(cur, new Node(cur.val));
    cur = cur.next;
  }
  cur = head;
  while (cur != null) {
    map.get(cur).next = map.get(cur.next) ?? null;
    map.get(cur).random = map.get(cur.random) ?? null;
    cur = cur.next;
  }
  return map.get(head);
}

/**
 * // 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(0);
  let tail = dummy;
  for (let cur = head; cur; cur = cur.next) {
    tail.next = new Node(cur.val);
    tail = tail.next;
    d.set(cur, tail);
  }
  tail = dummy.next;
  for (let cur = head; cur; cur = cur.next) {
    tail.random = d.get(cur.random);
    tail = tail.next;
  }
  return dummy.next;
};

/*
// 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) {
      tail.next = new Node(cur.val);
      tail = tail.next;
      d[cur] = tail;
    }
    tail = dummy.next;
    for (Node cur = head; cur != null; cur = cur.next) {
      tail.random = cur.random == null ? null : d[cur.random];
      tail = tail.next;
    }
    return dummy.next;
  }
}

方法二：拼接 + 拆分

遍历链表，将链表中的每个节点都复制一份，然后将复制节点插入到原节点的后面。

接下来再遍历链表，根据原节点的 $random$ 指针，将复制节点的 $random$ 指针连接好。

最后再遍历链表，将链表拆分成原链表和复制链表。

时间复杂度为 $O(n)$，空间复杂度为 $O(1)$。其中 $n$ 为链表的长度。

"""
# 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: "Node") -> "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:
      if cur.random:
        cur.next.random = cur.random.next
      cur = cur.next.next

    ans = head.next
    cur = head
    while cur:
      nxt = cur.next
      if nxt:
        cur.next = nxt.next
      cur = nxt
    return ans

/*
// 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) {
    if (head == null) {
      return null;
    }
    for (Node cur = head; cur != null;) {
      Node node = new Node(cur.val, cur.next);
      cur.next = node;
      cur = node.next;
    }
    for (Node cur = head; cur != null; cur = cur.next.next) {
      if (cur.random != null) {
        cur.next.random = cur.random.next;
      }
    }
    Node ans = head.next;
    for (Node cur = head; cur != null;) {
      Node nxt = cur.next;
      if (nxt != null) {
        cur.next = nxt.next;
      }
      cur = nxt;
    }
    return ans;
  }
}

/*
// 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;
    }
    for (Node* cur = head; cur;) {
      Node* node = new Node(cur->val);
      node->next = cur->next;
      cur->next = node;
      cur = node->next;
    }
    for (Node* cur = head; cur; cur = cur->next->next) {
      if (cur->random) {
        cur->next->random = cur->random->next;
      }
    }
    Node* ans = head->next;
    for (Node* cur = head; cur;) {
      Node* nxt = cur->next;
      if (nxt) {
        cur->next = nxt->next;
      }
      cur = nxt;
    }
    return ans;
  }
};

/**
 * 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 != nil; {
    nxt := cur.Next
    if nxt != nil {
      cur.Next = nxt.Next
    }
    cur = nxt
  }
  return ans
}

/**
 * // 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) {
    return null;
  }
  for (let cur = head; cur; ) {
    const node = new Node(cur.val, cur.next, null);
    cur.next = node;
    cur = node.next;
  }
  for (let cur = head; cur; cur = cur.next.next) {
    if (cur.random) {
      cur.next.random = cur.random.next;
    }
  }
  const ans = head.next;
  for (let cur = head; cur; ) {
    const nxt = cur.next;
    if (nxt) {
      cur.next = nxt.next;
    }
    cur = nxt;
  }
  return ans;
};

/*
// 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;
    }
    for (Node cur = head; cur != null; ) {
      Node node = new Node(cur.val, cur.next);
      cur.next = node;
      cur = node.next;
    }
    for (Node cur = head; cur != null; cur = cur.next.next) {
      if (cur.random != null) {
        cur.next.random = cur.random.next;
      }
    }
    Node ans = head.next;
    for (Node cur = head; cur != null; ) {
      Node nxt = cur.next;
      if (nxt != null) {
        cur.next = nxt.next;
      }
      cur = nxt;
    }
    return ans;
  }
}