题目:
解析:
偶尔做做水题挺爽的
两两之间先求出LCA,发现至少有两个LCA是相同的,这个重复LCA也是深度最浅的那个,那我们就选择那个不重复的LCA,因为若选这个重复的LCA的话,这个重复的LCA到另一个LCA的路径会走两遍,反之只会走一遍
三点间的距离就是
\(dis[x] + dis[y] + dis[z] - dis[LCA(x, y)]- dis[LCA(x, z)]- dis[LCA(y, z)]\)
代码:
#include <bits/stdc++.h> using namespace std; const int N = 1e6 + 10; int n, m, num; int head[N], dep[N], f[N], size[N], top[N], son[N]; struct node { int v, nx; } e[N]; template<class T>inline void read(T &x) { x = 0; int f = 0; char ch = getchar(); while (!isdigit(ch)) f |= (ch == '-'), ch = getchar(); while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar(); x = f ? -x : x; return ; } inline void add(int u, int v) { e[++num].nx = head[u], e[num].v = v, head[u] = num; } void dfs1(int u, int fa) { size[u] = 1; for (int i = head[u]; ~i; i = e[i].nx) { int v = e[i].v; if (v != fa) { dep[v] = dep[u] + 1; f[v] = u; dfs1(v, u); size[u] += size[v]; if (size[v] > size[son[u]]) son[u] = v; } } } void dfs2(int u, int t) { top[u] = t; if (son[u]) dfs2(son[u], t); for (int i = head[u]; ~i; i = e[i].nx) { int v = e[i].v; if (v != f[u] && v != son[u]) dfs2(v, v); } } int lca(int x, int y) { int fx = top[x], fy = top[y]; while (fx != fy) { if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy); x = f[fx], fx = top[x]; } return dep[x] < dep[y] ? x : y; } int main() { memset(head, -1, sizeof(head)); read(n), read(m); for (int i = 1, x, y; i < n; ++i) read(x), read(y), add(x, y), add(y, x); f[1] = 0, dep[1] = 1; dfs1(1, 0); dfs2(1, 1); for (int i = 1, x, y, z; i <= m; ++i) { read(x), read(y), read(z); int a = lca(x, y), b = lca(x, z), c = lca(y, z); int tmp = (dep[a] == dep[b]) ? c : ((dep[a] == dep[c]) ? b : a); printf("%d %d\n", tmp, dep[x] + dep[y] + dep[z] - dep[a] - dep[b] - dep[c]); } }