Graph
思路
图是联通的,并且加边的时候要保证环一定是异或值为0,所以我们可以保证从一个点到另一个点的路径异或值是不变的,这个时候就简单了,不就是一个异或最小生成树了嘛。
我们只要预处理一下,任选一个点作为根节点去得到从这个点到其他点的路径异或值,然后再做一遍异或最小生成树即可。
代码
/*
Author : lifehappy
*/
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#include <bits/stdc++.h>
#define mp make_pair
#define pb push_back
#define endl '\n'
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
const double pi = acos(-1.0);
const double eps = 1e-7;
const int inf = 0x3f3f3f3f;
inline ll read() {
ll f = 1, x = 0;
char c = getchar();
while(c < '0' || c > '9') {
if(c == '-') f = -1;
c = getchar();
}
while(c >= '0' && c <= '9') {
x = (x << 1) + (x << 3) + (c ^ 48);
c = getchar();
}
return f * x;
}
void print(ll x) {
if(x < 10) {
putchar(x + 48);
return ;
}
print(x / 10);
putchar(x % 10 + 48);
}
const int N = 1e5 + 10;
int trie[N * 30][2], tot, a[N];
int head[N], to[N << 1], nex[N << 1], value[N << 1], cnt = 1;
void add(int x, int y, int w) {
to[cnt] = y;
nex[cnt] = head[x];
value[cnt] = w;
head[x] = cnt++;
}
void insert(int x) {
int rt = 0;
for(int i = 29; i >= 0; i--) {
int now = x >> i & 1;
if(!trie[rt][now]) {
trie[rt][now] = ++tot;
rt = trie[rt][now];
trie[rt][0] = trie[rt][1] = 0;
}
else {
rt = trie[rt][now];
}
}
}
int find(int x) {
int ans = 0, rt = 0;
for(int i = 29; i >= 0; i--) {
int now = x >> i & 1;
if(trie[rt][now]) {
rt = trie[rt][now];
}
else {
ans |= 1 << i;
rt = trie[rt][now ^ 1];
}
}
return ans;
}
ll ans = 0;
void dfs1(int l, int r, int dep) {
if(dep < 0 || l >= r) return ;
int mid = l - 1;
while(mid < r && ((a[mid + 1] >> dep) & 1) == 0) mid++;
dfs1(l, mid, dep - 1);
dfs1(mid + 1, r, dep - 1);
if(mid == l - 1 || mid == r) return ;
tot = 0, trie[tot][1] = trie[tot][0] = 0;
for(int i = l; i <= mid; i++) {
insert(a[i]);
}
int now = INT_MAX;
for(int i = mid + 1; i <= r; i++) {
now = min(now, find(a[i]));
}
ans += now;
}
void dfs2(int rt, int fa, int w) {
a[rt] = w;
for(int i = head[rt]; i; i = nex[i]) {
if(to[i] == fa) continue;
dfs2(to[i], rt, w ^ value[i]);
}
}
int main() {
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
int n = read();
for(int i = 1; i < n; i++) {
int x = read(), y = read(), w = read();
add(x, y, w);
add(y, x, w);
}
dfs2(1, 0, 0);
sort(a, a + n);
dfs1(0, n - 1, 29);
printf("%lld\n", ans);
return 0;
}