uva 11354 - Bond(树链拆分)
2015-07-12 15:56
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题目链接:uva 11354 - Bond
题目大意:给定一张图。每次询问两个节点路径上进过边的危急值的最大值的最小值。
解题思路:首先建立最小生成数,然后依据这棵树做树链剖分。
题目大意:给定一张图。每次询问两个节点路径上进过边的危急值的最大值的最小值。
解题思路:首先建立最小生成数,然后依据这棵树做树链剖分。
#include <cstdio> #include <cstring> #include <vector> #include <algorithm> 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<Edge> 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; }
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