spoj DQUERY - D-query (询问区间中不同数的个数，线段树(离线) or 莫队算法（离线） or 主席树（在线）)
题目链接 题意：给出n个数，然后m个询问，每个询问一个区间[l,r],问该区间中不同的数有多少个。
思路：离线处理+线段树的做法不多说了：
/* ***********************************************
Author :111qqz
Created Time :Fri 16 Sep 2016 11:34:32 PM CST
File Name :code/spoj/dquery.cpp
************************************************ */
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <cstdlib>
#include <ctime>
#define fst first
#define sec second
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define ms(a,x) memset(a,x,sizeof(a))
typedef long long LL;
#define pi pair < int ,int >
#define MP make_pair
using namespace std;
const double eps = 1E-8;
const int dx4[4]={1,0,0,-1};
const int dy4[4]={0,-1,1,0};
const int inf = 0x3f3f3f3f;
const int N=3E4+7;
const int M=2E5+7;
int n,Q;
int a[N];
int tree[N<<2];
map<int,int>mp;
struct node
{
int l,r;
int id;
bool operator < (node b)const
{
if (r==b.r) return l<b.l;
return r<b.r;
}
}q[M];
void PushUp( int rt)
{
tree[rt] = tree[rt<<1] + tree[rt<<1|1];
}
void update( int p,int sc,int l,int r ,int rt)
{
if (l==r)
{
tree[rt]+=sc;
return;
}
int m = (l+r)>>1;
if (p<=m) update(p,sc,lson);
else update(p,sc,rson);
PushUp(rt);
}
int query(int L,int R,int l,int r,int rt)
{
if (L<=l&&r<=R) return tree[rt];
int m = (l+r)>>1;
int ret = 0 ;
if (L<=m) ret += query(L,R,lson);
if (R>=m+1) ret+=query(L,R,rson);
return ret;
}
int ans[M];
int main()
{
#ifndef ONLINE_JUDGE
freopen("code/in.txt","r",stdin);
#endif
cin>>n;
for ( int i = 1 ; i <= n ; i++) scanf("%d",&a[i]);
cin>>Q;
for ( int i = 1 ; i <= Q ; i++) scanf("%d %d",&q[i].l,&q[i].r),q[i].id = i ;
sort(q+1,q+Q+1);
int cur = 1;
for ( int i = 1 ; i <= Q ; i++)
{
for ( ; cur <= q[i].r ; cur++)
{
if (mp[a[cur]]) update(mp[a[cur]],-1,1,n,1);
mp[a[cur]] = cur;
update(mp[a[cur]],1,1,n,1);
}
ans[q[i].id] = query(q[i].l,q[i].r,1,n,1);
}
for ( int i = 1 ; i <= Q ; i++) printf("%d\n",ans[i]);
#ifndef ONLINE_JUDGE
fclose(stdin);
#endif
return 0;
}
之后补一个主席树的做法
先来补一个莫队的做法。
因为a[i]<=1E6,可以很方便得统计每个数出现的次数，update的时候，如果是1变成0，那么区间中不同的数的个数减1，如果是0变成1，那么区间中不同数个数+1
/* ***********************************************
Author :111qqz
Created Time :Fri 16 Sep 2016 11:34:32 PM CST
File Name :code/spoj/dquery.cpp
************************************************ */
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <cstdlib>
#include <ctime>
#define fst first
#define sec second
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define ms(a,x) memset(a,x,sizeof(a))
typedef long long LL;
#define pi pair < int ,int >
#define MP make_pair
using namespace std;
const double eps = 1E-8;
const int dx4[4]={1,0,0,-1};
const int dy4[4]={0,-1,1,0};
const int inf = 0x3f3f3f3f;
const int MAXN = 1E6+7;
const int N=3E4+7;
const int M=2E5+7;
int n,Q;
int a[N];
int pos[N];
int sum;
int cnt[MAXN]={0};
struct node
{
int l,r;
int id;
bool operator < (node b)const
{
if (pos[l]==pos[b.l]) return r<b.r;
return pos[l] < pos[b.l];
}
}q[M];
int ans[M];
void update ( int x,int d)
{
cnt[a[x]]+=d;
if (d==1&&cnt[a[x]]==1) sum++;
if (d==-1&&cnt[a[x]]==0) sum--;
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("./in.txt","r",stdin);
#endif
int bk = 173;// sqrt(30000)
cin>>n;
for ( int i = 1 ; i <= n ; i++)
{
scanf("%d",&a[i]);
pos[i] = (i-1)/bk;
}
cin>>Q;
for ( int i = 1 ; i <= Q ; i++) scanf("%d %d",&q[i].l,&q[i].r),q[i].id = i ;
sort(q+1,q+Q+1);
int pl=1,pr=0,id,l,r;
ms(cnt,0);
sum = 0 ;
for ( int i = 1 ; i <= Q ; i++)
{
id = q[i].id;
l = q[i].l;
r = q[i].r;
if (pr<r)
{
for ( int j = pr+1 ; j <= r ; j++)
update(j,1);
}
else
{
for ( int j = r+1 ; j <= pr ; j++)
update(j,-1);
}
pr = r;
if (pl<l)
{
for ( int j = pl ; j <= l-1 ; j++)
update(j,-1);
}
else
{
for ( int j = l ; j <= pl-1 ; j++)
update(j,1);
}
pl = l;
ans[id] = sum;
}
for ( int i = 1 ; i <= Q ; i++) printf("%d\n",ans[i]);
#ifndef ONLINE_JUDGE
fclose(stdin);
#endif
return 0;
}
补一个在线的做法，可持久化线段树，其实思路和离线线段树几乎一样。
/* ***********************************************
Author :111qqz
Created Time :Fri 16 Sep 2016 11:34:32 PM CST
File Name :code/spoj/dquery.cpp
************************************************ */
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <cstdlib>
#include <ctime>
#define fst first
#define sec second
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define ms(a,x) memset(a,x,sizeof(a))
typedef long long LL;
#define pi pair < int ,int >
#define MP make_pair
using namespace std;
const double eps = 1E-8;
const int dx4[4]={1,0,0,-1};
const int dy4[4]={0,-1,1,0};
const int inf = 0x3f3f3f3f;
const int N=3E4+7;
const int M=2E5+7;
int n,Q;
int a[N],root[N];
map<int,int>mp;
int cnt;
struct Ptree
{
int sum;
int left,right;
}tree[N*30];
void build (int &rt,int l,int r)
{
rt =++cnt;
tree[rt].sum = 0 ;
if (l==r) return;
int mid = (l+r)>>1;
build (tree[rt].left,l,mid);
build (tree[rt].right,mid+1,r);
}
inline int add_node(int _sum,int _left,int _right)
{
int idx = ++cnt;
tree[idx].sum = _sum;
tree[idx].left = _left;
tree[idx].right = _right;
return idx;
}
void Insert(int &root,int pre_rt,int pos,int val,int l,int r)
{
// printf("l:%d r:%d\n",l,r);
root = add_node(tree[pre_rt].sum + val,tree[pre_rt].left,tree[pre_rt].right);
// root = ++cnt;
// tree[root].sum = tree[pre_rt].sum+ val;
// tree[root].left = tree[pre_rt].left;
// tree[root].right = tree[pre_rt].right;
if (l==r) return;
int mid = (l+r)>>1;
if (pos<=mid) Insert(tree[root].left,tree[pre_rt].left,pos,val,l,mid);
else Insert(tree[root].right,tree[pre_rt].right,pos,val,mid+1,r);
}
int query(int pos,int l,int r,int rt)
{
if (l==r) return tree[rt].sum;
int mid = (l+r)>>1;
if (pos<=mid) return query(pos,l,mid,tree[rt].left);
else return tree[tree[rt].left].sum + query(pos,mid+1,r,tree[rt].right);
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("./in.txt","r",stdin);
#endif
ms(tree,0);
cnt = 0 ;
cin>>n;
for ( int i = 1 ; i <= n ; i++) scanf("%d",&a[i]);
build (root[n+1],1,n);
mp.clear();
for ( int i = n ; i >= 1 ; i--)
{
if (mp.find(a[i])==mp.end())
{
Insert(root[i],root[i+1],i,1,1,n);
}
else
{
Insert(root[i],root[i+1],mp[a[i]],-1,1,n);
Insert(root[i],root[i],i,1,1,n);
}
mp[a[i]] = i;
}
cin>>Q;
while (Q--)
{
int l,r;
scanf("%d %d",&l,&r);
// printf("l:%d r:%d\n",l,r);
int ans = query(r,1,n,root[l]);
printf("%d\n",ans);
}
#ifndef ONLINE_JUDGE
fclose(stdin);
#endif
return 0;
}