算法题② —— 链表专栏

1. 链表数据结构

struct ListNode {
	int val;
	ListNode *next;
	ListNode() : val(0), next(nullptr) {}
	ListNode(int x) : val(x), next(nullptr) {}
	ListNode(int x, ListNode *next) : val(x), next(next) {}
  };

2. 链表的删除

2.1 移除链表元素

力扣：https://leetcode.cn/problems/remove-linked-list-elements/description/

ListNode* removeElements(ListNode* head, int val) {
	if(head == NULL) return NULL;
	ListNode *dummy= new ListNode(-1);
    dummy->next = head;
    ListNode *pre = dummy;
    ListNode *cur = head;
    while(cur){
        if(cur->val == val){
            ListNode *tmp = cur->next;
            pre->next = tmp;
            delete(cur);
            cur = tmp;
        }
        else{
            pre = cur;
            cur = cur->next;
        }
    }
    return dummy->next;
}

2.2 删除链表的倒数第N个节点

力扣：https://leetcode.cn/problems/remove-nth-node-from-end-of-list/description/

ListNode* removeNthFromEnd(ListNode* head, int n) {
    ListNode* dummyHead = new ListNode(-1);
    dummyHead->next = head;
    ListNode* slow = dummyHead;
    ListNode* fast = dummyHead;
    while(n-- && fast) {
        fast = fast->next;
    }
    fast = fast->next; // fast再提前走一步，因为需要让slow指向删除节点的上一个节点
    while (fast) {
        fast = fast->next;
        slow = slow->next;
    }
    slow->next = slow->next->next; 
    ListNode *tmp = slow->next;
    slow->next = tmp->next;
    delete tmp;
    return dummyHead->next; 
}

3. 链表的移动

3.1 反转链表

力扣：https://leetcode.cn/problems/reverse-linked-list/description/

ListNode* reverseList(ListNode* head) {
    if(head == NULL) return NULL;
    if(head->next == NULL) return head;
    ListNode *pre = NULL;
    ListNode *cur = head;
    while(cur){
        ListNode *tmp = cur->next;
        cur->next = pre;
        pre = cur;
        cur = tmp;
    }
    return pre;
}

3.2 两两交换链表节点

力扣：https://leetcode.cn/problems/swap-nodes-in-pairs/description/

ListNode* swapPairs(ListNode* head) {
    if(head == NULL) return NULL;
    if(head->next == NULL) return head;
    ListNode *dummy = new ListNode(-1);
    dummy->next = head;
    ListNode *pre = dummy;
    ListNode *cur = head;
    while(cur && cur->next){
        ListNode *tmp = cur->next;
        cur->next = tmp->next;
        tmp->next = cur;
        pre->next = tmp;
        pre = cur;
        cur = cur->next;
    }
    return dummy->next;
}

3.3 反转链表的一部分

力扣：https://leetcode.cn/problems/reverse-linked-list-ii/description/

ListNode *reverseBetween(ListNode *head, int left, int right) {
    ListNode *dummy = new ListNode(-1);
    dummy->next = head;
    ListNode *pre = dummy;
    // 第 1 步：从虚拟头节点走 left - 1 步，来到 left 节点的前一个节点
    for (int i = 0; i < left - 1; i++) {
        pre = pre->next;
    }
    // 第 2 步：从 pre 再走 right - left + 1 步，来到 right 节点
    ListNode *rightNode = pre;
    for (int i = 0; i < right - left + 1; i++) {
        rightNode = rightNode->next;
    }
    // 第 3 步：切断出一个子链表（截取链表）
    ListNode *leftNode = pre->next;
    ListNode *curr = rightNode->next;
    pre->next = nullptr;
    rightNode->next = nullptr;
    // 第 4 步：同上一题，反转链表的子区间
    reverseLinkedList(leftNode);
    // 第 5 步：接回到原来的链表中
    pre->next = rightNode;
    leftNode->next = curr;
    return dummy->next;
}

3.4 K个一组反转链表

力扣：https://leetcode.cn/problems/reverse-nodes-in-k-group/description/

ListNode* reverseKGroup(ListNode* head, int k) {
    ListNode *dummy = new ListNode(-1);
    dummy->next = head;         
    ListNode *left = head;       //每组的第一个
    ListNode *right = dummy;     //每组的第k个，初始为left的前一个节点
    ListNode *beforePre = dummy; //反转前本组的前驱
    while(left){
        for(int i = 0; i < k; ++i){
            if(right->next) right = right->next;
            else return dummy->next;  //不足k个结点，反转结束
        }
        ListNode *beforeNext = right->next; //即为下一组的left
        ListNode *pre = nullptr;
        ListNode *cur = left;
        while(pre != right){
            ListNode *tmp = cur->next;
            cur->next = pre;
            pre = cur;
            cur = tmp;
        }
        beforePre->next = right;
        left->next = beforeNext;
        right = left;
        beforePre = left;
        left = beforeNext;
    }
    return dummy->next;
}

3.5 旋转链表

力扣：https://leetcode.cn/problems/rotate-list/description/

3.6 分隔链表

力扣：https://leetcode.cn/problems/partition-list/description/

4. 链表的相交

4.1 链表相交

力扣：https://leetcode.cn/problems/intersection-of-two-linked-lists-lcci/description/

ListNode *getIntersectionNode(ListNode *headA, ListNode *headB) {
    ListNode* curA = headA;
    ListNode* curB = headB;
    int lenA = 0, lenB = 0;
    while (curA) { 
        lenA++;
        curA = curA->next;
    }
    while (curB) { 
        lenB++;
        curB = curB->next;
    }
    curA = headA;
    curB = headB;
    int gap = 0;
    if (lenB > lenA) {
        gap = lenB -lenA;
        while(gap--) curB = curB->next;
    }
    else{ 
        gap = lenA - lenB;
        while (gap--) curA = curA->next;
    }
    while (curA) {
        if (curA == curB) return curA;
        curA = curA->next;
        curB = curB->next;
    }
	return NULL;
}

4.2 合并链表

力扣：https://leetcode.cn/problems/merge-two-sorted-lists/description/

4.3 环形链表

力扣：https://leetcode.cn/problems/linked-list-cycle-ii/description/

ListNode *detectCycle(ListNode *head) {
    ListNode* fast = head;
    ListNode* slow = head;
    while(fast && fast->next) {
        slow = slow->next;
        fast = fast->next->next;
        if (slow == fast) {
            ListNode* index1 = fast;
            ListNode* index2 = head;
            while (index1 != index2) {
                index1 = index1->next;
                index2 = index2->next;
            }
            return index2; // 返回环的入口
        }
    }
    return NULL;
}

判断环入口的方法：
- 相遇时，slow指针走过的节点数为: x + y， fast指针走过的节点数：x + y + n (y + z)
- 因为fast指针是一步走两个节点，slow指针一步走一个节点，所以 (x + y) * 2 = x + y + n (y + z)，得到 x = n (y + z) - y
- 整理公式之后为如下公式：x = (n - 1) (y + z) + z
- 当 n = 1 时，得到 x = z，这就意味着：从头结点出发一个指针，从相遇节点也出发一个指针，这两个指针每次只走一个节点，那么当这两个指针相遇的时候就是环形入口的节点

在这里插入图片描述