题目链接:洛谷
我们知道要求的是([l_1,r_1],[l_2,r_2],[l_3,r_3])的可重集取交的大小,肯定是要用bitset的,那怎么做可重集呢?
那就是要稍微动点手脚,首先在离散化的时候,将(a_x)设为(leq a_x)的数的个数,然后再插入一个数的时候,将(a_x-cnt_{a_x})设为1,删除的时候设为0,然后直接取交就可以了。正确性比较显然。
还有一个问题就是如何存下(100000*100000)的bitset,那肯定是存不下的,所以把询问分成3部分,然后每块分别做就可以用时间换空间了。
#include<bits/stdc++.h>
#define Rint register int
using namespace std;
typedef long long LL;
const int N = 100010, M = 33340;
int n, m, _n, len, a[N], val[N], cnt[N], ql, qr, tmp[M];
bitset<N> ans[M], now;
struct Query {
int l, r, id;
inline bool operator < (const Query &o) const {
if(l / len != o.l / len) return l / len < o.l / len;
if(l / len & 1) return r > o.r;
return r < o.r;
}
} que[N];
inline void add(int x){++ cnt[x]; now[x - cnt[x]] = 1;}
inline void del(int x){now[x - cnt[x]] = 0; -- cnt[x];}
inline void solve(int m){
for(Rint i = 1;i <= n;i ++) cnt[i] = 0;
for(Rint i = 1;i <= m;i ++) ans[i].set(), tmp[i] = 0; now.reset(); ql = 1; qr = 0;
for(Rint i = 1;i <= 3 * m;i ++) scanf("%d%d", &que[i].l, &que[i].r), tmp[que[i].id = (i + 2) / 3] += que[i].r - que[i].l + 1;
sort(que + 1, que + 3 * m + 1);
for(Rint i = 1;i <= 3 * m;i ++){
while(ql > que[i].l) add(a[-- ql]);
while(qr < que[i].r) add(a[++ qr]);
while(qr > que[i].r) del(a[qr --]);
while(ql < que[i].l) del(a[ql ++]);
ans[que[i].id] &= now;
}
for(Rint i = 1;i <= m;i ++) printf("%d
", tmp[i] - 3 * ans[i].count());
}
int main(){
scanf("%d%d", &n, &m); len = sqrt(n);
for(Rint i = 1;i <= n;i ++) scanf("%d", a + i), val[i] = a[i];
sort(val + 1, val + n + 1);
_n = unique(val + 1, val + n + 1) - val - 1;
for(Rint i = 1;i <= n;i ++) a[i] = lower_bound(val + 1, val + _n + 1, a[i]) - val;
for(Rint i = 1;i <= _n;i ++) val[i] = 0;
for(Rint i = 1;i <= n;i ++) ++ val[a[i]];
for(Rint i = 1;i <= _n;i ++) val[i] += val[i - 1];
for(Rint i = 1;i <= n;i ++) a[i] = val[a[i]];
solve(m / 3); solve((m + 1) / 3); solve((m + 2) / 3);
}