Balancing Act 树的重心模板题
Consider a tree T with N (1 <= N <= 20,000) nodes numbered 1…N. Deleting any node from the tree yields a forest: a collection of one or more trees. Define the balance of a node to be the size of the largest tree in the forest T created by deleting that node from T.
For example, consider the tree:
Deleting node 4 yields two trees whose member nodes are {5} and {1,2,3,6,7}. The larger of these two trees has five nodes, thus the balance of node 4 is five. Deleting node 1 yields a forest of three trees of equal size: {2,6}, {3,7}, and {4,5}. Each of these trees has two nodes, so the balance of node 1 is two.
For each input tree, calculate the node that has the minimum balance. If multiple nodes have equal balance, output the one with the lowest number.
#include <iostream> #include <cstdio> #include <cstring> using namespace std; const int N = 202020; int Next[N], head[N], ver[N], v[N], size[N]; int tot, pos, ans, n; void init(){ memset(Next, 0, sizeof(Next)); memset(head, 0, sizeof(head)); memset(v, 0, sizeof(v)); memset(size, 0, sizeof(size)); tot = 1; ans = 0x7fffffff; } void add(int x, int y){ ver[++tot] = y, Next[tot] = head[x], head[x] = tot; } void dfs(int x){ v[x] = 1; size[x] = 1; int max_part = 0; for (int i = head[x]; i; i = Next[i]){ int y = ver[i]; if(v[y]) continue; dfs(y); size[x] += size[y]; max_part = max(max_part, size[y]); } max_part = max(max_part, n - size[x]); if(max_part < ans){ ans = max_part; pos = x; } } int main(){ int t; init(); scanf("%d", &t); while(t--){ init(); scanf("%d", &n); for(int i = 1; i < n; i++){ int a, b; scanf("%d%d", &a, &b); add(a, b); add(b, a); } dfs(1); printf("%d %d\n", pos, ans); } return 0; }
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