題目鏈接:uva 11354 - Bond
題目大意:給定一張圖,每次詢問兩個節點路徑上進過邊的危險值的最大值的最小值。
解題思路:首先建立最小生成數,然後根據這棵樹做樹鏈剖分。
#include
#include
#include
#include
using namespace std;
const int maxn = 50005;
const int INF = 0x3f3f3f3f;
struct Edge {
int u, v, w;
Edge (int u = 0, int v = 0, int w = 0) { set(u, v, w); }
void set(int u, int v, int w) {
this->u = u;
this->v = v;
this->w = w;
}
friend bool operator < (const Edge& a, const Edge& b) {
return a.w < b.w;
}
}ed[maxn * 2];
int N, M, Q, ne, f[maxn], first[maxn], jump[maxn * 2], val[maxn];
int id, idx[maxn], top[maxn], far[maxn], son[maxn], dep[maxn], cnt[maxn];
vector vec;
inline int getfar(int x) {
return x == f[x] ? x : f[x] = getfar(f[x]);
}
inline void add_Edge (int u, int v, int w) {
ed[ne].set(u, v, w);
jump[ne] = first[u];
first[u] = ne++;
}
void dfs (int u, int pre, int d) {
far[u] = pre;
dep[u] = d;
son[u] = 0;
cnt[u] = 1;
for (int i = first[u]; i + 1; i = jump[i]) {
int v = ed[i].v;
if (v == pre)
continue;
dfs(v, u, d + 1);
cnt[u] += cnt[v];
if (cnt[son[u]] < cnt[v])
son[u] = v;
}
}
void dfs (int u, int rot) {
top[u] = rot;
idx[u] = ++id;
if (son[u])
dfs(son[u], rot);
for (int i = first[u]; i + 1; i = jump[i]) {
int v = ed[i].v;
if (v == far[u] || v == son[u])
continue;
dfs(v, v);
}
}
#define lson(x) ((x)<<1)
#define rson(x) (((x)<<1)|1)
int lc[maxn << 2], rc[maxn << 2], s[maxn << 2];
inline void pushup(int u) {
s[u] = max(s[lson(u)], s[rson(u)]);
}
void build (int u, int l, int r) {
lc[u] = l;
rc[u] = r;
if (l == r) {
s[u] = val[l];
return;
}
int mid = (l + r) / 2;
build(lson(u), l, mid);
build(rson(u), mid + 1, r);
pushup(u);
}
int query(int u, int l, int r) {
if (l <= lc[u] && rc[u] <= r)
return s[u];
int mid = (lc[u] + rc[u]) / 2, ret = 0;
if (l <= mid)
ret = max(ret, query(lson(u), l, r));
if (r > mid)
ret = max(ret, query(rson(u), l, r));
return ret;
}
void init () {
int u, v, w;
ne = id = 0;
vec.clear();
memset(first, -1, sizeof(first));
for (int i = 1; i <= N; i++)
f[i] = i;
for (int i = 0; i < M; i++) {
scanf("%d%d%d", &u, &v, &w);
vec.push_back(Edge(u, v, w));
}
sort(vec.begin(), vec.end());
for (int i = 0; i < vec.size(); i++) {
int p = getfar(vec[i].u);
int q = getfar(vec[i].v);
if (p == q)
continue;
add_Edge(vec[i].u, vec[i].v, vec[i].w);
add_Edge(vec[i].v, vec[i].u, vec[i].w);
f[p] = q;
}
dfs(1, 0, 0);
dfs(1, 1);
for (int i = 0; i < N - 1; i++) {
int t = i * 2;
u = (dep[ed[t].u] < dep[ed[t].v] ? ed[t].v : ed[t].u);
val[idx[u]] = ed[t].w;
}
build(1, 1, N);
}
int solve (int u, int v) {
int p = top[u], q = top[v], ret = 0;
while (p != q) {
if (dep[p] < dep[q]) {
swap(p, q);
swap(u, v);
}
ret = max(ret, query(1, idx[p], idx[u]));
u = far[p];
p = top[u];
}
if (u == v)
return ret;
if (dep[u] > dep[v])
swap(u, v);
ret = max(ret, query(1, idx[son[u]], idx[v]));
return ret;
}
int main () {
int cas = 0;
while (scanf("%d%d", &N, &M) == 2) {
if (cas++)
printf("\n");
init();
int u, v;
scanf("%d", &Q);
while (Q--) {
scanf("%d%d", &u, &v);
printf("%d\n", solve(u, v));
}
}
return 0;
}