HDU 4305 Lightning

Lightning

建無向圖。如果兩個點之間的距離小於R,並且兩點之間無第三點可以用向量判斷時間複雜度O(n^3).然後求生成樹的個數。這裏直接用Martix Tree定理。對於無向圖G，它的kirchhoff矩陣C定義爲它的度數矩陣D減去它的鄰接矩陣A.然後用martix_Tree定理：對於一個無向圖G，它的生成樹個數等於kirchhoff矩陣任何一個n-1階主子式的行列式的絕對值。關於無向圖的生成樹計數矩陣算法的相關的論文可以查看2007年周東《生成樹的計數及應用》

/*
    author    : csuchenan
    prog      : hdu 4305
    algorithm : martix tree
*/
#include <cstdio>
#include <cstring>
const int maxn = 305;
const int mod = 10007;

int degree[maxn][maxn];
int map[maxn][maxn];
int c[maxn][maxn];

bool vis[maxn];
struct Point{
    int x, y;
}point[maxn];
int N, R;

int dist(int i, int j){
    int x = point[i].x - point[j].x;
    int y = point[i].y - point[j].y;
    return x*x + y*y;
}

int min(int x, int y){
    if(x > y){
        return y;
    }
    return x;
}

int max(int x, int y){
    if(x > y)
        return y;
    return x;
}

//檢查三點共線的情況
bool check(int i, int j, int k){
    // 首先確定是不是在兩點之間
    bool temp = (point[j].x - point[i].x)*(point[k].y - point[i].y) == (point[k].x - point[i].x)*(point[j].y - point[i].y);
    bool flag = (point[k].x - point[i].x)*(point[j].x - point[k].x) >=0 &&
                (point[k].y - point[i].y)*(point[j].y - point[k].y) >=0 ;
    return flag && temp;
}

void dfs(int v){
    vis[v] = true;
    for(int i = 0; i < N; i ++){
        if(!vis[i] && map[v][i]==1){
            dfs(i);
        }
    }
}

void swap(int &x, int &y){
    int tmp = x ;
    x = y;
    y = tmp;
}

int exgcd(int a, int b, int &x, int&y){
    if(b==0){
        x = 1;
        y = 0;
        return a;
    }
    int d = exgcd(b, a%b, x, y);
    int t = x;
    x = y;
    y = t - a/b*y;
    return d;
}

int det(int n){
    int ans = 1;
    int flag = 1;
    int i,  j, k;
    for(i = 0 ; i < n; i++){
        if(c[i][i]==0){
            for(j = i + 1; j < n; j ++){
                if(c[j][i] != 0)
                    break;
            }
            if(j == n)
                return 0;
            flag = !flag;
            for(int k = i; k < n; k ++){
                swap(c[i][k], c[j][k]);
            }
        }
        ans = ans * c[i][i] %mod;
        int x,y;
        int tp = exgcd(c[i][i], mod, x, y);

        for(k = i + 1; k < n; k++)
            c[i][k] = c[i][k]*x%mod;

        for(j = i + 1; j < n; j ++){
            for(k = i + 1; k < n; k ++){
                c[j][k] = (c[j][k] - c[j][i] * c[i][k])%mod;
                if(j==k)
                    c[j][k] = (c[j][k] + mod)%mod;
            }
        }
    }
    ans = (ans%mod + mod)%mod;
    if(flag)
        return ans;
    return mod - ans;
}

void build(){
    //init
    memset(degree, 0, sizeof(degree));
    memset(map, 0, sizeof(map));
    memset(c, 0, sizeof(c));
    //build map and degree martix
    for(int i = 0; i < N; i ++){
        for(int j = i + 1 ; j < N; j ++){
            if(dist(i, j) <= R*R){
                bool flag = true;
                for(int k = 0; k < N; k ++){
                    if(k != i && k != j){
                        if(check(i, j, k)){
                            flag = false;
                            break;
                        }
                    }
                }
                if(flag){
                    map[i][j] = 1;
                    map[j][i] = 1;
                    degree[i][i] ++;
                    degree[j][j] ++;
                }
            }
        }
    }
    //build c
    for(int i = 0; i < N; i ++){
        for(int j = 0; j < N; j ++){
            c[i][j] = degree[i][j] - map[i][j];
//            printf("%d ", map[i][j]);
        }
//        printf("\n");
    }
}

int main(){
    int T;
//    freopen("test.in", "r", stdin);
    scanf("%d", &T);
    while(T--){
        scanf("%d%d", &N, &R);
        for(int i = 0 ; i < N; i ++){
            scanf("%d%d", &point[i].x, &point[i].y);
        }
        //build martix c ,
        build();
        memset(vis, false, sizeof(vis));
        dfs(0);
        bool flag= false;
        for(int i = 0; i < N; i ++){
            if(!vis[i]){
                flag = true;
                break;
            }
        }
        if(flag){
            printf("-1\n");
            continue;
        }
        printf("%d\n" , det(N-1));
    }
    return 0;
}