歸併排序

#include<iostream>

using namespace std;
const int N = 100010;
int q[N];
int tmp[N];
void merge_sort(int q[],int l, int r)
{
    if(l >= r) return ;
    int mid = l + r >> 1;
    merge_sort(q, l, mid);
    merge_sort(q, mid + 1, r);
    int k = 0, i = l ,j = mid + 1;
    while(i <=mid && j<= r)
        if(q[i] <= q[j]) tmp[k++] = q[i++];
        else tmp[k++] = q[j++];
    while(i <= mid) tmp[k++] = q[i++];
    while(j <= r) tmp[k++] = q[j++];
    for(i = l,j = 0;i <= r;i++, j++) q[i] = tmp[j];
    
}
int main()
{
    int n;
    scanf("%d",&n);
    for (int i = 0; i < n; i ++ )
    {
        scanf("%d",&q[i]);
    }
    merge_sort(q, 0, n - 1);
    for (int i = 0; i < n; i ++ )
    {
        printf("%d ",q[i]);
    }
    
}
 

1.先找中間的點，與快排不一樣的是，他要求是位置在中間
2.分成左右兩邊，歸併處理左右兩邊
3.歸併排序，將左右兩個有序序列合併成一個有序的序列

逆序對數量

#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;
typedef long long LL;

const int N = 100010;
int q[N], tmp[N];
LL merge_sort(int q[],int l, int r){
    if(l >= r) return 0;
    int mid = r + l >> 1;
    LL res = merge_sort(q, l, mid) + merge_sort(q, mid + 1, r);
    int k = 0, i = l, j = mid + 1;
    while(i <= mid && j <= r)
    {
        if(q[i] <= q[j]) tmp[k++] = q[i++];
        else
        {
            res += mid - i + 1;
            tmp[k++] = q[j++];
        }
    }
    while(i <= mid) tmp[k++] = q[i++];
    while(j <= r) tmp[k++] = q[j++];
    for(i = l, j = 0; i <= r;i++, j++) q[i] = tmp[j];
    return res;
}
int main()
{
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i ++ )
    {
        scanf("%d", &q[i]);
    }
    cout << merge_sort(q, 0, n - 1);
    return 0;
}

 

會產生逆序對只會在mid的左右兩邊時，此時若i的值大於j的值，那麼i後面的數的值必然會大於j的值。