B Graph（异或最小生成树）

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;
}