模板——补充

发表于 分类于 ， 阅读次数： 作者 Pomelorin

树上启发式合并。

树上启发式合并

例如计算 \(\sum_{d(x)=d(y),1\le x<y\le n}d(y)-d(lca(x,y))\)。

\(O(n\log n)\) 版：

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vector<ll> e[N];
ll a[N], d[N], cnt[N], big[N], siz[N], ans;
ll dfn[N], L[N], R[N], index;
ll n, m;

ll dfs(ll root, ll dad) {
    ll curb = 0;
    d[root] = d[dad] + 1;
    siz[root]++;
    dfn[++index] = root;
    L[root] = index;
    for (auto son: e[root]) {
        if (son == dad)
            continue;
        siz[root] += dfs(son, root);
        if (siz[son] > curb) {
            curb = siz[son];
            big[root] = son;
        }
    }
    R[root] = index;
    return siz[root];
}

void dsu(ll root, ll dad, ll keep) {
    for (auto son: e[root]) {
        if (son == dad || son == big[root])
            continue;
        dsu(son, root, 0);
    }
    if (big[root])
        dsu(big[root], root, 1);
    for (auto son: e[root]) {
        if (son == dad || son == big[root])
            continue;
        for (ll i = L[son]; i <= R[son]; i++) {
            ans += cnt[d[dfn[i]]] * (d[dfn[i]] - d[root]);
        }
        for (ll i = L[son]; i <= R[son]; i++) {
            cnt[d[dfn[i]]]++;
        }
    }
    cnt[d[root]]++;
    if (keep == 0) {
        for (ll i = L[root]; i <= R[root]; i++) {
            cnt[d[dfn[i]]]--;
        }
    }
}