【HDOJ】4305 Lightning

1. 题目描述
当一个结点lightning后，可以向其周围距离小于等于R的结点传播lightning。然后以该结点为中心继续传播。以此类推，
问最终形成的树形结构有多少个。

2. 基本思路
生成树级数模板题目。
Matrix-Tree定理（Kirchhoff矩阵-树定理）：
1） G的度数矩阵D[G]是一个n*n的矩阵，并且满足：当i≠j时,dij=0；当i=j时，dij等于vi的度数；
2） G的邻接矩阵A[G]也是一个n*n的矩阵， 并且满足：如果vi、vj之间有边直接相连，则aij=1，否则为0。
定义Kirchhoff矩阵C[G] = D[G]-A[G]。不同生成树的个数是C[G]的任何一个n-1阶主子式的行列式的绝对值。
行列式值通过化上三角可求。除法使用逆元可求。

3. 代码

 /* 4305 */
 #include <iostream>
 #include <sstream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <bitset>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 typedef struct Point {
     int x, y;

     Point() {}
     Point(int x, int y):
         x(x), y(y) {}

     Point operator - (const Point& a) const {
         return Point(x-a.x, y-a.y);
     }

     int operator ^ (const Point& a) const {
         return x*a.y - y*a.x;
     }

 } Point;

 typedef struct Segment {
     Point s, e;

     Segment() {}
     Segment(Point s, Point e):
         s(s), e(e) {}

 } Segment;

 bool onSegment(Point p, Point a, Point b) {
     return ((a-p)^(b-p))== && (p.x-a.x)*(p.x-b.x)<= && (p.y-a.y)*(p.y-b.y)<=;
 }

 int Length(Point a, Point b) {
     return (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y);
 }

 #define LL __int64

 const int mod = ;

 LL Pow(LL base, LL n, LL mod) {
     LL ret = ;

     while (n) {
         if (n & )
             ret = ret * base % mod;
         base = base * base % mod;
         n >>= ;
     }

     return ret;
 }

 int Inv(int x) {
     return Pow(x, mod-, mod);
 }

 typedef struct mat_t {
     static const int maxn = ;
     int m[maxn][maxn];

     void init() {
         memset(m, , sizeof(m));
     }

     int det(int n) {
         rep(i, , n)
             rep(j, , n)
                 m[i][j] = (m[i][j]%mod+mod) % mod;
         int ret = ;

         rep(i, , n) {
             rep(j, i, n) {
                 if (m[j][i]) {
                     rep(k, i, n)
                         swap(m[i][k], m[j][k]);
                     if (i != j)
                         ret = (-ret + mod) % mod;
                     break;
                 }
             }

             if (m[i][i] == ) {
                 ret = -;
                 break;
             }

             rep(j, i+, n) {
                 int tmp = m[j][i] * Inv(m[i][i]) % mod;
                 rep(k, i, n)
                     m[j][k] = ((m[j][k] - m[i][k]*tmp%mod) % mod + mod) % mod;
             }

             ret = ret * m[i][i] % mod;
         }

         return ret;
     }
 } mat_t;

 const int maxn = ;
 Point P[maxn];
 int n, R, R2;
 bool M[maxn][maxn];
 mat_t base;

 bool judge(int i, int j) {
     if (Length(P[i], P[j]) > R2)
         return false;

     rep(k, , n) {
         if (k==i || k==j)
             continue;

         if (onSegment(P[k], P[i], P[j]))
             return false;
     }

     return true;
 }

 void solve() {
     R2 = R * R;

     memset(M, false, sizeof(M));
     rep(i, , n) {
         rep(j, i+, n) {
             if (judge(i, j))
                 M[i][j] = M[j][i] = true;
         }
     }

     base.init();
     rep(i, , n) {
         rep(j, , n) {
             if (i==j || !M[i][j])
                 continue;

             ++base.m[i][i];
             base.m[i][j] = -;
         }
     }

     int ans = base.det(n-);

     printf("%d\n", ans);
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     int t;

     scanf("%d", &t);
     while (t--) {
         scanf("%d %d", &n, &R);
         rep(i, , n)
             scanf("%d %d", &P[i].x, &P[i].y);
         solve();
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }

4. 数据发生器

 import sys
 import string
 from random import randint

 def GenData(fileName):
     with open(fileName, "w") as fout:
         t = 20
         bound = 10**4
         fout.write("%d\n" % (t))
         for tt in xrange(t):
             n = randint(1, 300)
             r = randint(0, 20000)
             fout.write("%d %d\n" % (n, r))
             for i in xrange(n):
                 x = randint(-bound, bound)
                 y = randint(-bound, bound)
                 fout.write("%d %d\n" % (x, y))

 def MovData(srcFileName, desFileName):
     with open(srcFileName, "r") as fin:
         lines = fin.readlines()
     with open(desFileName, "w") as fout:
         fout.write("".join(lines))

 def CompData():
     print "comp"
     srcFileName = "F:\Qt_prj\hdoj\data.out"
     desFileName = "F:\workspace\cpp_hdoj\data.out"
     srcLines = []
     desLines = []
     with open(srcFileName, "r") as fin:
         srcLines = fin.readlines()
     with open(desFileName, "r") as fin:
         desLines = fin.readlines()
     n = min(len(srcLines), len(desLines))-1
     for i in xrange(n):
         ans2 = int(desLines[i])
         ans1 = int(srcLines[i])
         if ans1 > ans2:
             print "%d: wrong" % i

 if __name__ == "__main__":
     srcFileName = "F:\Qt_prj\hdoj\data.in"
     desFileName = "F:\workspace\cpp_hdoj\data.in"
     GenData(srcFileName)
     MovData(srcFileName, desFileName)

基本思路