#include "migrations.h"
#include <vector>
#include <array>
#include <utility>
#include <algorithm>
using namespace std;
// --------------------- Internal state for run #1 (send_message) ---------------------
namespace {
bool inited = false;
int Nglob = 0, LOGv = 0;
int startIdx = 1; // start of the last-50 suffix
// Lifting tables
vector<int> depth;
vector< vector<int> > up; // up[v][k], k in [0..LOGv-1]
// Online diameter
int A = 0, B = 0, D = 0; // endpoints and length
// Suffix init bookkeeping
bool sentInitA = false;
bool sentInitB = false;
inline void reset_test(int N) {
inited = true;
Nglob = N;
LOGv = 0; while ((1 << LOGv) <= (Nglob > 0 ? Nglob : 1)) ++LOGv;
depth.assign(Nglob, 0);
up.assign(Nglob, vector<int>(LOGv, 0));
for (int k = 0; k < LOGv; ++k) up[0][k] = 0;
A = B = 0; D = 0;
int K = (Nglob >= 2 ? 50 : max(1, Nglob - 1));
startIdx = max(1, Nglob - K);
sentInitA = false;
sentInitB = false;
}
inline int lca(int u, int v) {
if (depth[u] < depth[v]) swap(u, v);
int diff = depth[u] - depth[v];
for (int k = 0; k < LOGv; ++k) if (diff & (1 << k)) u = up[u][k];
if (u == v) return u;
for (int k = LOGv - 1; k >= 0; --k) {
if (up[u][k] != up[v][k]) {
u = up[u][k];
v = up[v][k];
}
}
return up[u][0];
}
inline int dist(int u, int v) {
int w = lca(u, v);
return depth[u] + depth[v] - 2 * depth[w];
}
}
int send_message(int N, int i, int Pi) {
// New test case begins at i == 1 (per problem statement).
if (!inited || i == 1) reset_test(N);
// add node i to lifting
depth[i] = depth[Pi] + 1;
up[i][0] = Pi;
for (int k = 1; k < LOGv; ++k) up[i][k] = up[ up[i][k-1] ][k-1];
// online diameter update
int dA = dist(i, A);
int dB = dist(i, B);
bool changed = false;
int other = -1;
if (dA > D) { changed = true; other = A; B = i; D = dA; }
else if (dB > D) { changed = true; other = B; A = i; D = dB; }
// default: no message
int out = 0;
// Communicate only in the last-50 suffix.
if (i >= startIdx) {
if (i == startIdx && !sentInitA) {
// First deterministic init: A
out = A + 1; // in [1..N] ≤ 10000
sentInitA = true;
} else if (i == startIdx + 1 && !sentInitB) {
// Second deterministic init: B
out = B + 1;
sentInitB = true;
} else if (changed) {
// Any real change inside suffix: send other endpoint
out = other + 1;
}
// else: silent
}
// 0 or [1..20000] is allowed; here values are ≤ 10000 by construction.
return out;
}
// --------------------- Run #2 (Museum) ---------------------
std::pair<int,int> longest_path(std::vector<int> S) {
int N = (int)S.size();
if (N <= 1) return {0, 0};
int K = (N >= 2 ? 50 : max(1, N - 1));
int startIdxLocal = max(1, N - K);
// Find the last message sent at or after startIdxLocal+2 (i.e., any "change" after the two inits)
int lastIdx = -1;
for (int i = N - 1; i >= startIdxLocal + 2; --i) {
if (S[i] != 0) { lastIdx = i; break; }
}
if (lastIdx != -1) {
// This is a real change message: (lastIdx, S[lastIdx]-1)
return { lastIdx, S[lastIdx] - 1 };
}
// Otherwise, no changes occurred in the suffix after the two inits.
// Use the two deterministic init messages placed at startIdxLocal and startIdxLocal+1.
// (They are guaranteed to be sent by the team code.)
int u = (S[startIdxLocal] > 0 ? S[startIdxLocal] - 1 : 0);
int v = (S[startIdxLocal + 1] > 0 ? S[startIdxLocal + 1] - 1 : 0);
return { u, v };
}
