2020年b组蓝桥杯真题 七段码

试题E 七段码

DFS+并查集，使用并查集判断是否连成一片

#include <cstdio>
using namespace std;

int res = 0;
bool visit[7];
int lian[7][7] = {
	{ 0, 1, 0, 0, 0, 1, 0 },
	{ 1, 0, 1, 0, 0, 0, 1 },
	{ 0, 1, 0, 1, 0, 0, 1 },
	{ 0, 0, 1, 0, 1, 0, 0 },
	{ 0, 0, 0, 1, 0, 1, 1 },
	{ 1, 0, 0, 0, 1, 0, 1 },
	{ 0, 1, 1, 0, 1, 1, 0 }
};

int fa[7];
int rank[7];
int find(int i) {
	while(i != fa[i]) {
		i = fa[i];
	}
	return i;
}

void merge(int a, int b) {
	int x = find(a);
	int y = find(b);
	if (rank[x] < rank[y]) {
		fa[x] = y;
	} else if (rank[x] > rank[y]) {
		fa[y] = x;
	} else {
		fa[x] = y;
		rank[y]++;
	}
}

bool check() {
	for (int i = 0; i < 7; i++) {
		fa[i] = i;
		rank[i] = 0;
	}
	for (int i = 0; i < 7; i++) {
		if (visit[i]) {
			for (int j = i+1; j < 7; j++) {
				if (visit[j] && lian[i][j]) {
					merge(i, j);
				}
			}
		}
	}
	int zu = 100;
	for (int i = 0; i < 7; i++) {
		if (visit[i]) {
			if (zu == 100) {
				zu = find(i);
			} else {
				if (find(i) != zu) {
					return false;
				}
			}
		}
	}
	return true;
}


void dfs(int i) {
	if (i == 7) {
		if (check()) {
			res++;
		}
		return;
	}
	visit[i] = true;
	dfs(i+1);
	visit[i] = false;
	dfs(i+1);
}


int main() {
	dfs(0);
	printf("%d", res - 1); // 减去全不亮的情况
	return 0;
}