HDU 4421 Bit Magic

pid=4421" target="_blank" style="">题目链接

题意：就依据题目，给定b数组。看能不能构造出一个符合的a数组

思路：把每一个数字的每一个二进制位单独考虑。就变成一个2-sat题目了，依据题目中的式子建立2-sat的边。然后每一位跑2-sat。假设每位都符合。就是YES，假设有一位不符合就是NO

代码：

#include <cstdio>

#include <cstring>

#include <cstdlib>

#include <vector>

#include <algorithm>

using namespace std;

const int MAXNODE = 505;

struct TwoSet {

	int n;

	vector<int> g[MAXNODE * 2];

	bool mark[MAXNODE * 2];

	int S[MAXNODE * 2], sn;

	void init(int tot) {

		n = tot * 2;

		for (int i = 0; i < n; i += 2) {

			g[i].clear();

			g[i^1].clear();

		}

		memset(mark, false, sizeof(mark));

	}

	void add_Edge(int u, int uval, int v, int vval) {

		u = u * 2 + uval;

		v = v * 2 + vval;

		g[u^1].push_back(v);

		g[v^1].push_back(u);

	}

	void delete_Edge(int u, int uval, int v, int vval) {

		u = u * 2 + uval;

		v = v * 2 + vval;

		g[u^1].pop_back();

		g[v^1].pop_back();

	}

	bool dfs(int u) {

		if (mark[u^1]) return false;

		if (mark[u]) return true;

		mark[u] = true;

		S[sn++] = u;

		for (int i = 0; i < g[u].size(); i++) {

			int v = g[u][i];

			if (!dfs(v)) return false;

		}

		return true;

	}

	bool solve() {

		for (int i = 0; i < n; i += 2) {

			if (!mark[i] && !mark[i + 1]) {

				sn = 0;

				if (!dfs(i)){

					for (int j = 0; j < sn; j++)

						mark[S[j]] = false;

					sn = 0;

					if (!dfs(i + 1)) return false;

				}

			}

		}

		return true;

	}

} gao;

const int N = 505;

int n, b[N][N];

bool solve() {

	for (int k = 0; k < 31; k++) {

		gao.init(n);

		for (int i = 0; i < n; i++)

			for (int j = 0; j < n; j++) {

				int tmp = (b[i][j]>>k)&1;

				if (i == j) {

					if (tmp) return false;

				}

				else if (i % 2 == 1 && j % 2 == 1) {

					if (tmp) gao.add_Edge(i, tmp, j, tmp);

					else {

						gao.add_Edge(i, tmp, i, tmp);

						gao.add_Edge(j, tmp, j, tmp);

					}

				}

				else if (i % 2 == 0 && j % 2 == 0) {

					if (tmp) {

						gao.add_Edge(i, tmp, i, tmp);

						gao.add_Edge(j, tmp, j, tmp);

					} else gao.add_Edge(i, tmp, j, tmp);

				} else {

					if (tmp) {

						gao.add_Edge(i, tmp, j, tmp);

						gao.add_Edge(i, !tmp, j, !tmp);

					} else {

						gao.add_Edge(i, tmp, j, !tmp);

						gao.add_Edge(i, !tmp, j, tmp);

					}

				}

			}

		if (!gao.solve()) return false;

	}

	return true;

}

int main() {

	while (~scanf("%d", &n)) {

		for (int i = 0; i < n; i++)

			for (int j = 0; j < n; j++)

				scanf("%d", &b[i][j]);

		printf("%s\n", solve() ? "YES" : "NO");

	}

	return 0;

}