BZOJ 1878 HH的项链(离线思想、BIT)

题意:

$N\le 5\times 10^4,Q\le 2\times 10^5,给定一个N大小序列,A_i\in[0,10^6],Q次询问$
$每次询问[L,R]区间有多少个不同的整数$

分析:

$经典离线套路题了,询问右端点排序$
$从左往右扫描每个数A_i(相当于固定了右端点)$
$维护A_i出现的前一个位置为last_{A_i},用BIT维护,只要单点更新last_{A_i}为1$
$发现所有以i为右端点的询问[L,i]中重复出现的数,查询[L,i]的区间和即可$
$此时不同的整数的个数,ans(L,i)=i-L+1-sum(L,i)$
$这里其实把BIT倒过来就可以完成了,向前更新,向后查询$
$时间复杂度为O(nlogn)$

代码:

//
//  Created by TaoSama on 2016-03-23
//  Copyright (c) 2016 TaoSama. All rights reserved.
//
#pragma comment(linker, "/STACK:102400000,102400000")
#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <string>
#include <set>
#include <vector>

using namespace std;
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
const int N = 2e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;

struct BIT {
    int n, b[N];
    void init(int _n) {
        n = _n;
        memset(b, 0, sizeof b);
    }
    void add(int i, int v) {
        for(; i; i -= i & -i) b[i] += v;
    }
    int sum(int i) {
        int ret = 0;
        for(; i <= n; i += i & -i) ret += b[i];
        return ret;
    }
} bit;

int n;
int a[N];
int q, ans[N];
vector<pair<int, int> > qs[N];

int main() {
#ifdef LOCAL
    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);
//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);
#endif
    ios_base::sync_with_stdio(0);

    scanf("%d", &n);
    for(int i = 1; i <= n; ++i) scanf("%d", a + i);
    scanf("%d", &q);
    for(int i = 1; i <= q; ++i) {
        int l, r; scanf("%d%d", &l, &r);
        qs[r].push_back(make_pair(l, i));
    }

    bit.init(n);
    map<int, int> last;
    for(int i = 1; i <= n; ++i) {
        int x = a[i];
        if(last.count(x)) bit.add(last[x], 1);
        last[x] = i;
        for(int j = 0; j < qs[i].size(); ++j) {
            pair<int, int>& q = qs[i][j];
            ans[q.second] = i - q.first + 1 - bit.sum(q.first);
        }
    }
    for(int i = 1; i <= q; ++i) printf("%d\n", ans[i]);
    return 0;
}