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c01da15 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 | #include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
if (!(cin >> T)) return 0;
while (T--) {
int n;
cin >> n;
vector<string> s(n);
for (int i = 0; i < n; ++i) cin >> s[i];
bool ok = true;
for (int i = 0; i < n && ok; ++i) {
if (s[i][i] != '1') ok = false;
for (int j = i + 1; j < n; ++j)
if (s[i][j] == '1' && s[j][i] == '1') ok = false;
}
if (!ok) {
cout << "No\n";
continue;
}
// descendants lists
vector<vector<int>> desc(n);
vector<int> cnt(n);
for (int i = 0; i < n; ++i) {
int c = 0;
for (int j = 0; j < n; ++j)
if (s[i][j] == '1') ++c;
cnt[i] = c;
}
for (int i = 0; i < n; ++i) desc[i].reserve(cnt[i]);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
if (s[i][j] == '1') desc[i].push_back(j);
// topological order: if u reaches v, then |Desc(v)| < |Desc(u)|
vector<int> order(n);
iota(order.begin(), order.end(), 0);
sort(order.begin(), order.end(),
[&](int a, int b) { return cnt[a] > cnt[b]; });
vector<int> seen(n, 0);
vector<pair<int,int>> edges;
edges.reserve(n - 1);
for (int i = 0; i < n && (int)edges.size() < n; ++i) {
int cur = i + 1;
seen[i] = cur; // i itself is not a child of i
for (int v : order) {
if (s[i][v] != '1' || seen[v] == cur) continue;
edges.emplace_back(i, v);
if ((int)edges.size() >= n) break;
for (int w : desc[v]) seen[w] = cur;
}
}
if ((int)edges.size() != n - 1) {
cout << "No\n";
continue;
}
vector<vector<int>> out(n), und(n);
for (auto [x, y] : edges) {
out[x].push_back(y);
und[x].push_back(y);
und[y].push_back(x);
}
// check connectedness
vector<char> vis(n, 0);
vector<int> st;
st.reserve(n);
st.push_back(0);
vis[0] = 1;
int visited = 0;
while (!st.empty()) {
int u = st.back(); st.pop_back();
++visited;
for (int w : und[u])
if (!vis[w]) {
vis[w] = 1;
st.push_back(w);
}
}
if (visited != n) {
cout << "No\n";
continue;
}
// verify reachability
vector<char> reach(n);
for (int u = 0; u < n && ok; ++u) {
fill(reach.begin(), reach.end(), 0);
vector<int> stack;
stack.reserve(n);
stack.push_back(u);
reach[u] = 1;
while (!stack.empty()) {
int x = stack.back(); stack.pop_back();
for (int y : out[x])
if (!reach[y]) {
reach[y] = 1;
stack.push_back(y);
}
}
for (int v = 0; v < n; ++v)
if ((s[u][v] == '1') != reach[v]) {
ok = false;
break;
}
}
if (!ok) {
cout << "No\n";
continue;
}
cout << "Yes\n";
for (auto [x, y] : edges)
cout << x + 1 << ' ' << y + 1 << '\n';
}
return 0;
} |