Submission #58813

#	Time	Username	Problem	Language	Result	Execution time	Memory
58813		Benq	Hard route (IZhO17_road)	C++14	100 / 100	1537 ms	255532 KiB

road

#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;

typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)

#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()

const int MOD = 1000000007;
const ll INF = 1e18;
const int MX = 500001;

int n, dist[MX], pre[MX], besDist[MX];
vi adj[MX];
pl bes = {-1,0};

void tri(pl x) {
    if (x.f > bes.f) bes = {x.f,0};
    if (x.f == bes.f) bes.s += x.s;
}

void dfs(int cur) {
    for (int i: adj[cur]) if (i != pre[cur]) {
        pre[i] = cur;
        dist[i] = dist[cur]+1;
        dfs(i);
    }
}

void genDist(int cur) {
    memset(dist,0,sizeof dist);
    pre[cur] = -1;
    dfs(cur);
}

int treeDiameter() {
    genDist(1);
    int bes = 0; FOR(i,1,n+1) if (dist[i] > dist[bes]) bes = i;
    genDist(bes); FOR(i,1,n+1) if (dist[i] > dist[bes]) bes = i;
    return dist[bes];
}

int t;
vi x;

vi genCenter() {
    t = treeDiameter();
    int bes = 0; FOR(i,1,n+1) if (dist[i] > dist[bes]) bes = i;
    
    F0R(i,t/2) bes = pre[bes];
    if (t&1) return {bes,pre[bes]};
    return {bes};
}

pi dfs(int a, int b, int c) {
    vpi v; 
    pi z = {0,0};
    for (int i: adj[a]) if (i != b) {
        pi t = dfs(i,a,c+1); t.f ++;
        v.pb(t);
        if (t.f > z.f) z.s = z.f, z.f = t.f;
        else if (t.f > z.s) z.s = t.f;
    }
    int co = 0;
    for (int i: adj[a]) if (i != b) {
        if (v[co].f == z.f) besDist[i] = z.s;
        else besDist[i] = z.f;
        co ++;
    }
    if (sz(v) == 0) v.pb({0,1});
    if (sz(v) == 1) return v[0];
    sort(v.rbegin(),v.rend());
    int ind = 0, sum = v[0].s; 
    while (ind+1 < sz(v) && v[ind+1].f == v[ind].f) 
        sum += v[++ind].s;
    if (ind > 0) {
        ll t = (ll)sum*(sum-1)/2;
        F0R(i,ind+1) t -= (ll)v[i].s*(v[i].s-1)/2;
        tri({(ll)v[0].f*2*c,t});
    } else {
        ll sum2 = 0;
        int ind = 1;
        while (ind < sz(v) && v[ind].f == v[1].f) sum2 += v[ind++].s;
        tri({(ll)(v[0].f+v[1].f)*c,(ll)sum2*sum});
    }
    return {v[0].f,sum};
}

vpi tmp;

void solveNoCenter() {
    if (sz(x) == 2) {
        tmp.pb(dfs(x[1],x[0],t/2+1));
        tmp.pb(dfs(x[0],x[1],t/2+1));
    } else {
        for (int i: adj[x[0]]) tmp.pb(dfs(i,x[0],t/2+1));    
    }
}

vpi z[2];

void dfs2(int cur, int pre, int cdist, int cmx, int ind) {
    bool isLeaf = 1;
    for (int i: adj[cur]) if (i != pre) {
        dfs2(i,cur,cdist+1,max(cmx,besDist[i]),ind);
        isLeaf = 0;
    }
    if (isLeaf) z[ind].pb({cmx,cdist});
}

int stor[2][500001];

void solveCenter() {
    vi maj;
    ll sum = 0, bad = 0;
    int mx = 0;
    if (sz(x) == 2) maj = x;
    else {
        F0R(i,sz(tmp)) if (tmp[i].f == t/2-1) {
            maj.pb(adj[x[0]][i]);
            sum += tmp[i].s;
            bad += (ll)tmp[i].s*(tmp[i].s-1)/2;
        } else {
            mx = max(mx,tmp[i].f+1);
        }
    }
    if (sz(maj) > 2) {
        tri({(ll)t*t/2,(ll)sum*(sum-1)/2-bad});
        return;
    }
    // cout << "OH " << sz(x) << " " << maj[0] << " " << maj[1] << "\n";
    //cout << sz(maj) << " " << x[0] << "\n";
    //exit(0);
    //cout << maj[0] << " " << maj[1] << " " << x[0] << " " << mx << "\n";
    if (sz(x) == 2) {
        dfs2(x[0],x[1],0,0,0);
        dfs2(x[1],x[0],1,0,1);
    } else {
        dfs2(maj[0],x[0],1,mx,0);
        dfs2(maj[1],x[0],1,mx,1);
    }
    
    sort(all(z[0])), sort(all(z[1]));
    
    F0R(k,2) for (auto a: z[k]) stor[k][a.s] ++;
    array<int,2> t = {500000,500000};
    while (sz(z[0]) && sz(z[1])) {
        F0R(k,2) while (!stor[k][t[k]]) t[k] --;
        if (z[0].back().f < z[1].back().f) {
            tri({(ll)(t[0]+z[1].back().s)*z[1].back().f,stor[0][t[0]]});
            stor[1][z[1].back().s] --; z[1].pop_back();
        } else {
            tri({(ll)(t[1]+z[0].back().s)*z[0].back().f,stor[1][t[1]]});
            stor[0][z[0].back().s] --; z[0].pop_back();
        }
    }
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin >> n;
    F0R(i,n-1) {
        int a, b; cin >> a >> b;
        adj[a].pb(b), adj[b].pb(a);
    }
    x = genCenter();
    solveNoCenter();
    // cout << bes.f << " " << bes.s << "\n";
    solveCenter();
    cout << bes.f << " " << bes.s;
}

/* Look for:
* the exact constraints (multiple sets are too slow for n=10^6 :( ) 
* special cases (n=1?)
* overflow (ll vs int?)
* array bounds
*/

• Subtask 1: 19 / 19
• Subtask 2: 33 / 33
• Subtask 3: 48 / 48