제출 #1287509

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1287509		Ice_man	Race (IOI11_race)	C++17	100 / 100	312 ms	80764 KiB

race

/**
 ____    ____    ____    __________________    ____    ____    ____
||I ||  ||c ||  ||e ||  ||                ||  ||M ||  ||a ||  ||n ||
||__||  ||__||  ||__||  ||________________||  ||__||  ||__||  ||__||
|/__\|  |/__\|  |/__\|  |/________________\|  |/__\|  |/__\|  |/__\|

*/

#include <iostream>
#include <vector>
#include <map>

#include "race.h"

#define maxn 500005
#define PB push_back
#define X first
#define Y second

typedef long long ll;
typedef std::pair<ll,ll> pll;

const ll INF = (ll)4e18;

std::vector<pll> v[maxn];
int n , k;
ll ans;

ll sumv[maxn];
int distv[maxn];

struct dsu
{
    struct component
    {
        int par, sz;
        std::map<ll,ll> store;

        void init(int x)
        {
            par = x;
            sz = 1;
            store.clear();
        }

        void _swap(component &other)
        {
            std::swap(sz, other.sz);
            store.swap(other.store);
        }

        void insert_min(ll key, ll val)
        {
            auto it = store.find(key);
            if(it == store.end()) store.emplace(key, val);
            else it->second = std::min(it->second, val);
        }

        ll get_min(ll key) const
        {
            auto it = store.find(key);
            if(it != store.end()) return it->second;
            return (ll)4e18;
        }

        // Merge 'other' into *this*: check complements against this->store,
        // then insert other's entries (keeping minimal depths).
        // target = k + 2*sum[u], depth_u is dist[u] used in candidate formula.
        void _merge_with(component &other, ll target, int depth_u)
        {
            // check complements (do this before mutating this->store)
            for (auto &pr : other.store)
            {
                ll keyB = pr.X;
                ll valB = pr.Y;
                ll need = target - keyB;
                auto it = store.find(need);
                if (it != store.end())
                {
                    ll cand = it->second + valB - 2LL * depth_u;
                    if (cand < ans) ans = cand;
                }
            }

            // merge other.store into store, keeping minimal depth
            for (auto &pr : other.store)
            {
                ll keyB = pr.X;
                ll valB = pr.Y;
                auto it = store.find(keyB);
                if (it == store.end()) store.emplace(keyB, valB);
                else it->second = std::min(it->second, valB);
            }

            sz += other.sz;
        }
    };

    std::vector<component> un;

    void init(int sz)
    {
        un.resize(sz + 1);
        for (int i = 1; i <= n; ++i) un[i].init(i);
    }

    int find_par(int node)
    {
        return node == un[node].par ? node : un[node].par = find_par(un[node].par);
    }
};

dsu uni;


// precompute prefix sums and depths, and insert (sum -> depth) into each node's component map
void precomp(int u, int p, ll acc, int depth)
{
    sumv[u] = acc;
    distv[u] = depth;
    uni.un[u].insert_min(acc, depth);

    for (auto &ed : v[u])
    {
        int to = (int)ed.X;
        ll w = ed.Y;
        if (to == p) continue;
        precomp(to, u, acc + w, depth + 1);
    }
}


// recursion that uses small-to-large merging; uses component._merge_with to do the actual merge
void small_to_large_merge(int u, int p)
{
    ll target = (ll)k + 2LL * sumv[u];

    for (auto &ed : v[u])
    {
        int to = (int)ed.X;
        if (to == p) continue;

        small_to_large_merge(to, u);

        // ensure we merge smaller into larger: if child's map bigger, swap component contents
        if (uni.un[to].store.size() > uni.un[u].store.size())
        {
            uni.un[to]._swap(uni.un[u]);
        }

        // now merge child's component into parent's component using component member
        uni.un[u]._merge_with(uni.un[to], target, distv[u]);

        // clear child's map to save memory
        uni.un[to].store.clear();
    }
}


int best_path(int N, int K, int h[][2], int L[])
{
    n = N;
    k = K;
    ans = INF;

    // clear adjacency
    for (int i = 1; i <= n; ++i) v[i].clear();

    for (int i = 0; i < n - 1; ++i)
    {
        int a = h[i][0] + 1;
        int b = h[i][1] + 1;
        ll w = L[i];
        v[a].PB({b, w});
        v[b].PB({a, w});
    }

    uni.init(n + 5);

    precomp(1, 0, 0LL, 0);
    small_to_large_merge(1, 0);

    if (ans == INF) return -1;
    return (int)ans;
}

• Subtask 1: 9 / 9
• Subtask 2: 12 / 12
• Subtask 3: 22 / 22
• Subtask 4: 57 / 57