【FJOI2014】最短路径树问题

题面

题解

强行将最短路和点分治（长链剖分）融合在一起的题目

构建出字典序最小的最短路树之后，就可以用点分治来解决了

不过有一些细节要注意：

3 3 k
1 2 1
2 3 1
1 3 2

这样建出的最短路树是\(1-2-3\)

而不是\(1-2,1-3\)

相信这组美妙的数据可以帮助你调错

再来一组数据

这组\(hack\)数据的核心和上面那个是一样的

代码

#include<cstdio>
#include<cstring>
#include<cctype>
#include<climits>
#include<algorithm>
#include<queue>
#define RG register
#define clear(x, y) memset(x, y, sizeof(x))

inline int read()
{
	int data = 0, w = 1; char ch = getchar();
	while(ch != '-' && (!isdigit(ch))) ch = getchar();
	if(ch == '-') w = -1, ch = getchar();
	while(isdigit(ch)) data = data * 10 + (ch ^ 48), ch = getchar();
	return data * w;
}

const int maxn(30010);
int n, m, K;
struct edge { int next, to, dis; };
inline void add_edge(int, int, int);

namespace Dij
{
	std::vector<std::pair<int, int> > g[maxn]; bool vis[maxn];
	int dis[maxn];
	inline void add_edge(int from, int to, int dis)
	{
		g[from].push_back(std::make_pair(to, dis));
		g[to].push_back(std::make_pair(from, dis));
	}

	std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int> >,
		std::greater<std::pair<int, int> > > Q;
	void dfs(int x)
	{
		vis[x] = 1;
		for(std::vector<std::pair<int, int> >::iterator
				i = g[x].begin(); i != g[x].end(); ++i)
		{
			int to = i -> first; if(vis[to]) continue;
			if(dis[to] == dis[x] + i -> second)
				::add_edge(x, to, i -> second), dfs(to);
		}
	}

	void main()
	{
		for(RG int i = 1; i <= n; i++) std::sort(g[i].begin(), g[i].end());
		for(RG int i = 1; i <= n; i++) dis[i] = INT_MAX >> 1;
		Q.push(std::make_pair(dis[1] = 0, 1));
		while(!Q.empty())
		{
			int x = Q.top().second; Q.pop(); if(vis[x]) continue;
			vis[x] = 1;
			for(std::vector<std::pair<int, int> >::iterator
				i = g[x].begin(); i != g[x].end(); ++i)
			{
				int to = i -> first; if(vis[to]) continue;
				if(dis[x] + i -> second < dis[to])
				{
					dis[to] = dis[x] + i -> second;
					Q.push(std::make_pair(dis[to], to));
				}
			}
		}
		clear(vis, 0); dfs(1);
	}
}

edge e[maxn << 1]; int head[maxn], e_num;
inline void add_edge(int from, int to, int dis)
{
	e[++e_num] = (edge) {head[from], to, dis}; head[from] = e_num;
	e[++e_num] = (edge) {head[to], from, dis}; head[to]   = e_num;
}

bool vis[maxn];
int SIZE, _min, root, size[maxn], stk[maxn], cnt_tdep[maxn];
int top, tdep[maxn], ans, cnt_ans, dep[maxn];

void GetRoot(int x, int fa)
{
	size[x] = 1; int tot = 0;
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to] || to == fa) continue;
		GetRoot(to, x); size[x] += size[to];
		tot = std::max(tot, size[to]);
	}
	tot = std::max(tot, SIZE - size[x]);
	if(tot < _min) _min = tot, root = x;
}

void GetDep(int x, int fa, int _dep, int _dis)
{
	stk[++top] = x;
	if(tdep[_dep] <= _dis)
	{
		if(tdep[_dep] == _dis) ++cnt_tdep[_dep];
		else tdep[_dep] = _dis, cnt_tdep[_dep] = 1;
	}

	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to] || to == fa) continue;
		GetDep(to, x, _dep + 1, _dis + e[i].dis);
	}
}

void Calc(int x, int fa, int _dep, int _dis)
{
	dep[x] = _dep;
	if(dep[x] < K - 1)
	{
		int nowdis = tdep[K - _dep - 1] + _dis;
		if(ans <= nowdis)
		{
			if(ans == nowdis) cnt_ans += cnt_tdep[K - _dep - 1];
			else ans = nowdis, cnt_ans = cnt_tdep[K - _dep - 1];
		}
	}
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to] || to == fa) continue;
		Calc(to, x, _dep + 1, _dis + e[i].dis);
	}
}

void dfs(int x)
{
	vis[x] = 1, top = 0;
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to]) continue;
		Calc(to, x, 1, e[i].dis), GetDep(to, x, 1, e[i].dis);
	}
	if(ans <= tdep[K - 1])
	{
		if(ans == tdep[K - 1]) cnt_ans += cnt_tdep[K - 1];
		else ans = tdep[K - 1], cnt_ans = cnt_tdep[K - 1];
	}
	for(RG int i = 1; i <= top; i++)
		cnt_tdep[dep[stk[i]]] = tdep[dep[stk[i]]] = 0;
	for(RG int i = head[x]; i; i = e[i].next)
	{
		int to = e[i].to; if(vis[to]) continue;
		SIZE = _min = size[to], root = 0; GetRoot(to, x);
		dfs(root);
	}
}

int main()
{
	n = read(), m = read(), K = read();
	for(RG int i = 1, a, b, c; i <= m; i++)
		a = read(), b = read(), c = read(),
		Dij::add_edge(a, b, c);
	Dij::main();
	SIZE = _min = n; GetRoot(1, 0); dfs(root);
	printf("%d %d\n", ans, cnt_ans);
	return 0;
}