#include "Alice.h"
#include <vector>
#include <utility>
using namespace std;
// Alice chooses n and encodes X in leaf‐edges:
// - central edge: (1,2)
// - for each bit j∈[0,3], R=3 leaves u=3+j*R…3+j*R+2:
// connect to 1 if bit j of X is 0, else to 2
vector<pair<int,int>> Alice() {
const int B = 4, R = 3;
int n = B*R + 2;
long long X = setN(n); // returns the secret X∈[1..10]​:contentReference[oaicite:1]{index=1}
vector<pair<int,int>> edges;
// central spine
edges.emplace_back(1,2);
// leaf equations
for (int j = 0; j < B; j++) {
int bit = (X >> j) & 1;
for (int r = 0; r < R; r++) {
int u = 3 + j*R + r;
edges.emplace_back(bit==0 ? 1 : 2, u);
}
}
return edges;
}
#include "Bob.h"
#include <vector>
#include <utility>
using namespace std;
// Bob receives the remaining m edges (sorted), deletes the central
// (1,2) if present, then for each bit j scans its 3 leaves to recover
// at least one surviving edge and hence that bit.
long long Bob(vector<pair<int,int>> V) {
// collect edges in a set for quick lookup
// skip center (1,2)
vector<bool> present(15, false);
for (auto &e : V) {
int u = e.first, v = e.second;
if (u > v) swap(u,v);
if (u==1 && v==2) continue; // ignore central​:contentReference[oaicite:4]{index=4}
present[v] = (u==1 ? false : true);
}
long long X = 0;
const int B = 4, R = 3;
for (int j = 0; j < B; j++) {
// scan the 3 leaves for bit j
int bit = 0;
for (int r = 0; r < R; r++) {
int u = 3 + j*R + r;
if (!present[u]) { bit = 0; break; }
else { bit = 1; break; }
}
X |= ((long long)(bit) << j);
}
return X;
}
