【BZOJ 1758】【WC 2010】重建计划 分数规划+点分治+单调队列

一开始看到$frac{sum_{}}{sum_{}}$就想到了01分数规划但最终还是看了题解

二分完后的点分治，只需要维护一个由之前处理过的子树得出的$tb数组$，然后根据遍历每个当前的子树上的结点的深度来确定$tb数组$中的滑块。

因为分数规划要找的是$max$，BFS遍历当前结点的深度越来越大，这样滑块也是单调向右滑动，所以滑块里的最大值就应当用单调队列解决

#include<cstdio>
#include<algorithm>
#define read(x) x=getint()
#define N 100003
#define eps 0.0001
#define max(a,b) (a)>(b)?a:b
using namespace std;
inline int getint() {
    char c; int fh = 1, k = 0;
    for( ; c < '0' || c > '9'; c = getchar()) if ( c == '-') fh = -1;
    for( ; c >= '0' && c <= '9'; c = getchar()) k = k * 10 + c - '0';
    return k * fh;
}
struct node {
    int nxt, to, w;
} E[N << 1];
bool vis[N];
double ans = 0.0, limi = 0.0, dis[N], tb[N];
int sz[N], n, cnt = 0, L, U, point[N], root, rtm = N, fa[N], q[N], dq[N], deep[N];
inline void ins( int x, int y, int z) {++cnt; E[cnt].nxt = point[x]; E[cnt].to = y; E[cnt].w = z; point[x] = cnt;}
inline void fdrt( int x, int fa, int s) {
    sz[x] = 1;
    int ma = 0;
    for( int tmp = point[x]; tmp; tmp = E[tmp].nxt)
        if ( !vis[E[tmp].to] && E[tmp].to != fa) {
            fdrt( E[tmp].to, x, s);
            sz[x] += sz[E[tmp].to];
            ma = max( ma, sz[E[tmp].to]);
        }
    ma = max( ma, s - ma);
    if ( ma < rtm) {
        rtm = ma;
        root = x;
    }
}
inline bool can( int x, double M) {
    int le = 0, head, tail, h, t, now;
    for( int tmp = point[x]; tmp; tmp = E[tmp].nxt)
        if ( !vis[E[tmp].to]) {
            head = 0;
            tail = 1;
            q[0] = E[tmp].to;
            fa[E[tmp].to] = x;
            deep[E[tmp].to] = 1;
            dis[E[tmp].to] = (double) E[tmp].w - M;
            while ( head != tail) {
                now = q[head];
                ++head; if ( head >= N) head %= N;
                for( int i = point[now]; i; i = E[i].nxt)
                    if ( !vis[E[i].to] && E[i].to != fa[now]) {
                        q[tail] = E[i].to;
                        fa[E[i].to] = now;
                        deep[E[i].to] = deep[now] + 1;
                        dis[E[i].to] = dis[now] + (double) E[i].w - M;
                        ++tail; if ( tail >= N) tail %= N;
                    }
            }
            h = 1;
            t = 0;
            now = le;
            for( int i = 0; i < tail; ++i) {
                while ( deep[q[i]] + now >= L && now >= 0) {
                    while ( h <= t && tb[dq[t]] < tb[now])
                        --t;
                    dq[++t] = now;
                    --now;
                }
                while ( h <= t && deep[q[i]] + dq[h] > U)
                    ++h;
                if ( h <= t && dis[q[i]] + tb[dq[h]] >= 0)
                    return 1;
            }
            for( int i = le + 1; i <= deep[q[tail-1]]; ++i)
                tb[i] = -1E9;
            for( int i = 0; i < tail; ++i)
                tb[deep[q[i]]] = max( tb[deep[q[i]]], dis[q[i]]);
            le = max( le, deep[q[tail-1]]);
        }
    return 0;
}
inline void work( int x) {
    double left = ans, right = limi, mid;
    while ( right - left > eps) {
        mid = ( left + right) / 2;
        if ( can ( x, mid))
            left = mid;
        else
            right = mid;
    }
    ans = left;
}
inline void dfs( int x, int s) {
    vis[x] = 1;
    work( x);
    for( int tmp = point[x]; tmp; tmp = E[tmp].nxt)
        if ( !vis[E[tmp].to]) {
            rtm = N;
            int ss = sz[E[tmp].to] < sz[x] ? sz[E[tmp].to] : s - sz[x];
            fdrt( E[tmp].to, -1, ss);
            if ( sz[E[tmp].to] > L)
                dfs( root, ss);
        }
}
int main() {
    read(n); read(L); read(U);
    int a, b, c;
    for( int i = 1; i < n; ++i) {
        read(a); read(b); read(c);
        ins( a, b, c);
        ins( b, a, c);
        limi = max( limi, c);
    }
    fdrt( 1, -1, n);
    dfs( 1, n);
    printf( "%.3lf
", ans);
    return 0;
}

这样就可以了