Codeforces 431E Chemistry Experiment 线段树 + 二分

Chemistry Experiment

维护一个权值线段树，然后二分答案。

#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()

using namespace std;

const int N = 2e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

template<class T, class S> inline void add(T& a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T& a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T& a, S b) {return a < b ? a = b, true : false;}
template<class T, class S> inline bool chkmin(T& a, S b) {return a > b ? a = b, true : false;}

#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
vector<LL> oo;
int getPos(double x) {
    return upper_bound(ALL(oo), x) - oo.begin();
}
int cnt[N << 2]; LL sum[N << 2];
void update(int p, int op, int l, int r, int rt) {
    if(l == r) {
        cnt[rt] += op;
        sum[rt] += op * oo[p - 1];
        return;
    }
    int mid = (l + r) >> 1;
    if(p <= mid) update(p, op, lson);
    else update(p, op, rson);
    cnt[rt] = cnt[rt << 1] + cnt[rt << 1 | 1];
    sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
}

PLI query(int L, int R, int l, int r, int rt) {
    if(L > R) return mk(0, 0);
    if(R < l || r < L) return mk(0, 0);
    if(L <= l && r <= R) return mk(sum[rt], cnt[rt]);
    int mid = (l + r) >> 1;
    PLI tmpL = query(L, R, lson);
    PLI tmpR = query(L, R, rson);
    return mk(tmpL.fi + tmpR.fi, tmpL.se + tmpR.se);
}

bool check(double tar, LL v) {
    PLI ret = query(1, getPos(tar), 1, SZ(oo), 1);
    return ret.se * tar - ret.fi > v;
}

int n, q;
LL qus[N][3], h[N];

int main() {
    scanf("%d%d", &n, &q);
    for(int i = 1; i <= n; i++) {
        scanf("%d", &h[i]);
        oo.push_back(h[i]);
    }
    for(int i = 1; i <= q; i++) {
        scanf("%d", &qus[i][0]);
        if(qus[i][0] == 1) {
            scanf("%lld%lld", &qus[i][1], &qus[i][2]);
            oo.push_back(qus[i][2]);
        } else {
            scanf("%lld", &qus[i][1]);
        }
    }
    sort(ALL(oo));
    oo.erase(unique(ALL(oo)), oo.end());
    for(int i = 1; i <= n; i++) update(getPos(h[i]), 1, 1, SZ(oo), 1);
    for(int i = 1; i <= q; i++) {
        if(qus[i][0] == 1) {
            int p = qus[i][1], x = qus[i][2];
            update(getPos(h[p]), -1, 1, SZ(oo), 1);
            h[p] = x;
            update(getPos(h[p]), 1, 1, SZ(oo), 1);
        } else {
            LL v = qus[i][1];
            double low = 0, high = 1e9 + v + 1;
            for(int o = 0; o < 100; o++) {
                double mid = (low + high) / 2;
                if(check(mid, v)) high = mid;
                else low = mid;
            }
            printf("%.15f\n", (low + high) / 2);
        }
    }
    return 0;
}

/*
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