【BZOJ4016】[FJOI2014]最短路径树问题

时间：2022-10-03 15:11:38

【BZOJ4016】[FJOI2014]最短路径树问题

题面

bzoj

洛谷

题解

虽然调了蛮久，但是思路还是蛮简单的2333

把最短路径树构出来，然后点分治就好啦

ps:如果树构萎了，这组数据可以卡掉

代码

#include <iostream>

#include <cstdio>

#include <cstdlib>

#include <cstring>

#include <cmath>

#include <algorithm>

#include <queue>

#include <map>

#include <vector>

using namespace std;

inline int gi() {

    register int data = 0, w = 1;

    register char ch = 0;

    while (!isdigit(ch) && ch != '-') ch = getchar();

    if (ch == '-') w = -1, ch = getchar();

    while (isdigit(ch)) data = 10 * data + ch - '0', ch = getchar();

    return w * data;

}

const int MAX_N = 3e4 + 5;

const int MAX_M = 6e4 + 5;

const int INF = 1e9;

int N, M, K;

struct Graph { int to, next, cost; } e[MAX_M << 2];

int fir1[MAX_N], fir2[MAX_N], e_cnt;

void clearGraph() {

    memset(fir1, -1, sizeof(fir1));

    memset(fir2, -1, sizeof(fir2));

    e_cnt = 0;

}

void Add_Edge(int *fir, int u, int v, int w) { e[e_cnt] = (Graph){v, fir[u], w}; fir[u] = e_cnt++; }

vector<int> vec[MAX_N];

bool vis[MAX_N];

bool cmp(int i, int j) { return e[i].to < e[j].to; }

void dijkstra() {

    static priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > que;

    static int dis[MAX_N];

    fill(&dis[1], &dis[N + 1], INF);

    dis[1] = 0, que.push(make_pair(0, 1));

    while (!que.empty()) {

        pair<int, int> p = que.top(); que.pop();

        int x = p.second;

        if (p.first > dis[x]) continue;

		for (int i = fir1[x]; ~i; i = e[i].next) {

			int v = e[i].to;

			if (dis[v] + e[i].cost == dis[x]) vec[v].push_back(i ^ 1);

		}

        for (int i = fir1[x]; ~i; i = e[i].next) {

            int v = e[i].to;

            if (dis[x] + e[i].cost < dis[v]) {

                dis[v] = dis[x] + e[i].cost;

                que.push(make_pair(dis[v], v));

            }

        }

    }

}

void dfs(int x) {

	vis[x] = 1;

	sort(vec[x].begin(), vec[x].end(), cmp);

	for (int i = 0, sz = vec[x].size(); i < sz; i++) {

		int j = vec[x][i]; if (vis[e[j].to]) continue;

		Add_Edge(fir2, x, e[j].to, e[j].cost), Add_Edge(fir2, e[j].to, x, e[j].cost);

		dfs(e[j].to);

	}

}

bool used[MAX_N];

int size[MAX_N], dep[MAX_N], dis[MAX_N], centroid, sz, rmx, mx;

int stk[MAX_N], top = 0;

int ans1 = 0, ans2 = 0;

void search_centroid(int x, int fa) {

    size[x] = 1;

    int mx = 0;

    for (int i = fir2[x]; ~i; i = e[i].next) {

        int v = e[i].to;

        if (v == fa || used[v]) continue;

   		search_centroid(v, x);

   		size[x] += size[v];

       	mx = max(mx, size[v]);

    }

    mx = max(mx, sz - size[x]);

    if (mx < rmx) centroid = x, rmx = mx;

}

namespace cpp1 {

    int bln[MAX_N];

    void getans(int x, int fa) {

        if (dep[x] < K - 1) ans1 = max(ans1, bln[K - 1 - dep[x]] + dis[x]);

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v] || v == fa) continue;

            dep[v] = dep[x] + 1;

            dis[v] = dis[x] + e[i].cost;

            getans(v, x);

        }

    }

    void getdis(int x, int fa) {

        stk[++top] = x; bln[dep[x]] = max(bln[dep[x]], dis[x]);

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v] || v == fa) continue;

            getdis(v, x);

        }

    }

    void Div(int x) {

        used[x] = 1; top = 0;

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v]) continue;

            dep[v] = 1, dis[v] = e[i].cost;

            getans(v, 0), getdis(v, 0);

        }

        ans1 = max(ans1, bln[K - 1]);

        for (int i = 1; i <= top; i++) bln[dep[stk[i]]] = 0;

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v]) continue;

            rmx = sz = size[v], centroid = 0;

            search_centroid(v, 0);

            Div(centroid);

        }

    }

}

namespace cpp2 {

    map<pair<int, int>, int> mp;

    void getans(int x, int fa) {

        if (dep[x] < K - 1) ans2 += mp[make_pair(ans1 - dis[x], K - 1 - dep[x])];

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v] || v == fa) continue;

            dep[v] = dep[x] + 1;

            dis[v] = dis[x] + e[i].cost;

            getans(v, x);

        }

    }

    void getdis(int x, int fa) {

        mp[make_pair(dis[x], dep[x])]++;

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v] || v == fa) continue;

            getdis(v, x);

        }

    }

    void Div(int x) {

        used[x] = 1;

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v]) continue;

            dep[v] = 1, dis[v] = e[i].cost;

            getans(v, 0), getdis(v, 0);

        }

        ans2 += mp[make_pair(ans1, K - 1)];

        mp.clear();

        for (int i = fir2[x]; ~i; i = e[i].next) {

            int v = e[i].to; if (used[v]) continue;

            rmx = sz = size[v], centroid = 0;

            search_centroid(v, 0);

            Div(centroid);

        }

    }

}

int main () {

    N = gi(), M = gi(), K = gi();

    clearGraph();

    for (int i = 1; i <= M; i++) {

        int u = gi(), v = gi(), w = gi();

        Add_Edge(fir1, u, v, w), Add_Edge(fir1, v, u, w);

    }

    dijkstra();

	dfs(1);

    sz = rmx = N;

    search_centroid(1, 0);

    cpp1::Div(centroid);

    memset(used, 0, sizeof(used));

    sz = rmx = N, centroid = 0;

    search_centroid(1, 0);

    cpp2::Div(centroid);

    printf("%d %d\n", ans1, ans2);

    return 0;

}

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