Submission #10101450

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Source Code Expand

#include <iostream>
#include <algorithm>
#include <numeric>
#include <vector>
#include <queue>
#include <tuple>

using lint = long long;

template <class Cost = int>
struct Edge {
    int src, dst;
    Cost cost;
    Edge(int src = -1, int dst = -1, Cost cost = 1)
        : src(src), dst(dst), cost(cost){};

    bool operator<(const Edge<Cost>& e) const { return this->cost < e.cost; }
    bool operator>(const Edge<Cost>& e) const { return this->cost > e.cost; }
};

template <class Cost = int>
using Edges = std::vector<Edge<Cost>>;

template <class T>
using MinHeap = std::priority_queue<T, std::vector<T>, std::greater<T>>;

struct UnionFind {
    std::vector<int> par, sz;
    int gnum;

    explicit UnionFind(int n)
        : par(n), sz(n, 1), gnum(n) {
        std::iota(par.begin(), par.end(), 0);
    }

    int find(int v) {
        return (par[v] == v) ? v : (par[v] = find(par[v]));
    }

    void unite(int u, int v) {
        u = find(u), v = find(v);
        if (u == v) return;

        if (sz[u] < sz[v]) std::swap(u, v);
        sz[u] += sz[v];
        par[v] = u;
        --gnum;
    }

    bool same(int u, int v) { return find(u) == find(v); }
    bool ispar(int v) { return v == find(v); }
    int size(int v) { return sz[find(v)]; }
};

void solve() {
    int n;
    lint d;
    std::cin >> n >> d;

    std::vector<lint> xs(n);
    for (auto& x : xs) std::cin >> x;

    MinHeap<Edge<lint>> heap;
    std::queue<std::pair<int, int>> que;
    que.emplace(0, n);

    while (!que.empty()) {
        int l, r;
        std::tie(l, r) = que.front();
        que.pop();
        if (r - l <= 1) continue;

        // 区間を分割
        int m = (l + r) / 2;
        que.emplace(l, m);
        que.emplace(m, r);

        // 左右で最もコストが小さい頂点を探す
        int li = l;
        for (int i = l + 1; i < m; ++i) {
            if (xs[i] - i * d < xs[li] - li * d) li = i;
        }
        int ri = m;
        for (int i = m + 1; i < r; ++i) {
            if (xs[i] + i * d < xs[ri] + ri * d) ri = i;
        }

        // 辺を追加
        for (int i = l; i < m; ++i) {
            heap.emplace(i, ri, xs[i] + xs[ri] + (ri - i) * d);
        }
        for (int i = m; i < r; ++i) {
            heap.emplace(li, i, xs[li] + xs[i] + (i - li) * d);
        }
    }

    // Kruskal
    lint ans = 0;
    UnionFind uf(n);
    while (!heap.empty()) {
        auto e = heap.top();
        heap.pop();

        if (uf.same(e.src, e.dst)) continue;
        ans += e.cost;
        uf.unite(e.src, e.dst);
    }

    std::cout << ans << std::endl;
}

int main() {
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}

Submission Info

Judge Result