Bzoj1901 Dynamic Ranking

动态区间第k小

离散化后

那么每个点开一棵线段树(主席树)再套一个树状数组在外面

每次询问区间内的树的个数时
相当于进行了一次树状数组求区间和的操作,只是是把树状数组那个点看做主席树,对log棵主席树求区间和

然后每次询问,修改时就是把log棵主席树同时跳到儿子,修改也是log棵

时间复杂度O(nlogn*logn)空间复杂度O(nlogn*logn)

# include <bits/stdc++.h>
# define IL inline
# define RG register
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(2e4 + 10), __(2e6 + 10); IL ll Read(){
RG char c = getchar(); RG ll x = 0, z = 1;
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
return x * z;
} int n, m, len, p[_], a[_], ql[_], qr[_], qk[_], qo[_];
int ls[__], rs[__], sz[__], rt[__], num, tmp[2][20]; IL void Modify(RG int &x, RG int l, RG int r, RG int pos, RG int val){
if(!x) x = ++num;
sz[x] += val;
if(l == r) return;
RG int mid = (l + r) >> 1;
if(pos <= mid) Modify(ls[x], l, mid, pos, val);
else Modify(rs[x], mid + 1, r, pos, val);
} IL void PreModify(RG int x, RG int val){
RG int k = lower_bound(p + 1, p + len + 1, a[x]) - p;
for(RG int i = x; i <= n; i += i & -i) Modify(rt[i], 1, len, k, val);
} IL int Query(RG int l, RG int r, RG int k){
if(l == r) return l;
RG int mid = (l + r) >> 1, sum = 0;
for(RG int i = 1; i <= tmp[1][0]; i++) sum += sz[ls[tmp[1][i]]];
for(RG int i = 1; i <= tmp[0][0]; i++) sum -= sz[ls[tmp[0][i]]];
if(k <= sum){
for(RG int i = 1; i <= tmp[1][0]; i++) tmp[1][i] = ls[tmp[1][i]];
for(RG int i = 1; i <= tmp[0][0]; i++) tmp[0][i] = ls[tmp[0][i]];
return Query(l, mid, k);
}
else{
for(RG int i = 1; i <= tmp[1][0]; i++) tmp[1][i] = rs[tmp[1][i]];
for(RG int i = 1; i <= tmp[0][0]; i++) tmp[0][i] = rs[tmp[0][i]];
return Query(mid + 1, r, k - sum);
}
} IL int PreQuery(RG int l, RG int r, RG int k){
Fill(tmp, 0);
for(RG int i = r; i; i -= i & -i) tmp[1][++tmp[1][0]] = rt[i];
for(RG int i = l - 1; i; i -= i & -i) tmp[0][++tmp[0][0]] = rt[i];
return Query(1, len, k);
} int main(RG int argc, RG char* argv[]){
n = Read(); m = Read();
for(RG int i = 1; i <= n; i++) a[i] = Read(), p[++len] = a[i];
for(RG int i = 1; i <= m; i++){
RG char c; scanf(" %c", &c);
qo[i] = c == 'Q';
if(qo[i]) ql[i] = Read(), qr[i] = Read(), qk[i] = Read();
else ql[i] = qr[i] = Read(), qk[i] = Read(), p[++len] = qk[i];
}
sort(p + 1, p + len + 1); len = unique(p + 1, p + len + 1) - p - 1;
for(RG int i = 1; i <= n; i++) PreModify(i, 1);
for(RG int i = 1; i <= m; i++)
if(qo[i]) printf("%d\n", p[PreQuery(ql[i], qr[i], qk[i])]);
else{
PreModify(ql[i], -1);
a[ql[i]] = qk[i];
PreModify(ql[i], 1);
}
return 0;
}
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