結果

問題 No.2764 Warp Drive Spacecraft
ユーザー 👑 Nachia
提出日時 2024-05-18 00:30:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 301 ms / 3,000 ms
コード長 12,475 bytes
コンパイル時間 1,734 ms
コンパイル使用メモリ 131,432 KB
最終ジャッジ日時 2025-02-21 15:35:03
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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

diff #
プレゼンテーションモードにする

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
#include <atcoder/modint>
#include <cassert>
namespace nachia{
template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};
} // namespace nachia
namespace nachia{
struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
        m_n = newV;
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};
} // namespace nachia
namespace nachia{
// require :
//   Weight + Weight
//   Weight < Weight
//   constructor Weight(Weight2)
template<class Weight = long long, class Weight2 = Weight>
struct DijkstraShortestPath {
private:
    nachia::Graph g;
    std::vector<Weight> dist;
    std::vector<int> pre;
    std::vector<int> ord;
public:
    DijkstraShortestPath(
        nachia::Graph graph,
        const std::vector<Weight2>& weight,
        const std::vector<std::pair<int, Weight>>& starting,
        const Weight Inf,
        int goal = -1
    ){
        using T = std::pair<Weight, int>;
        g = std::move(graph);
        auto adj = g.getEdgeIndexArray();
        std::vector<Weight> D(g.numVertices(), Inf);
        std::vector<int> E(g.numVertices(), -1);
        struct Comp { bool operator()(T a, T b) const noexcept { return b < a; }; };
        std::priority_queue<T, std::vector<T>, Comp> Q;
        ord.clear();
        for(auto a : starting) if(a.second < D[a.first]){
            D[a.first] = a.second;
            Q.push({ a.second, a.first });
        }
        while(Q.size()){
            int p = Q.top().second;
            Weight d = Q.top().first; Q.pop();
            if(D[p] < d) continue;
            ord.push_back(p);
            if(p == goal) break;
            for(auto e : adj[p]){
                int q = g[e].from ^ g[e].to ^ p;
                Weight nxd = d + Weight(weight[e]);
                if(!(nxd < D[q])) continue;
                E[q] = e;
                D[q] = nxd;
                Q.emplace(nxd, q);
            }
        }
        dist = std::move(D);
        pre = std::move(E);
    }
    Weight distTo(int v) const noexcept { return dist[v]; }
    const std::vector<Weight>& distTable() const { return dist; }
    int prevEdge(int v) const noexcept { return pre[v]; }
    int prevVertex(int v) const noexcept { return pre[v] >= 0 ? g[pre[v]].from ^ g[pre[v]].to ^ v : -1; }
    std::vector<int> pathTo(int v) const {
        std::vector<int> res;
        while(pre[v] >= 0){
            res.push_back(pre[v]);
            v = prevVertex(v);
        }
        std::reverse(res.begin(), res.end());
        return res;
    }
    std::vector<int> getSearchOrder() const { return ord; }
    Graph getTree() const {
        Graph res(g.numVertices(), false);
        for(int i=0; i<g.numVertices(); i++) if(pre[i] >= 0){
            res.addEdge(prevVertex(i), i);
        }
        return res;
    }
};
} // namespace nachia
namespace nachia {
template<class Elem>
struct SmawkAlgorithm {
template<class Gen, class Cmp = std::less<Elem>>
static std::vector<std::pair<Elem, int>> Solve(
    int height, int width,
    Gen gen,
    Cmp cmp = Cmp()
){
    if(height == 0) return std::vector<std::pair<Elem, int>>(0);
    auto reduce = [&](int yst, const std::vector<int>& cols)
     -> std::vector<int> {
        int w = int(cols.size());
        std::vector<int> idx;
        int r = -1;
        for(int q=0; q<w; q++){
            if(idx.empty()){
                idx.push_back(q);
                r += yst;
                continue;
            }
            int a = cols[idx.back()];
            int b = cols[q];
            if(cmp(gen(r,a), gen(r,b))){
                if(r+yst < height){ idx.push_back(q); r += yst; }
            } else {
                idx.pop_back(); q--; r -= yst;
            }
        }
        return idx;
    };
    auto ysts = std::vector<int>(1,1);
    auto cols = std::vector<std::vector<int>>(1);
    for(int i=0; i<width; i++) cols[0].push_back(i);
    cols[0] = reduce(1, cols[0]);
    while(true){
        int nxst = ysts.back() * 2;
        if(height < nxst) break;
        auto nxc = reduce(nxst, cols.back());
        int w = nxc.size();
        for(int i=0; i<w; i++) nxc[i] = cols.back()[nxc[i]];
        cols.push_back(move(nxc));
        ysts.push_back(nxst);
    }
    std::vector<std::pair<Elem,int>> ans(height, std::make_pair(gen(0,0), 0));
    while(cols.size()){
        auto x = std::move(cols.back()); cols.pop_back();
        int st = ysts.back(); ysts.pop_back();
        int p = 0;
        for(int y=st-1; y<height; y+=st*2){
            int r = y+st < height ? ans[y+st].second : width-1;
            ans[y] = std::make_pair(gen(y,x[p]), x[p]);
            while(p+1 < int(x.size()) && x[p+1] <= r){
                int xp = x[++p];
                auto fxp = gen(y,xp);
                if(!cmp(ans[y].first, fxp)) ans[y] = std::make_pair(fxp, xp);
            }
        }
    }
    return ans;
}
};
// bool Func(y, xl, xr) , xl < xr
//   returns if A[y][xl] < A[y][xr]
template<class Func>
std::vector<int> SmawkAlgorithmIndependent(
    int height, int width,
    Func f
){
    auto tmp = SmawkAlgorithm<std::pair<int,int>>::Solve(
        height, width,
        [](int r, int c){ return std::make_pair(r,c); },
        [&f](std::pair<int,int> l, std::pair<int,int> r) -> bool {
            return f(l.first, l.second, r.second); } );
    std::vector<int> res(height);
    for(int i=0; i<height; i++) res[i] = tmp[i].first;
    return res;
}
} // namespace nachia
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
#define repr(i,n) for(int i=int(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
template<typename A> using nega_queue = std::priority_queue<A,std::vector<A>,std::greater<A>>;
using Modint = atcoder::static_modint<998244353>;
using namespace std;
void testcase(){
    int N, M; cin >> N >> M;
    vector<i64> W(N); rep(i,N) cin >> W[i];
    auto graph = nachia::Graph(N, true);
    vector<i64> D(M);
    rep(i,M){
        int u,v; cin >> u >> v >> D[i]; u--; v--;
        graph.addEdge(u, v);
    }
    auto D0 = nachia::DijkstraShortestPath<i64>(graph, D, {{0,0}}, INF).distTable();
    auto DN = nachia::DijkstraShortestPath<i64>(graph, D, {{N-1,0}}, INF).distTable();
    i64 ans = D0[N-1];
    vector<int> X(N);
    rep(i,N) X[i] = i;
    sort(X.begin(), X.end(), [&](int l, int r){ return W[l] < W[r]; });
    auto smawk = nachia::SmawkAlgorithm<i64>::Solve(N, N, [&](int r, int c){
        r = X[r]; c = X[c];
        return W[r] * W[c] + D0[r] + DN[c]; });
    rep(i,N) chmin(ans, smawk[i].first);
    cout << ans << endl;
}
int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    #ifdef NACHIA
    int T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)
    #endif
    testcase();
    return 0;
}
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