思路:很简单的种类并查集,利用并查集可以将所有的人分成几个集合,每个集合又分为好人和坏人集合,直接进行背包dp判断有多少种方法可以在取了所有集合并且人数正好凑足p1个好人的方案。dp(i, j)表示前i和集合有j个好人的方案,如果dp(n, p1)不等于1说明方案不止一种或则根本不存在。注意在dp时,记录路径。
AC代码
#include <cstdio> #include <cmath> #include <cctype> #include <algorithm> #include <cstring> #include <utility> #include <string> #include <iostream> #include <map> #include <set> #include <vector> #include <queue> #include <stack> using namespace std; #pragma comment(linker, "/STACK:1024000000,1024000000") #define eps 1e-10 #define inf 0x3f3f3f3f #define PI pair<int, int> typedef long long LL; const int maxn = 600 + 5; struct node{ int par; int real; }a[maxn]; int find(int x, int &r) { if(a[x].par == x) { r = x; return 0; } int w = find(a[x].par, r); a[x].par = r; return a[x].real = (a[x].real + w) % 2; } void unionset(int x, int y, int real) { int r1, r2; int rx = find(x, r1), ry = find(y, r2); if(r1 != r2) { a[r1].par = y; a[r1].real = (real + rx) % 2; } } int dp[maxn][maxn], pre[maxn][maxn], cnt[maxn][2]; bool vis[maxn]; vector<int>pep[maxn][2]; int main() { int n, p1, p2; while(scanf("%d%d%d", &n, &p1, &p2) == 3) { if(!p1 && !n && !p2) break; int num = p1 + p2; for(int i = 1; i <= num; ++i) { a[i].par = i; a[i].real = 0; } int x, y; char s[5]; for(int i = 0; i < n; ++i) { scanf("%d%d%s", &x, &y, s); int f = s[0] == 'y' ? 0 : 1; unionset(x, y, f); } memset(cnt, 0, sizeof(cnt)); memset(vis, 0, sizeof(vis)); int r, r1, c = 1; for(int i = 1; i <= num; ++i) { if(!vis[i]) { pep[c][0].clear(); pep[c][1].clear(); find(i, r); for(int j = i; j <= num; ++j) { int k = find(j, r1); if(r1 == r) { vis[j] = 1; pep[c][k].push_back(j); cnt[c][k]++; } } ++c; } } memset(dp, 0, sizeof(dp)); dp[0][0] = 1; //边界 for(int i = 1; i < c; ++i) for(int j = p1; j >= 0; --j) { if(j-cnt[i][0] >= 0 && dp[i-1][j-cnt[i][0]]) { dp[i][j] += dp[i-1][j-cnt[i][0]]; pre[i][j] = j - cnt[i][0]; } if(j-cnt[i][1] >= 0 && dp[i-1][j-cnt[i][1]]) { dp[i][j] += dp[i-1][j-cnt[i][1]]; pre[i][j] = j - cnt[i][1]; } } if(dp[c-1][p1] != 1) { printf("no\n"); continue; } vector<int>ans; ans.clear(); int t = p1; for(int i = c-1; i >= 1; --i) { int tmp = t - pre[i][t]; if(cnt[i][0] == tmp) { for(int j = 0; j < pep[i][0].size(); ++j) ans.push_back(pep[i][0][j]); } else { for(int j = 0; j < pep[i][1].size(); ++j) ans.push_back(pep[i][1][j]); } t = pre[i][t]; } sort(ans.begin(), ans.end()); for(int i = 0; i < ans.size(); ++i) { printf("%d\n", ans[i]); } printf("end\n"); } return 0; }
如有不当之处欢迎指出!