zoj 2112 (主席树,树状数组套线段树)
来源:互联网 发布:mac 查看php版本 编辑:程序博客网 时间:2024/06/06 09:25
The Company Dynamic Rankings has developed a new kind of computer that is no longer satisfied with the query like to simply find the k-th smallest number of the given N numbers. They have developed a more powerful system such that for N numbers a[1], a[2], ..., a[N], you can ask it like: what is the k-th smallest number of a[i], a[i+1], ..., a[j]? (For some i<=j, 0<k<=j+1-i that you have given to it). More powerful, you can even change the value of some a[i], and continue to query, all the same.
Your task is to write a program for this computer, which
- Reads N numbers from the input (1 <= N <= 50,000)
- Processes M instructions of the input (1 <= M <= 10,000). These instructions include querying the k-th smallest number of a[i], a[i+1], ..., a[j] and change some a[i] to t.
Input
The first line of the input is a single number X (0 < X <= 4), the number of the test cases of the input. Then X blocks each represent a single test case.
The first line of each block contains two integers N and M, representing N numbers and M instruction. It is followed by N lines. The (i+1)-th line represents the number a[i]. Then M lines that is in the following format
Q i j k or
C i t
It represents to query the k-th number of a[i], a[i+1], ..., a[j] and change some a[i] to t, respectively. It is guaranteed that at any time of the operation. Any number a[i] is a non-negative integer that is less than 1,000,000,000.
There're NO breakline between two continuous test cases.
Output
For each querying operation, output one integer to represent the result. (i.e. the k-th smallest number of a[i], a[i+1],..., a[j])
There're NO breakline between two continuous test cases.
Sample Input
2
5 3
3 2 1 4 7
Q 1 4 3
C 2 6
Q 2 5 3
5 3
3 2 1 4 7
Q 1 4 3
C 2 6
Q 2 5 3
Sample Output
3
6
3
6
题意:查找区间第K大值,值可修改
分析:
每一棵线段树是维护每一个序列前缀的值在任意区间的个数,
如果还是按照静态的来做的话,那么每一次修改都要遍历O(n)棵树,
时间就是O(2*M*nlogn)->TLE
考虑到前缀和,我们通过树状数组来优化,即树状数组套主席树,
每个节点都对应一棵主席树,那么修改操作就只要修改logn棵树,
o(nlognlogn+Mlognlogn)时间是可以的,
但是直接建树要nlogn*logn(10^7)会MLE
我们发现对于静态的建树我们只要nlogn个节点就可以了,
而且对于修改操作,只是修改M次,每次改变俩个值(减去原先的,加上现在的)
也就是说如果把所有初值都插入到树状数组里是不值得的,
所以我们分两部分来做,所有初值按照静态来建,内存O(nlogn),
而修改部分保存在树状数组中,每次修改logn棵树,每次插入增加logn个节点
代码:
//#pragma comment(linker,"/STACK:102400000,102400000")#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>#include <stack>#include <map>#include <set>#include <vector>#include <queue>#define mem(p,k) memset(p,k,sizeof(p));#define pb push_back//#define lson l,m,rt<<1//#define rson m+1,r,rt<<1|1#define inf 0x3f3f3f3f#define ll long longusing namespace std;const int N=50010 ;struct SD{ int flag,l,r,k;}que[10010];int T,n,q,len,tot;int num[N],head1[N],head2[N];int tree[N*50],lson[N*50],rson[N*50],use[N];char s[2];vector<int> vec;int Hash(int k){ //cout<<lower_bound(vec.begin(),vec.end(),k)-vec.begin()+1; return lower_bound(vec.begin(),vec.end(),k)-vec.begin()+1;}void update(int pre,int &now,int k,int val,int l,int r){ now=tot++; tree[now]=tree[pre]+val; lson[now]=lson[pre];rson[now]=rson[pre]; if(l==r)return; int m=(l+r)>>1; if(k<=m)update(lson[pre],lson[now],k,val,l,m); else update(rson[pre],rson[now],k,val,m+1,r);}int lowbit(int i){ return -i&i; }void add(int k,int f,int val){ for(int i=k;i<=n;i+=lowbit(i)){ update(head2[i],head2[i],f,val,1,len); }}int sum(int k){ int s=0; for(int i=k;i>0;i-=lowbit(i)){ s+=tree[lson[use[i]]]; } return s;}int Query(int L,int R,int k){ int s1=head1[L-1],s2=head1[R],l=1,r=len; for(int i=L-1;i>0;i-=lowbit(i))use[i]=head2[i]; for(int i=R;i>0;i-=lowbit(i))use[i]=head2[i]; //cout<<L<<R<<"==="<<endl; while(l<r){ int tmp=sum(R)-sum(L-1)+tree[lson[s2]]-tree[lson[s1]]; int m=(l+r)>>1;//cout<<tmp<<" "<<k<<endl; if(k<=tmp){ r=m; s1=lson[s1];s2=lson[s2]; for(int i=L-1;i>0;i-=lowbit(i))use[i]=lson[use[i]]; for(int i=R;i>0;i-=lowbit(i))use[i]=lson[use[i]]; } else{ k-=tmp; l=m+1; s1=rson[s1],s2=rson[s2]; for(int i=L-1;i>0;i-=lowbit(i))use[i]=rson[use[i]]; for(int i=R;i>0;i-=lowbit(i))use[i]=rson[use[i]]; }//cout<<l<<r<<endl; } //cout<<" ~~~~~~ "<<endl; return vec[l-1];}int main(){ cin>>T; while(T--){ cin>>n>>q; tot=1; vec.clear(); mem(tree,0); mem(lson,0); mem(rson,0); for(int i=1;i<=n;i++)scanf("%d",num+i),vec.pb(num[i]); for(int i=1;i<=q;i++){ scanf("%s",s); if(s[0]=='Q'){ que[i].flag=0; scanf("%d%d%d",&que[i].l,&que[i].r,&que[i].k); } else{ que[i].flag=1; scanf("%d%d",&que[i].l,&que[i].k); vec.pb(que[i].k); } } sort(vec.begin(),vec.end()); vec.erase(unique(vec.begin(),vec.end()),vec.end()); len=vec.size(); //for(int i=0;i<vec.size();i++)cout<<vec[i]<<endl; head1[0]=0; for(int i=1;i<=n;i++){ update(head1[i-1],head1[i],Hash(num[i]),1,1,len); } for(int i=1;i<=n;i++){ head2[i]=0; } for(int i=1;i<=q;i++){ if(que[i].flag){ add(que[i].l,Hash(num[que[i].l]),-1); add(que[i].l,Hash(que[i].k),1); num[que[i].l]=que[i].k; } else{ printf("%d\n",Query(que[i].l,que[i].r,que[i].k)); } } } return 0;}
- zoj 2112 (主席树,树状数组套线段树)
- zoj 2112 (主席树,树状数组套线段树)
- ZOJ 2112 [树状数组套主席树]
- bzoj 1901 ZOJ 2112 Dynamic Rankings [树状数组套主席树] [线段树套平衡树]
- ZOJ 2112 Dynamic Rankings(树状数组套主席树)
- ZOJ 2112 Dynamic Rankings(主席树套树状数组+静态主席树)
- ZOJ 2112 Dynamic Rankings [树状数组套主席树]
- zoj 2112(主席树套树状数组+优化)
- ZOJ 2112 Dynamic Rankings (动态第k大,树状数组套主席树)★★
- ZOJ 2112 Dynamic Rankings (动态第k大,树状数组套主席树)
- zoj 2112 Dynamic Rankings(动态第k大,树状数组套主席树)
- 主席树&树状数组套主席树
- ZOJ 2112 Dynamic Rankings 树状数组套主席树 动态第K大
- ZOJ 2112 Dynamic Rankings [树状数组套主席树 || CDQ分治&整体二分]
- zoj 2112 树状数组 套主席树 动态求区间 第k个数
- 动态区间第k小(主席树+线段树套树状数组)
- bzoj 1901(主席树套树状数组)
- bzoj1901 [ Zju2112 ] --树状数组套主席树
- JS实现网页换肤
- 面试->面试题
- 洛谷 p1137 topsort正解的证明
- 12判词
- Logistic回归简介
- zoj 2112 (主席树,树状数组套线段树)
- 前端常见跨域解决方案(全)
- CNN for Face Alignment 深度神经网络的初次尝试
- 如何快速阅读——《应用篇》
- and...or的 彻底研究
- 从后台获得数据,前台实现数据加载和异步查询
- JDK9的32位版本下载
- GNU常用命令
- unity3D与Socket通信_01