Description
Input
Output
Sample Input
6 6 4 1 2 1 2 3 1 3 4 1 2 5 1 3 6 1 5 6 1
Sample Output
3 4
Hint
对于所有数据n<=30000,m<=60000，2<=K<=n。数据保证最短路径树上至少存在一条长度为K的路径。
#include<queue>
#include<cstdio>
#include<algorithm>
using namespace std;
const int INF = 0x7FFFFFFF;
const int maxn = 2e5 + 10;
int n, m, x, y, z, K;
char ch;
struct Tree
{
int ft[maxn], nt[maxn], u[maxn], v[maxn], sz, n;
int vis[maxn], cnt[maxn], mx[maxn], a, b;
void clear(int n)
{
this->n = n;
a = b = sz = 0;
for (int i = 1; i <= n; i++)
{
ft[i] = -1;
vis[i] = 0;
}
}
void AddEdge(int x, int y, int z)
{
u[sz] = y; v[sz] = z;
nt[sz] = ft[x]; ft[x] = sz++;
}
int dfs(int x, int fa, int sum)
{
int ans = mx[x] = 0;
cnt[x] = 1;
for (int i = ft[x]; i != -1; i = nt[i])
{
if (vis[u[i]] || u[i] == fa) continue;
int y = dfs(u[i], x, sum);
if (mx[y]<mx[ans]) ans = y;
cnt[x] += cnt[u[i]];
mx[x] = max(mx[x], cnt[u[i]]);
}
mx[x] = max(mx[x], sum - cnt[x]);
return mx[x] < mx[ans] ? x : ans;
}
int deep(int x, int fa, int dep)
{
if (dep == K) return K - 1;
int ans = dep;
mx[dep] = cnt[dep] = 0;
for (int i = ft[x]; i != -1; i = nt[i])
{
if (vis[u[i]] || u[i] == fa) continue;
ans = max(ans, deep(u[i], x, dep + 1));
}
return ans;
}
void get(int x, int fa, int dep, int len, int kind, int lit)
{
if (dep == K) return;
if (!kind)
{
if (K - 1 - dep <= lit && cnt[K - 1 - dep])
{
if (a<len + mx[K - 1 - dep])
{
a = len + mx[K - 1 - dep];
b = cnt[K - 1 - dep];
}
else if (a == len + mx[K - 1 - dep]) b += cnt[K - 1 - dep];
}
}
else
{
if (mx[dep]<len) mx[dep] = len, cnt[dep] = 1;
else if (mx[dep] == len) cnt[dep]++;
}
for (int i = ft[x]; i != -1; i = nt[i])
{
if (vis[u[i]] || u[i] == fa) continue;
get(u[i], x, dep + 1, len + v[i], kind, lit);
}
}
void find(int x)
{
int len = deep(x, -1, 0);
if (len + len + 1 < K) return;
cnt[0] = 1;
for (int i = ft[x]; i != -1; i = nt[i])
{
if (vis[u[i]]) continue;
get(u[i], x, 1, v[i], 0, len);
get(u[i], x, 1, v[i], 1, len);
}
}
void work(int x, int sum)
{
mx[0] = INF;
int y = dfs(x, -1, sum);
vis[y] = 1; find(y);
for (int i = ft[y]; i != -1; i = nt[i])
{
if (vis[u[i]]) continue;
if (cnt[u[i]]<cnt[y]) work(u[i], cnt[u[i]]);
else work(u[i], sum - cnt[y]);
}
}
}solve;
struct DAG
{
int ft[maxn], nt[maxn], u[maxn], v[maxn], sz, n;
int dis[maxn], vis[maxn];
struct point
{
int x, y;
point(int x = 0, int y = 0) :x(x), y(y) {}
bool operator<(const point& a)const
{
return y == a.y ? x > a.x : y >a.y;
}
};
void clear(int n)
{
this->n = n; sz = 0;
for (int i = 1; i <= n; i++)
{
ft[i] = dis[i] = -1;
vis[i] = 0;
}
}
void AddEdge(int x, int y, int z)
{
u[sz] = y; v[sz] = z;
nt[sz] = ft[x]; ft[x] = sz++;
}
void dfs(int x)
{
vis[x] = 0;
for (int i = ft[x]; i != -1; i = nt[i])
{
if (dis[u[i]] == dis[x] + v[i])
{
if (!vis[u[i]]) continue;
solve.AddEdge(x, u[i], v[i]);
solve.AddEdge(u[i], x, v[i]);
dfs(u[i]);
}
}
}
void dijkstra()
{
priority_queue<point> p;
p.push(point(1, dis[1] = 0));
while (!p.empty())
{
point q = p.top(); p.pop();
if (vis[q.x]) continue; else vis[q.x] = 1;
for (int i = ft[q.x]; i != -1; i = nt[i])
{
if (dis[u[i]] == -1 || dis[u[i]] > q.y + v[i])
{
p.push(point(u[i], dis[u[i]] = q.y + v[i]));
}
}
}
solve.clear(n);
dfs(1);
solve.work(1, n);
printf("%d %d\n", solve.a, solve.b);
}
}dag;
void read(int &x)
{
while ((ch = getchar()) < '0' || ch > '9');
x = ch - '0';
while ((ch = getchar()) >= '0' && ch <= '9') x = x * 10 + ch - '0';
}
struct point
{
int x, y, z;
void scan() { read(x); read(y); read(z); }
bool operator<(const point &a)const
{
return x == a.x ? y > a.y:x < a.x;
}
}p[maxn];
int main()
{
while (~scanf("%d%d%d", &n, &m, &K))
{
dag.clear(n);
for (int i = 0; i < m + m; i += 2)
{
p[i].scan();
p[i ^ 1] = p[i];
swap(p[i ^ 1].x, p[i ^ 1].y);
}
sort(p, p + m + m);
for (int i = 0; i < m + m; i++)
{
dag.AddEdge(p[i].x, p[i].y, p[i].z);
}
dag.dijkstra();
}
return 0;
}