#include <bits/stdc++.h>
#define boost \
ios_base::sync_with_stdio(0); \
cin.tie(0); \
cout.tie(0)
#define ALL(x) (x).begin(), (x).end()
using namespace std;
#define sim template <class c
#define ris return *this
#define dor > debug& operator<<
#define eni(x) sim > typename enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge {
c b, e;
};
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i;
ris;
} eni(==) ris << range(begin(i), end(i));
}
sim, class b dor(pair<b, c> d) { ris << "(" << d.first << ", " << d.second << ")"; }
sim dor(rge<c> d) {
*this << "[";
for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it;
ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
}
;
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define dbg(x) cerr << #x << " = " << x << "\n"
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
int R(int a, int b) {
static mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
return uniform_int_distribution<int>(a, b)(rng);
}
const int MOD = 1'000'000'007;
int power(int x, int y) {
int res = 1;
int pot = x;
while (y) {
if (y & 1) res = 1LL * res * pot % MOD;
pot = 1LL * pot * pot % MOD;
y /= 2;
}
return res;
}
int inv(int x) {
return power(x, MOD - 2);
}
constexpr int MAXN = 3005;
int perm[MAXN][MAXN];
int n, k;
int color[MAXN][MAXN];
int res;
int COLOR;
pii ulamki[MAXN * MAXN];
vector<pii> g[MAXN][MAXN];
void bfs(int pos_i, int pos_j) {
COLOR++;
queue<pii> q;
q.push({pos_i, pos_j});
color[pos_i][pos_j] = COLOR;
while (!q.empty()) {
auto [pos_i, pos_j] = q.front();
q.pop();
ulamki[COLOR].second++;
if (pos_i > pos_j) ulamki[COLOR].first++;
for (int p = 0; p < k; p++) {
int x = perm[p][pos_i];
int y = perm[p][pos_j];
if (!color[x][y]) {
color[x][y] = COLOR;
q.push({x, y});
}
}
}
}
int32_t main() {
boost;
cin >> n >> k;
for (int i = 0; i < k; i++) {
for (int j = 0; j < n; j++) {
int x;
cin >> x;
perm[i][j] = x-1;
}
}
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
COLOR++;
if (!color[i][j]) bfs(i, j);
res += 1LL * ulamki[color[i][j]].first * inv(ulamki[color[i][j]].second) % MOD;
if (res >= MOD) res -= MOD;
}
}
cout << res << "\n";
}
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 | #include <bits/stdc++.h> #define boost \ ios_base::sync_with_stdio(0); \ cin.tie(0); \ cout.tie(0) #define ALL(x) (x).begin(), (x).end() using namespace std; #define sim template <class c #define ris return *this #define dor > debug& operator<< #define eni(x) sim > typename enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) { sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; } sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...); struct debug { #ifdef LOCAL ~debug() { cerr << endl; } eni(!=) cerr << boolalpha << i; ris; } eni(==) ris << range(begin(i), end(i)); } sim, class b dor(pair<b, c> d) { ris << "(" << d.first << ", " << d.second << ")"; } sim dor(rge<c> d) { *this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]"; } #else sim dor(const c&) { ris; } #endif } ; #define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] " #define dbg(x) cerr << #x << " = " << x << "\n" using ll = long long; using ld = long double; using pii = pair<int, int>; int R(int a, int b) { static mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); return uniform_int_distribution<int>(a, b)(rng); } const int MOD = 1'000'000'007; int power(int x, int y) { int res = 1; int pot = x; while (y) { if (y & 1) res = 1LL * res * pot % MOD; pot = 1LL * pot * pot % MOD; y /= 2; } return res; } int inv(int x) { return power(x, MOD - 2); } constexpr int MAXN = 3005; int perm[MAXN][MAXN]; int n, k; int color[MAXN][MAXN]; int res; int COLOR; pii ulamki[MAXN * MAXN]; vector<pii> g[MAXN][MAXN]; void bfs(int pos_i, int pos_j) { COLOR++; queue<pii> q; q.push({pos_i, pos_j}); color[pos_i][pos_j] = COLOR; while (!q.empty()) { auto [pos_i, pos_j] = q.front(); q.pop(); ulamki[COLOR].second++; if (pos_i > pos_j) ulamki[COLOR].first++; for (int p = 0; p < k; p++) { int x = perm[p][pos_i]; int y = perm[p][pos_j]; if (!color[x][y]) { color[x][y] = COLOR; q.push({x, y}); } } } } int32_t main() { boost; cin >> n >> k; for (int i = 0; i < k; i++) { for (int j = 0; j < n; j++) { int x; cin >> x; perm[i][j] = x-1; } } for (int i = 0; i < n; i++) { for (int j = i + 1; j < n; j++) { COLOR++; if (!color[i][j]) bfs(i, j); res += 1LL * ulamki[color[i][j]].first * inv(ulamki[color[i][j]].second) % MOD; if (res >= MOD) res -= MOD; } } cout << res << "\n"; } |
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