排序算法-归并排序(C++、链表)
归并排序采用分而治之的方法,把n个元素按照非递减顺序排列。常用结构是:若n为1,则算法终止;否则,将序列划分为k个子序列(int k>=2)。先对每一个子序列进行排序,然后将有序子序列归并为一个序列。
归并排序的时间复杂度是Ω(nlogn),平均复杂度和最坏复杂度均为Ω(nlogn)。
假设现在初始段为[8,4,5,6,2,1,7,3]
先分:[8,4,5,6],[2,1,7,3]
再分:[8,4],[5,6],[2,1],[7,3]
子序列单独排序:[4,8],[5,6],[1,2],[3,7]
归并:[4,5,6,8],[1,2,3,7]
归并:[1,2,3,4,5,6,7,8]
代码实现:
C++实现:
#include<iostream>
#include<vector>
using namespace std;
void mergearray(vector<int>&a, int first, int mid, int last)
{
int i = first, j = mid + 1;
int m = mid, n = last;
int k = 0;
vector<int> temp;
while (i <= m && j <= n)
{
if (a[i] <= a[j])
temp.push_back(a[i++]);
else
temp.push_back(a[j++]);
k++;
}
while (i <= m)
{
temp.push_back(a[i++]); k++;
}
while (j <= n)
{
temp.push_back(a[j++]); k++;
}
for (i = 0; i <k; i++)
a[first + i] = temp[i];
}
void mergesort(vector<int>&a, int first, int last)
{
if (first < last)
{
int mid = (first + last) / 2;
mergesort(a, first, mid); //左边有序
mergesort(a, mid + 1, last); //右边有序
mergearray(a, first, mid, last); //再将二个有序数列合并
}
}
int main()
{
vector<int> a;
int i;
while (cin >> i)
{
a.push_back(i);
if (cin.get() == '\n') break;
}
mergesort(a, 0, a.size()-1);
for (auto j : a)
cout << j << ' ';
system("pause");
return 0;
}
链表实现:
class Solution {
public:
ListNode *sortList(ListNode *head) {
if(!head||!head->next) return head;
ListNode *p=head; // 第一步:快慢指针找中点
ListNode *q=head->next;
while(q&&q->next)
{
p=p->next;
q=q->next->next;
}
ListNode *right=sortList(p->next);// 后一半链表
p->next=NULL; // 注意前一半链表尾结点的next置NULL
ListNode *left=sortList(head); // 前一半链表
return merge(left,right);//归并
}
ListNode *merge(ListNode *left, ListNode *right) {
ListNode *dummy = new ListNode(-1);
ListNode *p = dummy;
// ListNode dummy(0);
//ListNode *p = &dummy;
while(left && right) {
if(left->val < right->val) {
p->next = left;
left = left->next;
}
else {
p->next = right;
right = right->next;
}
p = p->next;
}
if (left) p->next = left;
if (right) p->next = right;
//return dummy.next;
return dummy->next;
}
};