ZOJ -2112 Dynamic Rankings 主席树 待修改的区间第K大

Dynamic Rankings

带修改的区间第K大其实就是先和静态区间第K大的操作一样。先建立一颗主席树， 然后再在树状数组的每一个节点开线段树（其实也是主席树，共用节点）， 每次修改的时候都按照树状数组的方式去修改，并且修改那些地方。查询的时候就是查询原主席树+树状数组的值。

代码：

 #include<bits/stdc++.h>
 using namespace std;
 #define Fopen freopen("_in.txt","r",stdin); freopen("_out.txt","w",stdout);
 #define LL long long
 #define ULL unsigned LL
 #define fi first
 #define se second
 #define pb push_back
 //#define lson l,m,rt<<1
 //#define rson m+1,r,rt<<1|1
 #define max3(a,b,c) max(a,max(b,c))
 #define min3(a,b,c) min(a,min(b,c))
 typedef pair<int,int> pll;
 const int INF = 0x3f3f3f3f;
 const LL mod =  (int)1e9+;
 const int N = ;
 const int M = ;
 int root[N], S[N], lson[M], rson[M], ll[N], rr[N], cnt[M];
 int tot, t;
 int lsz, rsz;
 int a[N], b[N];
 struct Node{
     int l, r, op, k;
 }A[N];
 int Build(int l, int r){
     int now = ++tot;
     cnt[now] = ;
     if(l < r){
         int m = l+r >> ;
         lson[now] = Build(l,m);
         rson[now] = Build(m+,r);
     }
     return now;
 }
 int Update(int l, int r, int pre, int pos, int v){
     int now = ++tot;
     cnt[now] = cnt[pre] + v;
     if(l < r){
         int m = l+r >> ;
         if(pos <= m){
             rson[now] = rson[pre];
             lson[now] = Update(l, m, lson[pre], pos, v);
         }
         else {
             lson[now] = lson[pre];
             rson[now] = Update(m+, r, rson[pre], pos, v);
         }
         cnt[now] = cnt[lson[now]] + cnt[rson[now]];
     }
     return now;
 }
 int Query(int l, int r, int L, int R, int k){
     if(l == r) return l;
     int num1 = cnt[lson[L]];
     int num2 = cnt[lson[R]];
     for(int i = ; i <= lsz; i++) num1 += cnt[lson[ll[i]]];
     for(int i = ; i <= rsz; i++) num2 += cnt[lson[rr[i]]];
     num2 -= num1;
     int m = l+r >> ;
     if(num2 >= k){
         for(int i = ; i <= lsz; i++) ll[i] = lson[ll[i]];
         for(int i = ; i <= rsz; i++) rr[i] = lson[rr[i]];
         return Query(l, m, lson[L], lson[R], k);
     }
     else {
         for(int i = ; i <= lsz; i++) ll[i] = rson[ll[i]];
         for(int i = ; i <= rsz; i++) rr[i] = rson[rr[i]];
         return Query(m+, r, rson[L], rson[R], k-num2);
     }
 }
 int id(int x){
     return lower_bound(b+, b++t, x) - b;
 }
 int lowbit(int x){
     return x&(-x);
 }
 int main(){
     int T;
     scanf("%d", &T);
     while(T--){
         tot = t = ;
         int n, m;
         char s[];
         scanf("%d%d", &n, &m);
         for(int i = ; i <= n; i++) scanf("%d", &a[i]), b[++t] = a[i];
         for(int i = ; i <= m; i++){
             scanf("%s", s);
             if(s[] == 'Q'){
                 A[i].op = ;
                 scanf("%d%d%d", &A[i].l, &A[i].r, &A[i].k);
             }
             else {
                 A[i].op = ;
                 scanf("%d%d", &A[i].l, &A[i].r);
                 b[++t] = A[i].r;
             }
         }
         sort(b+, b++t);
         int tmp = ;
         for(int i = ; i <= t; i++)
             if(b[i] != b[i-]) b[++tmp] = b[i];
         t = tmp;
         root[] = Build(, t);
         for(int i = ; i <= n; i++){
             root[i] = Update(, t, root[i-], id(a[i]), );
         }
         for(int i = ; i <= n; i++) S[i] = root[];
         for(int i = ; i <= m; i++){
             if(A[i].op == ){
                 lsz = rsz = ;
                 for(int j = A[i].l-; j; j-=lowbit(j)) ll[++lsz] = S[j];
                 for(int j = A[i].r; j; j-=lowbit(j)) rr[++rsz] = S[j];
                 printf("%d\n", b[Query(,t,root[A[i].l-], root[A[i].r], A[i].k)]);
             }
             else {
                 for(int j = A[i].l; j <= t; j += lowbit(j)) S[j] = Update(, t, S[j], id(a[A[i].l]), -);
                 for(int j = A[i].l; j <= t; j += lowbit(j)) S[j] = Update(, t, S[j], id(A[i].r), );
                 a[A[i].l] = A[i].r;
             }
         }
     }
     return ;
 }

ZOJ 2112