結果

問題 No.1488 Max Score of the Tree
ユーザー iiljjiiljj
提出日時 2021-04-23 23:21:05
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 24 ms / 2,000 ms
コード長 11,610 bytes
コンパイル時間 1,856 ms
コンパイル使用メモリ 150,232 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-04 08:45:40
合計ジャッジ時間 3,165 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 20 ms
6,816 KB
testcase_01 AC 23 ms
6,940 KB
testcase_02 AC 24 ms
6,944 KB
testcase_03 AC 23 ms
6,944 KB
testcase_04 AC 24 ms
6,944 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 7 ms
6,940 KB
testcase_07 AC 14 ms
6,944 KB
testcase_08 AC 9 ms
6,944 KB
testcase_09 AC 9 ms
6,940 KB
testcase_10 AC 13 ms
6,940 KB
testcase_11 AC 24 ms
6,944 KB
testcase_12 AC 3 ms
6,940 KB
testcase_13 AC 5 ms
6,944 KB
testcase_14 AC 12 ms
6,940 KB
testcase_15 AC 8 ms
6,944 KB
testcase_16 AC 3 ms
6,940 KB
testcase_17 AC 7 ms
6,940 KB
testcase_18 AC 16 ms
6,940 KB
testcase_19 AC 10 ms
6,940 KB
testcase_20 AC 6 ms
6,944 KB
testcase_21 AC 5 ms
6,940 KB
testcase_22 AC 8 ms
6,940 KB
testcase_23 AC 2 ms
6,944 KB
testcase_24 AC 2 ms
6,940 KB
testcase_25 AC 2 ms
6,944 KB
testcase_26 AC 8 ms
6,940 KB
testcase_27 AC 3 ms
6,940 KB
testcase_28 AC 4 ms
6,940 KB
testcase_29 AC 5 ms
6,940 KB
testcase_30 AC 16 ms
6,940 KB
testcase_31 AC 24 ms
6,940 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

/* #region Head */

// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath>   // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                                                        \
    sort(ALL(c));                                                                                                      \
    for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define CEIL(a, b) (((a) + (b)-1) / (b))

#define endl '\n'

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
    for (T &x : vec) is >> x;
    return is;
}
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)
    REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
    return os;
}

template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
    REP(i, 0, SIZE(arr)) is >> arr[i];
    return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    return os;
}

template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
    is >> pair_var.first >> pair_var.second;
    return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, const T &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        auto [key, value] = *itr;
        os << "(" << key << ", " << value << ")";
        auto itrcp = itr;
        if (++itrcp != map_var.end()) os << ", ";
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {
    pq<T> pq_cp(pq_var);
    os << "{";
    if (!pq_cp.empty()) {
        os << pq_cp.top(), pq_cp.pop();
        while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
    }
    return os << "}";
}

void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail) > 0) cout << ' ';
    pprint(move(tail)...);
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) DUMPOUT << ", ";
    dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
    if (comp(xmax, x)) {
        xmax = x;
        return true;
    }
    return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
    if (comp(x, xmin)) {
        xmin = x;
        return true;
    }
    return false;
}

// ローカル用
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif

#ifdef DEBUG_
#define DEB
#define dump(...)                                                                                                      \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                                                                    \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl                                        \
            << "    ",                                                                                                 \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

#define VAR(type, ...)                                                                                                 \
    type __VA_ARGS__;                                                                                                  \
    cin >> __VA_ARGS__;

template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }

struct AtCoderInitialize {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;
    AtCoderInitialize() {
        ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
        cout << fixed << setprecision(IOS_PREC);
        if (AUTOFLUSH) cout << unitbuf;
    }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

// #include <atcoder/all>
// using namespace atcoder;

/* #region Graph */

// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
template <class weight_t = int, class flow_t = int> struct Edge {
    ll src;          // エッジ始点となる頂点
    ll dst;          // エッジ終点となる頂点
    weight_t weight; // 重み
    flow_t cap;
    Edge() : src(0), dst(0), weight(0) {}
    Edge(ll src, ll dst, weight_t weight) : src(src), dst(dst), weight(weight) {}
    Edge(ll src, ll dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {}
    // Edge 標準出力
    friend ostream &operator<<(ostream &os, Edge &edge) {
        os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
        return os;
    }
};
// 同じ頂点を始点とするエッジ集合
template <class weight_t = int, class flow_t = int> class Node : public vc<Edge<weight_t, flow_t>> {
  public:
    ll idx;
    Node() : vc<Edge<weight_t, flow_t>>() {}
    // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); };
};
// graph[i] := 頂点 i を始点とするエッジ集合
template <class weight_t = int, class flow_t = int> class Graph : public vc<Node<weight_t, flow_t>> {
  public:
    Graph() : vc<Node<weight_t, flow_t>>() {}
    Graph(int n) : vc<Node<weight_t, flow_t>>(n) { REP(i, 0, n)(*this)[i].idx = i; }
    // 単方向
    void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); }
    // 双方向
    void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); }
};
// using Array = vc<Weight>;
// using Matrix = vc<Array>;

/* #endregion */

pll simple_knapsack_value_maximization(ll cap, ll n, vll value, vll weight) {
    // dp[(i+1)%2][w] := i 番目までの商品を用いて総重量をちょうど w にするときの，総価値の最大値
    constexpr ll INVALID_VALUE = -1;
    vvll dp(2, vll(cap + 1, INVALID_VALUE));
    // 初期条件 dp[0%2][w=0] = 0
    dp[0][0] = 0;
    REP(i, 0, n)    // 品物の種類 i ごと
    REPM(w, 0, cap) // i 番目までの商品を用いたときの総重量 w ごと
    {
        if (w < weight[i])
            dp[(i + 1) % 2][w] = dp[i % 2][w];
        else if (dp[i % 2][w - weight[i]] == INVALID_VALUE)
            dp[(i + 1) % 2][w] = dp[i % 2][w];
        else if (dp[i % 2][w] == INVALID_VALUE)
            dp[(i + 1) % 2][w] = dp[i % 2][w - weight[i]] + value[i];
        else
            dp[(i + 1) % 2][w] = max(dp[i % 2][w], dp[i % 2][w - weight[i]] + value[i]);
    }
    ll max_sum_value = 0; // 価値の総和の最大値
    ll sum_weight = 0;    // 重量の総和
    REPM(w, 0, cap) if (dp[n % 2][w] != INVALID_VALUE && chmax(max_sum_value, dp[n % 2][w])) sum_weight = w;

    return make_pair(max_sum_value, sum_weight);
}

// Problem
void solve() {
    VAR(ll, n, k);
    vll a(n - 1), b(n - 1), c(n - 1);
    REP(i, 0, n - 1) {
        cin >> a[i] >> b[i] >> c[i];
        --a[i], --b[i];
    }

    Graph<> graph(n);
    REP(i, 0, n - 1) graph.add_edge(a[i], b[i], i);

    vll w(n - 1, -1);
    vll visited(n, false);
    // ll leaf = 0;
    auto dfs = [&](auto &&dfs, ll v_idx, ll e_idx) -> ll {
        if (visited[v_idx]) return 0;
        visited[v_idx] = true;
        ll ret = 0;
        for (Edge<> &edge : graph[v_idx]) ret += dfs(dfs, edge.dst, edge.weight);
        if (ret == 0) ret = 1;
        if (e_idx != -1) w[e_idx] = ret;
        return ret;
    };
    dfs(dfs, 0, -1);
    // dump(w);
    // dump(c);

    vll value(n - 1);
    REP(i, 0, n - 1) value[i] = w[i] * c[i];
    // sort(ALL(value));
    // reverse(ALL(value));
    // REP(i, 0, k) value[i] *= 2;

    ll sum = accumulate(ALL(value), 0LL);
    // pprint(ans);

    // 長さの総和が k 以下となるように選ぶ
    // dump(value, sum);
    auto [max_sum_value, sum_weight] = simple_knapsack_value_maximization(k, n - 1, value, c);
    // dump(max_sum_value, sum_weight);
    pprint(sum + max_sum_value);
}

// entry point
int main() {
    solve();
    return 0;
}
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