Va 1086-The Ministers 'major mess (2-Sat)

Va 1086-The Ministers 'major mess

Question Link

Question: There are n schemes. Each person can vote for a maximum of 4 votes. Now there is a scheme to satisfy more than half of all voting schemes, and the right and wrong of the scheme is output, if a scheme is right or wrong, it is output?

Idea: it is obviously a bipartite graph. I thought it was wrong at the beginning. I want to simplify the conditional form from the beginning, which is not feasible at all.

The correct way is to think about it, because up to four tickets and more than half of them, if you want to choose which solutions are not satisfied, then there will be only one and zero, it is easy to construct the expression, and then 2-Sat,? In this case, you just need to traverse it again, and add an edge opposite to the original condition for each position, and then perform a 2-Sat operation. If yes ?, If not, Y or N is the position.

Code:

#include <cstdio>#include <cstring>#include <cstdlib>#include <vector>#include <algorithm>using namespace std;const int MAXNODE = 105;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 = 105;int n, m;int a[5];bool b[5], save[N];int bitcount(int x) {int ans = 0;while (x) {ans += (x&1);x >>= 1;}return ans;}int main() {int cas = 0;while (~scanf("%d%d", &n, &m) && n || m) {int k;gao.init(n);while (m--) {scanf("%d", &k);char c;for (int i = 0; i < k; i++) {scanf("%d %c", &a[i], &c);a[i]--;if (c == 'y') b[i] = true;else b[i] = false;}if (k <= 2) {for (int i = 0; i < k; i++)gao.add_Edge(a[i], b[i], a[i], b[i]);}else {for (int i = 0; i < k; i++) {for (int j = i + 1; j < k; j++) {gao.add_Edge(a[i], b[i], a[j], b[j]);}}}}printf("Case %d: ", ++cas);if (!gao.solve()) printf("impossible\n");else {for (int i = 0; i < n; i++)save[i] = gao.mark[i * 2 + 1];for (int i = 0; i < n; i++) {memset(gao.mark, false, sizeof(gao.mark));gao.add_Edge(i, !save[i], i, !save[i]);if (gao.solve()) printf("?");else printf("%c", save[i] ? 'y' : 'n');gao.delete_Edge(i, !save[i], i, !save[i]);}printf("\n");}}return 0;}

Va 1086-The Ministers 'major mess (2-Sat)