#include <bits/stdc++.h> using namespace std; using LL = long long; #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define REP(i, n) FOR(i, 0, (n) - 1) #define ssize(x) int(x.size()) template<class A, class B> auto &operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for (auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } #ifdef DEBUG #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'; #else #define debug(...) {} #endif constexpr LL mod = (LL) (1e9 + 7); int n; vector<int> repr, siz; int fnd(int x) { if (repr[x] == x) return x; repr[x] = fnd(repr[x]); return repr[x]; } void onion(int x, int y) { x = fnd(x); y = fnd(y); if (x == y) return; if (siz[x] < siz[y]) swap(x, y); siz[x] += siz[y]; repr[y] = x; } int convert(int x, int y) { return x * n + y; } LL fastpow(LL x, LL y) { LL res = 1; while (y > 0) { if (y % 2 == 1) { res *= x; res %= mod; } x *= x; x %= mod; y /= 2; } return res; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int k; cin >> n >> k; int m = n * n; vector<int> perm(n), pos(n); repr.resize(m); siz.resize(m); REP(i, m) { repr[i] = i; siz[i] = 1; } while (k--) { REP(i, n) { cin >> perm[i]; perm[i]--; pos[perm[i]] = i; } REP(i, n) { REP(j, n) { if (i == j) continue; int me = convert(i, j); int neigh = convert(pos[i], pos[j]); onion(me, neigh); } } } vector<int> invs(m); REP(i, n) { REP(j, i) { int x = convert(i, j); x = fnd(x); invs[x]++; } } LL ans = 0; REP(i, n) { FOR(j, i + 1, n - 1) { int x = convert(i, j); x = fnd(x); LL num = invs[x]; LL den = siz[x]; ans += num * fastpow(den, mod - 2) % mod; if (ans >= mod) ans -= mod; } } cout << ans << '\n'; return 0; }
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 | #include <bits/stdc++.h> using namespace std; using LL = long long; #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define REP(i, n) FOR(i, 0, (n) - 1) #define ssize(x) int(x.size()) template<class A, class B> auto &operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for (auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } #ifdef DEBUG #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'; #else #define debug(...) {} #endif constexpr LL mod = (LL) (1e9 + 7); int n; vector<int> repr, siz; int fnd(int x) { if (repr[x] == x) return x; repr[x] = fnd(repr[x]); return repr[x]; } void onion(int x, int y) { x = fnd(x); y = fnd(y); if (x == y) return; if (siz[x] < siz[y]) swap(x, y); siz[x] += siz[y]; repr[y] = x; } int convert(int x, int y) { return x * n + y; } LL fastpow(LL x, LL y) { LL res = 1; while (y > 0) { if (y % 2 == 1) { res *= x; res %= mod; } x *= x; x %= mod; y /= 2; } return res; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int k; cin >> n >> k; int m = n * n; vector<int> perm(n), pos(n); repr.resize(m); siz.resize(m); REP(i, m) { repr[i] = i; siz[i] = 1; } while (k--) { REP(i, n) { cin >> perm[i]; perm[i]--; pos[perm[i]] = i; } REP(i, n) { REP(j, n) { if (i == j) continue; int me = convert(i, j); int neigh = convert(pos[i], pos[j]); onion(me, neigh); } } } vector<int> invs(m); REP(i, n) { REP(j, i) { int x = convert(i, j); x = fnd(x); invs[x]++; } } LL ans = 0; REP(i, n) { FOR(j, i + 1, n - 1) { int x = convert(i, j); x = fnd(x); LL num = invs[x]; LL den = siz[x]; ans += num * fastpow(den, mod - 2) % mod; if (ans >= mod) ans -= mod; } } cout << ans << '\n'; return 0; } |