一、归并排序
代码：
1 #include <bits/stdc++.h> 2 using namespace std; 3 int a[10010];//实际排序数组 4 int b[10010];//辅助排序数组 5 int c[20030]; 6 void merge_sort(int l,int r){ 7 if(l==r){ 8 return; 9 } 10 int mid = (l+r)>>1; 11 merge_sort(l,mid); 12 merge_sort(mid+1,r); 13 14 int i = l,j = mid+1,k=l; 15 while(i<=mid&&j<=r){ 16 if(a[i]<=a[j]){ 17 b[k++] = a[i]; 18 i++; 19 }else{ 20 b[k++] = a[j]; 21 j++; 22 } 23 } 24 while(i<=mid){ 25 b[k++] = a[i]; 26 i++; 27 } 28 while(j<=r){ 29 b[k++] = a[j]; 30 j++; 31 } 32 for(int p = l;p<=r;p++){ 33 a[p] = b[p],b[p] = 0; 34 } 35 36 37 } 38 int n; 39 int main(){ 40 cin>>n; 41 for(int i = 1;i<=n;i++){ 42 cin>>a[i]; 43 } 44 merge_sort(1,n); 45 for(int i = 1;i<=n;i++){ 46 cout<<a[i]<<' '; 47 } 48 return 0; 49 }
二、merge函数
现有a数组，b数组，及用于存放结果的c数组，下标分别为1~n1,1~n2,1~n1+n2，且a与b保证有序
用法：merge（a+1,a+n1+1,b+1,b+n+1,c+1);
作用：将ab数组合并成一个有序数组，结果为c
三、瑞士轮
链接：https://www.luogu.com.cn/problem/P1309
代码：
1 #include <bits/stdc++.h> 2 using namespace std; 3 struct node{ 4 int w; 5 int s; 6 int bian; 7 }e[200010]; 8 bool cmp(const node &a,const node &b){ 9 if(a.s!=b.s){ 10 return a.s>b.s; 11 }else{ 12 return a.bian<b.bian; 13 } 14 } 15 node a[200010]; 16 node b[100010]; 17 node c[200010]; 18 int n,r,q; 19 int main(){ 20 cin>>n>>r>>q; 21 for(int i = 1;i<=2*n;i++){ 22 cin>>e[i].s; 23 e[i].bian = i; 24 } 25 for(int i = 1;i<=2*n;i++){ 26 cin>>e[i].w; 27 } 28 sort(e+1,e+2*n+1,cmp); 29 int biao1 = 0,biao2 = 0; 30 for(int i = 1;i<=r;i++){ 31 biao1 = 0,biao2 = 0; 32 for(int j = 1;j<=2*n-1;j+=2){ 33 if(e[j].w>e[j+1].w){ 34 e[j].s++; 35 a[biao1++] = e[j]; 36 b[biao2++] = e[j+1]; 37 }else{ 38 e[j+1].s++; 39 a[biao1++] = e[j+1]; 40 b[biao2++] = e[j]; 41 } 42 } 43 merge(a,a+biao1,b,b+biao2,e+1,cmp); 44 } 45 cout<<e[q].bian<<endl; 46 return 0; 47 }
思路：结构体存各选手信息
开两个数组记录每次比赛的胜者组，败者组，最后merge
四、逆序对
链接：https://www.luogu.com.cn/problem/P1908#submit
代码：
1 #include <bits/stdc++.h> 2 using namespace std; 3 long long a[500100];//实际排序数组 4 long long b[500100];//辅助排序数组 5 long long ans; 6 void merge_sort(long long l,long long r){ 7 if(l==r){ 8 return; 9 } 10 long long mid = (l+r)>>1; 11 merge_sort(l,mid); 12 merge_sort(mid+1,r); 13 14 int i = l,j = mid+1,k=l; 15 while(i<=mid&&j<=r){ 16 if(a[i]<=a[j]){ 17 b[k++] = a[i]; 18 i++; 19 }else{ 20 ans+=mid-i+1; 21 b[k++] = a[j]; 22 j++; 23 } 24 } 25 while(i<=mid){ 26 b[k++] = a[i]; 27 i++; 28 } 29 while(j<=r){ 30 b[k++] = a[j]; 31 j++; 32 } 33 for(int p = l;p<=r;p++){ 34 a[p] = b[p],b[p] = 0; 35 } 36 37 38 } 39 int n; 40 int main(){ 41 cin>>n; 42 for(int i = 1;i<=n;i++){ 43 scanf("%lld",&a[i]); 44 } 45 ans = 0; 46 merge_sort(1,n); 47 cout<<ans<<endl; 48 return 0; 49 }