File size: 3,120 Bytes
d3f4f72 |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 |
#include <algorithm>
#include <iostream>
#include <vector>
#include <utility>
using namespace std;
const int LIM = 800008, LIM2 = 20;
const int MOD = 1000000007;
class UnionFind {
int N;
int root[LIM], rank[LIM], size[LIM];
void init(int _N) {
N = _N;
for (int i = 0; i < N; i++) {
root[i] = i;
size[i] = 1;
}
}
public:
UnionFind(int _N) {
init(_N);
}
int find(int i) {
if (root[i] != i) {
root[i] = find(root[i]);
}
return root[i];
}
bool merge(int i, int j) {
i = find(i);
j = find(j);
if (i == j) {
return false;
}
if (rank[i] > rank[j]) {
swap(i, j);
}
root[i] = j;
size[j] += size[i];
if (rank[i] == rank[j]) {
rank[j]++;
}
return true;
}
int get_size(int i) {
return size[find(i)];
}
};
int N, ans, tot;
vector<pair<int, int>> adj[LIM];
int dynU[LIM][LIM2 + 2]; // dynU[i][j] = # of nodes reachable up from i (through edge to parent) via capacity >= j edges
int dynD[LIM][LIM2 + 2]; // dynD[i][j] = # of nodes reachable down from i via capacity >= j edges
// Populate dynD.
void recD(int i, int p) {
for (int j = 1; j <= LIM2; j++) {
dynD[i][j] = 1;
}
for (auto e : adj[i]) {
int b = e.first, c = e.second;
if (b == p) {
continue;
}
recD(b, i);
for (int j = 1; j <= c; j++) {
dynD[i][j] += dynD[b][j];
}
}
}
// Populate dynU (and answer).
void recU(int i, int p) {
for (auto e : adj[i]) {
int b = e.first, c = e.second;
if (b == p) {
continue;
}
for (int j = 1; j <= LIM2; j++) {
if (j <= c) {
dynU[b][j] = (dynU[i][j] + dynD[i][j] - dynD[b][j] + MOD) % MOD;
} else {
dynU[b][j] = 0;
}
}
int totE = tot, prev = 0;
for (int j = c; j > 0; j--) {
int curr = (long long)dynD[b][j]*dynU[b][j] % MOD;
int cnt = (curr - prev + MOD) % MOD;
int s = (long long)cnt*j % MOD;
totE = (totE - s + MOD) % MOD;
prev = curr;
}
ans = (long long)ans*totE % MOD;
recU(b, i);
}
}
int solve() {
for (int i = 0; i < LIM; i++) {
adj[i].clear();
}
// Input.
cin >> N;
vector<pair<int, pair<int, int>>> E;
for (int i = 0; i < N - 1; i++) {
int a, b, c;
cin >> a >> b >> c;
a--;
b--;
adj[a].push_back(make_pair(b, c));
adj[b].push_back(make_pair(a, c));
E.push_back(make_pair(c, make_pair(a, b)));
}
// Compute initial capacity sum.
tot = 0;
UnionFind U(N);
sort(E.begin(), E.end());
for (int i = (int)E.size() - 1; i >= 0; i--) {
int a = E[i].second.first, b = E[i].second.second, c = E[i].first;
tot = (tot + (long long)c*U.get_size(a)*U.get_size(b)) % MOD;
U.merge(a, b);
}
// Compute reduced capacity sums via DP.
ans = 1;
recD(0, -1);
recU(0, -1);
return ans;
}
int main() {
int T;
cin >> T;
for (int t = 1; t <= T; t++) {
cout << "Case #" << t << ": " << solve() << endl;
}
return 0;
}
|