#1049140 (C++23) No.2764 Warp Drive Spacecraft

提出ソース
結果

問題	No.2764 Warp Drive Spacecraft
ユーザー	noya2
提出日時	2025-03-04 06:16:38
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	297 ms / 3,000 ms
コード長	19,476 bytes
コンパイル時間	4,914 ms
コンパイル使用メモリ	313,552 KB
実行使用メモリ	26,728 KB
最終ジャッジ日時	2025-03-04 06:16:53
合計ジャッジ時間	14,046 ms
ジャッジサーバーID （参考情報）	judge1 / judge3
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 4
other	AC * 35
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ソースコード

raw source code
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

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

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/li_chao_tree.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/li_chao_tree.hpp"

namespace noya2{

template<typename T>
struct LiChaoTree {
    static constexpr T ymax = 3e18;
    struct Line {
        T a, b;
        Line (T _a = 0, T _b = ymax) : a(_a), b(_b) {}
        T get(T x){return a * x + b;}
    };
    LiChaoTree (const vector<T> &_xs){
        xs = _xs;
        sort(xs.begin(),xs.end());
        xs.erase(unique(xs.begin(),xs.end()),xs.end());
        int _n = xs.size();
        n = 1;
        while (n < _n) n *= 2;
        xs.resize(n);
        for (int i = _n; i < n; i++) xs[i] = xs[_n-1];
        seg.resize(n*2-1);
    }
    void line_add(T a, T b){ inner_line_add(Line(a,b),0,0,n);}
    void segment_add(T a, T b, T l, T r){
        int sl = lower_bound(xs.begin(),xs.end(),l) - xs.begin();
        int sr = lower_bound(xs.begin(),xs.end(),r) - xs.begin();
        inner_segment_add(sl,sr,Line(a,b),0,0,n);
    }
    T get(T x){
        int s = lower_bound(xs.begin(),xs.end(),x) - xs.begin();
        s += n-1;
        T res = ymax;
        res = min(res,seg[s].get(x));
        while (s > 0){
            s = (s-1) / 2;
            res = min(res,seg[s].get(x));
        }
        return res;
    }
  private:
    int n;
    vector<T> xs;
    vector<Line> seg;
    void inner_line_add(Line L, int i, int l, int r){
        T la = L.get(xs[l]);
        T lb = seg[i].get(xs[l]);
        T ra = L.get(xs[r-1]);
        T rb = seg[i].get(xs[r-1]);
        if (la >= lb && ra >= rb) return ;
        if (la <= lb && ra <= rb) {
            seg[i] = L;
            return ;
        }
        int m = (l + r) / 2;
        T ma = L.get(xs[m]);
        T mb = seg[i].get(xs[m]);
        if (ma < mb){
            swap(L,seg[i]);
            swap(la,lb);
            swap(ra,rb);
        }
        if (la < lb) inner_line_add(L,2*i+1,l,m);
        if (ra < rb) inner_line_add(L,2*i+2,m,r);
    }
    void inner_segment_add(int L, int R, Line S, int i, int l, int r){
        if (r <= L || R <= l) return ;
        if (L <= l && r <= R) inner_line_add(S,i,l,r);
        else {
            int m = (l + r) / 2;
            inner_segment_add(L,R,S,2*i+1,l,m);
            inner_segment_add(L,R,S,2*i+2,m,r);
        }
    }
};

} // namespace noya2
#line 4 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"
#include<ranges>
#line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp"

namespace noya2::internal {

template<class E>
struct csr {
    csr () {}
    csr (int _n) : n(_n) {}
    csr (int _n, int m) : n(_n){
        start.reserve(m);
        elist.reserve(m);
    }
    // ACL style constructor (do not have to call build)
    csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) {
        for (auto &[i, e] : idx_elem){
            start[i + 2]++;
        }
        for (int i = 1; i < n; i++){
            start[i + 2] += start[i + 1];
        }
        for (auto &[i, e] : idx_elem){
            elist[start[i + 1]++] = e;
        }
        prepared = true;
    }
    int add(int idx, E elem){
        int eid = start.size();
        start.emplace_back(idx);
        elist.emplace_back(elem);
        return eid;
    }
    void build(){
        if (prepared) return ;
        int m = start.size();
        std::vector<E> nelist(m);
        std::vector<int> nstart(n + 2, 0);
        for (int i = 0; i < m; i++){
            nstart[start[i] + 2]++;
        }
        for (int i = 1; i < n; i++){
            nstart[i + 2] += nstart[i + 1];
        }
        for (int i = 0; i < m; i++){
            nelist[nstart[start[i] + 1]++] = elist[i];
        }
        swap(elist,nelist);
        swap(start,nstart);
        prepared = true;
    }
    const auto operator[](int idx) const {
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    auto operator[](int idx){
        return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]);
    }
    const auto operator()(int idx, int l, int r) const {
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    auto operator()(int idx, int l, int r){
        return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r);
    }
    size_t size() const {
        return n;
    }
    int n;
    std::vector<int> start;
    std::vector<E> elist;
    bool prepared = false;
};

} // namespace noya2::internal
#line 2 "/Users/noya2/Desktop/Noya2_library/graph/unweighted_type.hpp"

namespace noya2 {

struct unweighted {};

} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp"

#line 12 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp"

namespace noya2 {

template<typename Cost>
struct graph {
    int n;
    internal::csr<std::pair<int,Cost>> g;
    Cost dist_inf = std::numeric_limits<Cost>::max() / 3;
    graph (int _n = 0) : n(_n), g(_n) {}
    graph (int _n, int _m) : n(_n), g(_n,_m) {}
    // 有向辺を追加 (無向辺ではないことに注意！)
    int add_edge(int u, int v, Cost cost = 1){
        int id = g.add(u, {v,cost});
        return id;
    }
    template<bool directed>
    static graph input(int _n, int _m, int indexed = 1){
        if constexpr (directed){
            graph g(_n, _m*2);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                Cost c; std::cin >> c;
                g.add_edge(u, v, c);
                g.add_edge(v, u, c);
            }
            g.build();
            return g;
        }
        else {
            graph g(_n, _m);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                Cost c; std::cin >> c;
                g.add_edge(u, v, c);
            }
            g.build();
            return g;
        }
    }
    void build(){
        g.build();
    }
    void set_inf(Cost new_inf){
        dist_inf = new_inf;
    }
    std::vector<Cost> dijkstra(int s){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        dist[s] = 0;
        using P = std::pair<Cost,int>;
        std::priority_queue<P,std::vector<P>,std::greater<P>> pque;
        pque.push(P(0,s));
        while (!pque.empty()){
            auto [d, v] = pque.top(); pque.pop();
            if (dist[v] < d) continue;
            for (auto [u, c] : g[v]){
                if (chmin(dist[u],d+c)){
                    pque.push(P(dist[u],u));
                }
            }
        }
        return dist;
    }
    std::vector<int> reconstruct(int s, int t, const std::vector<Cost> &dist){
        if (dist[t] == dist_inf) return {};
        g.build();
        std::vector<int> from(n,-1);
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto [u, c] : g[v]){
                if (from[u] == -1 && dist[u] == dist[v] + c){
                    from[u] = v;
                    que.push(u);
                }
            }
        }
        std::vector<int> ans = {t};
        while (t != s){
            t = from[t];
            ans.emplace_back(t);
        }
        std::reverse(ans.begin(),ans.end());
        return ans;
    }
    std::vector<Cost> bfs01(int s){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        dist[s] = 0;
        std::deque<int> que;
        que.push_back(s);
        while (!que.empty()){
            int v = que.front(); que.pop_front();
            for (auto [u, c] : g[v]){
                if (chmin(dist[u],dist[v]+c)){
                    if (c == 0) que.push_front(u);
                    else que.push_back(u);
                }
            }
        }
        return dist;
    }
    std::vector<Cost> bfs1(int s){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        dist[s] = 0;
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto [u, c] : g[v]){
                if (chmin(dist[u],dist[v]+c)){
                    que.push(u);
                }
            }
        }
        return dist;
    }
    std::vector<Cost> bellman_ford(int s, bool &ng_cycle){
        g.build();
        std::vector<Cost> dist(n,dist_inf);
        std::vector<int> ng;
        dist[s] = 0;
        int tm = 0;
        while (tm < n){
            bool finish = true;
            for (int v = 0; v < n; v++){
                if (dist[v] == dist_inf) continue;
                for (auto [u, c] : g[v]){
                    if (chmin(dist[u],dist[v]+c)){
                        finish = false;
                        if (tm == n-1) ng.emplace_back(u);
                    }
                }
            }
            if (finish) break;
            tm++;
        }
        ng_cycle = (tm == n);
        if (ng_cycle){
            for (auto v : ng) dist[v] = -dist_inf;
            tm = n;
            while (tm--){
                for (int v = 0; v < n; v++){
                    if (dist[v] != -dist_inf) continue;
                    for (auto [u, c] : g[v]){
                        dist[u] = -dist_inf;
                    }
                }
            }
        }
        return dist;
    }
    std::vector<std::vector<Cost>> warshall_floyd(){
        g.build();
        std::vector<std::vector<Cost>> dist(n,std::vector<Cost>(n,dist_inf));
        for (int v = 0; v < n; v++){
            dist[v][v] = 0;
            for (auto [u, c] : g[v]){
                chmin(dist[v][u],c);
            }
        }
        for (int k = 0; k < n; k++){
            for (int i = 0; i < n; i++){
                for (int j = 0; j < n; j++){
                    chmin(dist[i][j],dist[i][k]+dist[k][j]);
                }
            }
        }
        return dist;
    }
    const auto operator[](int idx) const { return g[idx]; }
    auto operator[](int idx) { return g[idx]; }
};


template<>
struct graph<unweighted> {
    int n;
    internal::csr<int> g;
    int dist_inf = std::numeric_limits<int>::max() / 2;
    graph (int _n = 0) : n(_n), g(_n) {}
    graph (int _n, int _m) : n(_n), g(_n,_m) {}
    // 有向辺を追加 (無向辺ではないことに注意！)
    int add_edge(int u, int v){
        int id = g.add(u, v);
        return id;
    }
    template<bool directed>
    static graph input(int _n, int _m, int indexed = 1){
        if constexpr (directed){
            graph g(_n, _m*2);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                g.add_edge(u, v);
                g.add_edge(v, u);
            }
            g.build();
            return g;
        }
        else {
            graph g(_n, _m);
            for (int i = 0; i < _m; i++){
                int u, v; std::cin >> u >> v;
                u -= indexed, v -= indexed;
                g.add_edge(u, v);
            }
            g.build();
            return g;
        }
    }
    void build(){
        g.build();
    }
    void set_inf(int new_inf){
        dist_inf = new_inf;
    }
    std::vector<int> reconstruct(int s, int t, const std::vector<int> &dist){
        if (dist[t] == dist_inf) return {};
        g.build();
        std::vector<int> from(n,-1);
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto u : g[v]){
                if (from[u] == -1 && dist[u] == dist[v] + 1){
                    from[u] = v;
                    que.push(u);
                }
            }
        }
        std::vector<int> ans = {t};
        while (t != s){
            t = from[t];
            ans.emplace_back(t);
        }
        std::reverse(ans.begin(),ans.end());
        return ans;
    }
    std::vector<int> bfs(int s){
        g.build();
        std::vector<int> dist(n,dist_inf);
        dist[s] = 0;
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto u : g[v]){
                if (chmin(dist[u],dist[v]+1)){
                    que.push(u);
                }
            }
        }
        return dist;
    }
    const auto operator[](int idx) const { return g[idx]; }
    auto operator[](int idx) { return g[idx]; }
};

template<>
struct graph<bool> {
    int n;
    internal::csr<std::pair<int,bool>> g;
    int dist_inf = std::numeric_limits<int>::max() / 2;
    graph (int _n = 0) : n(_n), g(_n) {}
    graph (int _n, int _m) : n(_n), g(_n,_m) {}
    // 有向辺を追加 (無向辺ではないことに注意！)
    int add_edge(int u, int v, bool cost){
        int id = g.add(u, {v, cost});
        return id;
    }
    void build(){
        g.build();
    }
    void set_inf(int new_inf){
        dist_inf = new_inf;
    }
    std::vector<int> reconstruct(int s, int t, const std::vector<int> &dist){
        if (dist[t] == dist_inf) return {};
        g.build();
        std::vector<int> from(n,-1);
        std::queue<int> que;
        que.push(s);
        while (!que.empty()){
            int v = que.front(); que.pop();
            for (auto [u, b] : g[v]){
                int c = (int)b;
                if (from[u] == -1 && dist[u] == dist[v] + c){
                    from[u] = v;
                    que.push(u);
                }
            }
        }
        std::vector<int> ans = {t};
        while (t != s){
            t = from[t];
            ans.emplace_back(t);
        }
        std::reverse(ans.begin(),ans.end());
        return ans;
    }
    std::vector<int> bfs01(int s){
        g.build();
        std::vector<int> dist(n,dist_inf);
        dist[s] = 0;
        std::deque<int> que;
        que.push_back(s);
        while (!que.empty()){
            int v = que.front(); que.pop_front();
            for (auto [u, b] : g[v]){
                int c = (int)b;
                if (chmin(dist[u],dist[v]+c)){
                    if (c == 0) que.push_front(u);
                    else que.push_back(u);
                }
            }
        }
        return dist;
    }
    const auto operator[](int idx) const { return g[idx]; }
    auto operator[](int idx) { return g[idx]; }
};

} // namespace noya2
#line 6 "c.cpp"

void solve(){
    int n, m; in(n,m);
    vector<ll> a(n); in(a);
    graph<ll> g(n);
    rep(i,m){
        int u, v; in(u,v); u--, v--;
        ll c; in(c);
        g.add_edge(u,v,c);
        g.add_edge(v,u,c);
    }
    auto b = g.dijkstra(0);
    auto c = g.dijkstra(n-1);
    LiChaoTree<ll> lct(a);
    rep(i,n){
        lct.line_add(a[i],b[i]);
    }
    ll ans = b[n-1];
    rep(i,n){
        chmin(ans,lct.get(a[i])+c[i]);
    }
    out(ans);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
yukicoder

結果

ソースコード
