Codeforces 138C(区间更新+离散化)

Posted 2020-10-03 llguanli

题意：有n棵树在水平线上，给出每棵树的坐标和高度，然后向左倒的概率和向右倒的概率，和为1，然后给出了m个蘑菇的位置，每一个蘑菇都有一个魔法值，假设蘑菇被压死了，也就是在某棵树[a[i] - h[i], a[i]) 或 (a[i], a[i] + h[i]]范围内。魔法值就没有了。仅仅有生存下来的蘑菇才有魔法值，问生存下来的蘑菇的魔法值的期望。
题解：能够看到n和m的范围是1e5。而坐标范围是1e9。所以肯定要离散化，然后更新每一个区间的概率值，单点查询每一个蘑菇所在区间的概率值乘其魔法值。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <map>
using namespace std;
const int N = 100005;
int n, m, a[N], h[N], b[N], z[N], c[N << 2];
double tree[N << 4], flag[N << 4], pl[N], pr[N];
map<int, int> mp;

void pushdown(int k) {
    if (flag[k]) {
        tree[k * 2] *= tree[k];
        tree[k * 2 + 1] *= tree[k];
        flag[k * 2] = flag[k * 2 + 1] = 1;
        tree[k] = 1.0;
        flag[k] = 0;
    }
}

void build(int k, int left, int right) {
    flag[k] = 0;
    tree[k] = 1.0;
    if (left != right) {
        int mid = (left + right) / 2;
        build(k * 2, left, mid);
        build(k * 2 + 1, mid + 1, right);
    }
}

void modify(int k, int left, int right, int l1, int r1, double x) {
    if (l1 <= left && right <= r1) {
        tree[k] *= x;
        flag[k] = 1;
        return;
    }
    pushdown(k);
    int mid = (left + right) / 2;
    if (l1 <= mid)
        modify(k * 2, left, mid, l1, r1, x);
    if (r1 > mid)
        modify(k * 2 + 1, mid + 1, right, l1, r1, x);
}

double query(int k, int left, int right, int pos) {
    if (left == right)
        return tree[k];
    pushdown(k);
    int mid = (left + right) / 2;
    if (pos <= mid)
        return query(k * 2, left, mid, pos);
    else
        return query(k * 2 + 1, mid + 1, right, pos);
}

int main() {
    scanf("%d%d", &n, &m);
    mp.clear();
    int cnt = 0;
    for (int i = 1; i <= n; i++) {
        scanf("%d%d%lf%lf", &a[i], &h[i], &pl[i], &pr[i]);
        pl[i] /= 100.0, pr[i] /= 100.0; 
        c[++cnt] = a[i];
        c[++cnt] = a[i] - h[i];
        c[++cnt] = a[i] + h[i];
    }
    for (int i = 1; i <= m; i++) {
        scanf("%d%d", &b[i], &z[i]);
        c[++cnt] = b[i];
    }
    sort(c + 1, c + 1 + cnt);
    cnt = unique(c + 1, c + 1 + cnt) - (c + 1);
    for (int i = 1; i <= cnt; i++)
        mp[c[i]] = i;
    build(1, 1, cnt);
    for (int i = 1; i <= n; i++) {
        modify(1, 1, cnt, mp[a[i] - h[i]], mp[a[i]] - 1, 1.0 - pl[i]);
        modify(1, 1, cnt, mp[a[i]] + 1, mp[a[i] + h[i]], 1.0 - pr[i]);
    }
    double res = 0;
    for (int i = 1; i <= m; i++)
        res += z[i] * query(1, 1, cnt, mp[b[i]]);
    printf("%lf\n", res);
    return 0;
}