【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))==0 && (p.x-a.x)*(p.x-b.x)<=0 && (p.y-a.y)*(p.y-b.y)<=0;
}

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 = 10007;


LL Pow(LL base, LL n, LL mod) {
    LL ret = 1;
    
    while (n) {
        if (n & 1)
            ret = ret * base % mod;
        base = base * base % mod;
        n >>= 1;
    }
    
    return ret;
}

int Inv(int x) {
    return Pow(x, mod-2, mod);
}

typedef struct mat_t {
    static const int maxn = 305;
    int m[maxn][maxn];
    
    void init() {
        memset(m, 0, sizeof(m));
    }
    
    int det(int n) {
        rep(i, 0, n)
            rep(j, 0, n)
                m[i][j] = (m[i][j]%mod+mod) % mod;
        int ret = 1;
        
        rep(i, 0, 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] == 0) {
                ret = -1;
                break;
            }
            
            rep(j, i+1, 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 = 305;
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, 0, 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, 0, n) {
        rep(j, i+1, n) {
            if (judge(i, j))
                M[i][j] = M[j][i] = true;
        }
    }
    
    base.init();
    rep(i, 0, n) {
        rep(j, 0, n) {
            if (i==j || !M[i][j])
                continue;
            
            ++base.m[i][i];
            base.m[i][j] = -1;
        }
    }
    
    int ans = base.det(n-1);
    
    printf("%d
", 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, 0, n)
            scanf("%d %d", &P[i].x, &P[i].y);
        solve();
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}

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
" % (t))
        for tt in xrange(t):
            n = randint(1, 300)
            r = randint(0, 20000)
            fout.write("%d %d
" % (n, r))
            for i in xrange(n):
                x = randint(-bound, bound)
                y = randint(-bound, bound)
                fout.write("%d %d
" % (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_prjhdojdata.out"
    desFileName = "F:workspacecpp_hdojdata.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_prjhdojdata.in"
    desFileName = "F:workspacecpp_hdojdata.in"
    GenData(srcFileName)
    MovData(srcFileName, desFileName)
    
    

基本思路