bzoj2117

Posted 2020-10-16 123456

动态电分治+二分

肯定要枚举所有点对，那么我们建出点分树降低树高，然后每个点存下点分树中所有子树到这个点的距离，然后二分+lower_bound就行了。

#include<bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
namespace IO 
{
    const int Maxlen = N * 50;
    char buf[Maxlen], *C = buf;
    int Len;
    inline void read_in()
    {
        Len = fread(C, 1, Maxlen, stdin);
        buf[Len] = ‘\0‘;
    }
    inline void fread(int &x) 
    {
        x = 0;
        int f = 1;
        while (*C < ‘0‘ || ‘9‘ < *C) { if(*C == ‘-‘) f = -1; ++C; }
        while (‘0‘ <= *C && *C <= ‘9‘) x = (x << 1) + (x << 3) + *C - ‘0‘, ++C;
        x *= f;
    }
    inline void fread(long long &x) 
    {
        x = 0;
        long long f = 1;
        while (*C < ‘0‘ || ‘9‘ < *C) { if(*C == ‘-‘) f = -1; ++C; }
        while (‘0‘ <= *C && *C <= ‘9‘) x = (x << 1) + (x << 3) + *C - ‘0‘, ++C;
        x *= f;
    }
    inline void read(int &x)
    {
        x = 0;
        int f = 1; char c = getchar();
        while(c < ‘0‘ || c > ‘9‘) { if(c == ‘-‘) f = -1; c = getchar(); }
        while(c >= ‘0‘ && c <= ‘9‘) { x = (x << 1) + (x << 3) + c - ‘0‘; c = getchar(); }
        x *= f;
    }
    inline void read(long long &x)
    {
        x = 0;
        long long f = 1; char c = getchar();
        while(c < ‘0‘ || c > ‘9‘) { if(c == ‘-‘) f = -1; c = getchar(); }
        while(c >= ‘0‘ && c <= ‘9‘) { x = (x << 1ll) + (x << 3ll) + c - ‘0‘; c = getchar(); }
        x *= f;
    } 
} using namespace IO;
int rd()
{
    int x = 0, f = 1; char c = getchar();
    while(c < ‘0‘ || c > ‘9‘) { if(c == ‘-‘) f = -1; c = getchar(); }
    while(c >= ‘0‘ && c <= ‘9‘) { x = x * 10 + c - ‘0‘; c = getchar(); }
    return x * f;
}
struct edge {
    int nxt, to, w;
} e[N << 1];
int n, q, cnt = 1, root, rt, tot, k;
int head[N], size[N], f[N], Fa[N], dep[N], val[N << 1], vis[N], Log[N << 1], pos[N << 1], mn[N << 1][19], dis[N];
vector<int> ddis[N], DDis[N];
void link(int u, int v, int w)
{
    e[++cnt].nxt = head[u];
    head[u] = cnt;
    e[cnt].to = v;
    e[cnt].w = w;
}
void getroot(int u, int last, int S) 
{
    f[u] = 0;
    size[u] =1 ;
    for(int i = head[u]; i; i = e[i].nxt) if(!vis[e[i].to] && e[i].to != last) 
    {
        getroot(e[i].to, u, S);
        size[u] += size[e[i].to];
        f[u] = max(f[u], size[e[i].to]);
    }
    f[u] = max(f[u], S - size[u]);
    if(f[u] < f[root]) root = u;
}
int getsize(int u, int last)
{
    int ret = 1;
    for(int i = head[u]; i; i = e[i].nxt) if(e[i].to != last && !vis[e[i].to]) 
        ret += getsize(e[i].to, u);
    return ret;
}
void divide(int u) 
{
    vis[u] = 1;
    for(int i = head[u]; i; i = e[i].nxt) if(!vis[e[i].to]) 
    {
        root = 0;
        getroot(e[i].to, u, getsize(e[i].to, u));
        Fa[root] = u;
        divide(root);
    }
}
void dfs(int u, int last) 
{
    mn[pos[u] = ++tot][0] = dis[u];
    for(int i = head[u]; i; i = e[i].nxt) if(e[i].to != last) 
    {
        dis[e[i].to] = dis[u] + e[i].w;
        dep[e[i].to] = dep[u] + 1;
        dfs(e[i].to, u);
        mn[++tot][0] = dis[u];
    }
}
int Dis(int u, int v) 
{
    int ret = dis[u] + dis[v];
    if(pos[u] < pos[v]) swap(u, v);
    int x = Log[pos[u] - pos[v] + 1];
    return ret - 2 * min(mn[pos[v]][x], mn[pos[u] - (1 << x) + 1][x]);
}
int ask(vector<int> &t, int x) 
{
    return upper_bound(t.begin(), t.end(), x) - t.begin();
}
int check(int u, int x) 
{
    int ret = 0;
    for(int i = u; i; i = Fa[i]) 
    {
        int d = ask(ddis[i], x - Dis(u, i));
        ret += d;
        if(ret > 2 * n) return ret;
    }
    for(int i = Fa[u]; i; i = Fa[i]) if(Dis(u, i) <= x) ++ret;
    for(int i = u; Fa[i]; i = Fa[i]) 
    {
        int d = ask(DDis[i], x - Dis(u, Fa[i]));
        ret -= d;
    }
    return ret;
}
int query(int u, int k)
{
    int l = 0, r = 1e9 + 5, ret = 0;
    while(r - l > 1) 
    {
        int mid = (l + r) >> 1;
        int tmp = check(u, mid);
        if(check(u, mid) >= k) r = ret = mid;
        else l = mid;
    }
    return ret;
}
int main()
{
    char opt[2];
    scanf("%s", opt);
    read(n);
    read(k);
    for(int i = 1; i < n; ++i) 
    {
        int u, v, w;
        read(u);
        read(v);
        read(w);
        link(u, v, w);
        link(v, u, w);
    }
    dfs(1, 0);
    for(int i = 2; i <= tot; ++i) Log[i] = Log[i >> 1] + 1;
    for(int j = 1; j <= 18; ++j)
        for(int i = 1; i + (1 << j) - 1 <= tot; ++i)
            mn[i][j] = min(mn[i][j - 1], mn[i + (1 << (j - 1))][j - 1]);
    f[0] = 1e9;
    getroot(1, 0, getsize(1, 0));
    rt = root;
    divide(root);
    for(int i = 1; i <= n; ++i) 
    {
        for(int j = Fa[i]; j; j = Fa[j]) ddis[j].push_back(Dis(i, j));
        for(int j = i; Fa[j]; j = Fa[j]) DDis[j].push_back(Dis(i, Fa[j]));
    }
    for(int i = 1; i <= n; ++i) 
    {
        sort(ddis[i].begin(), ddis[i].end());
        sort(DDis[i].begin(), DDis[i].end());
    }
    for(int i = 1; i <= n; ++i) printf("%d\n", query(i, k));
    return 0;
}

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