Uoj 33 树上GCD (树分治)

#include <iostream>#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>#include <queue>#include <vector>using namespace std;#define N 300020#define B 300#define M 600200#define inf 0x3f3f3f3f#define mod 1000000007#define LL long long#define ls (i << 1)#define rs (ls | 1)#define md (ll + rr >> 1)#define lson ll, md, ls#define rson md + 1, rr, rs#define MP make_pair#define ui unsigned intint n, fa[N];int fst[N], nxt[M], vv[M], e;int q[N], qh, qt;int dep[N], sz[N], mx[N];LL ans1[N], ans2[N];bool vis[N];int rt;LL x[N], y[N], xx[N], yy[N];LL F[B + 10][B + 10];void init() {memset(fst, -1, sizeof fst);e = 0;}void add(int u, int v) {vv[e] = v, nxt[e] = fst[u], fst[u] = e++;}void bfs(int s, int fd) {dep[s] = fd;qh = qt = 0;q[qt++] = s;while(qh < qt) {int u = q[qh++];for(int i = fst[u]; ~i; i = nxt[i]) {int v = vv[i];if(vis[v]) continue;dep[v] = dep[u] + 1;q[qt++] = v;}}}void get_rt(int u) {bfs(u, 0);for(int i = qt - 1; i >= 0; --i) {int u = q[i];sz[u] = 1;for(int j = fst[u]; ~j; j = nxt[j]) {int v = vv[j];if(vis[v]) continue;sz[u] += sz[v];}}int tmp = n + 1;for(int i = 0; i < qt; ++i) {int u = q[i];mx[u] = 0;for(int j = fst[u]; ~j; j = nxt[j]) {int v = vv[j];if(vis[v]) continue;mx[u] = max(mx[u], sz[v]);}mx[u] = max(mx[u], qt - sz[u]);if(mx[u] < tmp) tmp = mx[u], rt = u;}}void divide(int s) {get_rt(s);vis[rt] = 1;int rrt = rt;int tp = 0;for(int i = fst[rt]; ~i; i = nxt[i]) {int v = vv[i];if(vis[v]) continue;bfs(v, 1);tp = max(tp, qt);for(int j = 0; j < qt; ++j) {int u = q[j];y[dep[u]]++;ans2[dep[u]]++;}for(int j = 1; j <= qt; ++j) {x[j] += y[j];for(int k = j; k <= qt; k += j) {yy[j] += y[k];}}for(int j = 1; j <= qt; ++j) {ans1[j] += 1LL * xx[j] * yy[j];xx[j] += yy[j];yy[j] = y[j] = 0;}}x[0]++;int mx_qt = 0;int t = 1;for(int u = rt; u != s; ++t) {u = fa[u];bfs(u, 0);mx_qt = max(mx_qt, qt);for(int i = 1; i < qt; ++i) {y[dep[q[i]]]++;}for(int i = 1; i <= qt; ++i) {for(int j = i; j <= qt; j += i)yy[i] += y[j];}for(int i = 1; i <= min(qt, B); ++i) {if(F[i][t%i] == -1) {F[i][t%i] = 0;for(int j = (i - t % i) % i; j <= tp; j += i) {F[i][t%i] += x[j];}}ans1[i] += F[i][t%i] * yy[i];}for(int i = B + 1; i <= qt; ++i) {for(int j = (i - t % i) % i; j <= tp; j += i)ans1[i] += x[j] * yy[i];}for(int i = 1; i <= qt; ++i) y[i] = yy[i] = 0;vis[u] = 1;}for(int i = 1; i <= min(mx_qt, B); ++i) {for(int j = 0; j < i; ++j)F[i][j] = -1;}for(int u = rt; u != s;) {u = fa[u];vis[u] = 0;}--t;LL tmp = 0;for(int k = 1; k <= tp + t; ++k) {if(k - 1 <= tp) tmp += x[k-1];if(k - t - 1 >= 0 && k - t - 1 <= tp) tmp -= x[k-t-1];ans2[k] += tmp;}for(int i = 0; i <= tp; ++i) x[i] = xx[i] = 0;if(rrt != s) divide(s);for(int i = fst[rrt]; ~i; i = nxt[i]) {int v = vv[i];if(!vis[v]) {divide(v);}}}int main() {scanf("%d", &n);init();for(int i = 2; i <= n; ++i) {scanf("%d", &fa[i]);add(fa[i], i);}memset(F, -1, sizeof F);divide(1);for(int i = n - 1; i >= 1; --i) {for(int j = i + i; j <= n - 1; j += i) {ans1[i] -= ans1[j];}}for(int i = 1; i <= n - 1; ++i) {printf("%lld\n", ans1[i] + ans2[i]);}return 0;}