{"id":1758,"date":"2021-09-08T13:07:29","date_gmt":"2021-09-08T05:07:29","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=1758"},"modified":"2021-09-08T13:35:01","modified_gmt":"2021-09-08T05:35:01","slug":"spoj-cot3","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/spoj-cot3\/","title":{"rendered":"SPOJ COT3"},"content":{"rendered":"

https:\/\/www.spoj.com\/problems\/COT3\/<\/a>
\nhttps:\/\/blog.csdn.net\/huzecong\/article\/details\/9142121<\/a>
\nhttps:\/\/my.oschina.net\/u\/4321213\/blog\/3694105<\/a><\/p>\n

\u975e\u5e38 nice \u7684\u9898\u76ee… \u540c\u65f6\u8003\u5bdf\u7ec4\u5408\u535a\u5f08\u548c\u7ebf\u6bb5\u6811\u5408\u5e76\u3002\u3002\u3002
\n\u4e0d\u59a8\u5148\u8003\u8651\u7b80\u5355\u7684\u95ee\u9898\uff0c\u5982\u4f55\u8f93\u51fa\u7b2c\u4e00\u6b65\u7684\u65b9\u6848\u3002
\n\u6211\u4eec\u679a\u4e3e\u7b2c\u4e00\u6b65\u843d\u5728\u54ea\u91cc\uff0c\u90a3\u4e48\u5f62\u6210\u7684\u9ed1\u94fe\u4f1a\u628a\u539f\u6811\u5212\u5206\u4e3a\u82e5\u5e72\u5b50\u6811\uff0c\u6bcf\u7ec4\u5b50\u6811\u76f8\u4e92\u72ec\u7acb\uff0c\u4e8e\u662f\u53d8\u6210\u6e38\u620f\u7684\u548c\uff0c
\n\u6839\u636e SG \u5b9a\u7406\uff0c\u6211\u4eec\u53ea\u8981\u80fd\u6c42\u51fa\u6bcf\u4e2a\u8282\u70b9\u4e3a\u6839\u7684 sg \u503c\u5373\u53ef\u3002<\/p>\n

\r\nvoid gao(int u = 1, int p = -1, int SG = 0) { \/\/ \u9012\u5f52\u8fdb\u6765\u7684 SG \u8868\u793a\u5b50\u6811\u5916\u7684\u6e38\u620f\r\n    for (auto v: adj[u]) if (v != p) SG ^= sg[v]; \/\/ \u518d xor \u4e0a\u5b50\u6811\u5185\u7684\u6e38\u620f\r\n    if (!col[u] && !SG) Z.PB(u);\r\n    for (auto v: adj[u]) if (v != p) gao(v, u, SG^sg[v]);\r\n}\r\n<\/pre>\n
\u518d\u8003\u8651\u5982\u4f55\u6c42\u4ee5 u \u4e3a\u6839\u7684\u5b50\u6811\u7684 sg \u503c\uff0c\u6211\u4eec\u8003\u8651\u7b2c\u4e00\u6b65\u600e\u4e48\u8d70\uff0c\u5e76\u4e14\u7ef4\u62a4\u6240\u6709\u80fd\u8f6c\u79fb\u5230\u7684 sg \u503c\u7684\u96c6\u5408\u3002
\n\u8ba8\u8bba\u8282\u70b9 u \u7684\u989c\u8272\u3002
\n\u5982\u679c\u662f\u9ed1\u8272\uff0c\u6211\u4eec\u8fd8\u662f\u679a\u4e3e\u7b2c\u4e00\u6b65\u843d\u5728\u5b50\u6811\u4e2d\u54ea\u4e00\u4e2a\u8282\u70b9\u91cc\uff0c\u90a3\u4e48\u548c\u4e0a\u9762\u7684\u60c5\u51b5\u4e00\u6837\uff0c\u4e5f\u662f\u62c6\u5206\u6210\u4e86\u82e5\u5e72\u6e38\u620f\u7684\u548c\u3002
\n\u5982\u679c\u662f\u767d\u8272\uff0c\u90a3\u4e48\u591a\u4e00\u79cd\u64cd\u4f5c\uff0c\u628a\u8fd9\u4e2a sg \u4e5f\u4e22\u5230\u96c6\u5408\u91cc\u3002\uff08\u5bf9\u5e94\u4e0b\u9762 !col[u] \u7684\u60c5\u51b5\uff09
\n\u6700\u540e\u628a\u6240\u6709 sg \u503c\u7684\u96c6\u5408 mex \u4e00\u4e0b\u5373\u53ef\u3002
\n\u8fd9\u6837\u66b4\u529b O(n2) \u7684\u7b97\u6cd5\u5c31\u6709\u4e86\u3002<\/p>\n
\r\nvoid dfs(int u = 1, int p = -1) {\r\n    int s = 0;\r\n    for (auto v: adj[u]) if (v != p) {\r\n        dfs(v, u); s ^= sg[v];\r\n    }\r\n    if (!col[u]) Init(rt[u], LV, s);\r\n    for (auto v: adj[u]) if (v != p) {\r\n        put_xor(rt[v], LV, s ^ sg[v]);\r\n        rt[u] = Merge(rt[u], rt[v]);\r\n    }\r\n    sg[u] = Mex(rt[u], LV);\r\n}\r\n<\/pre>\n
\u8003\u8651\u4f18\u5316\uff0c\u6211\u4eec\u53ef\u4ee5\u7528 01-Trie \u53bb\u7ef4\u62a4 sg \u503c\u7684\u96c6\u5408\uff0c\u90a3\u4e48\u4e0a\u9762\u7684\u679a\u4e3e\u8fc7\u7a0b\u5c31\u4e0d\u9700\u8981\u8fdb\u5165\u5b50\u6811\u679a\u4e3e\u3002
\n\u800c\u53ea\u8981\u5206\u6210 v \u8282\u70b9\u4e2d\u7684 sg \u96c6\u5408\uff0c\u548c v \u8282\u70b9\u5916\u7684\u7ec4\u6210\u7684 sg \u4e24\u4e2a\u72b6\u6001\u5373\u53ef\uff0c\u800c\u8fd9\u4e2a\u76f8\u5f53\u4e8e\u7ed9\u6574\u4e2a\u96c6\u5408\u6253 xor tag \u7136\u540e\u518d\u5408\u5e76\u3002
\n\u800c 01-Trie \u548c\u7ebf\u6bb5\u6811\u7ed3\u6784\u51e0\u4e4e\u4e00\u6837\uff0c\u7a0d\u5fae\u6539\u6539\u5373\u53ef\u3002<\/p>\n
\u590d\u6742\u5ea6 O(nlogn)\u3002<\/p>\n
\r\n\/*\r\n    This code has been written by MinakoKojima, feel free to ask me question. Blog: https:\/\/www.shuizilong.com\/house\r\n    Template Date: 2015.10.12\r\n    Note: ...\r\n*\/\r\n\r\n#pragma comment(linker, "\/STACK:36777216")\r\n\/\/#pragma GCC optimize ("O2")\r\n#define LOCAL\r\n#include <functional>\r\n#include <algorithm>\r\n#include <iostream>\r\n#include <fstream>\r\n#include <sstream>\r\n#include <iomanip>\r\n#include <numeric>\r\n#include <cstring>\r\n#include <climits>\r\n#include <cassert>\r\n#include <complex>\r\n#include <cstdio>\r\n#include <string>\r\n#include <vector>\r\n#include <bitset>\r\n#include <queue>\r\n#include <stack>\r\n#include <cmath>\r\n#include <ctime>\r\n#include <list>\r\n#include <set>\r\n#include <map>\r\n\r\n\/\/#include <tr1\/unordered_set>\r\n\/\/#include <tr1\/unordered_map>\r\n\/\/#include <array>\r\n\r\nusing namespace std;\r\n\r\n#define REP(i, n) for (int i=0;i<n;++i)\r\n#define FOR(i, a, b) for (int i=a;i<b;++i)\r\n#define DWN(i, b, a) for (int i=b-1;i>=a;--i)\r\n#define REP_1(i, n) for (int i=1;i<=n;++i)\r\n#define FOR_1(i, a, b) for (int i=a;i<=b;++i)\r\n#define DWN_1(i, b, a) for (int i=b;i>=a;--i)\r\n#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)\r\n#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)\r\n#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)\r\n#define REP_N(i, n) for (i=0;i<n;++i)\r\n#define FOR_N(i, a, b) for (i=a;i<b;++i)\r\n#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)\r\n#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)\r\n#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)\r\n#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)\r\n#define REP_1_N(i, n) for (i=1;i<=n;++i)\r\n#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)\r\n#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)\r\n#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)\r\n#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)\r\n#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)\r\n#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)\r\n#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)\r\n#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)\r\n\r\n#define ECH(it, A) for (__typeof((A).begin()) it=(A).begin(); it != (A).end(); ++it)\r\n#define rECH(it, A) for (__typeof((A).rbegin()) it=(A).rbegin(); it != (A).rend(); ++it)\r\n#define REP_S(i, str) for (char*i=str;*i;++i)\r\n#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])\r\n#define REP_G(i, u) REP_L(i,hd[u],suc)\r\n#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)\r\n#define DO(n) for ( int ____n = n; ____n-->0; )\r\n#define REP_2(i, j, n, m) REP(i, n) REP(j, m)\r\n#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)\r\n#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)\r\n#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)\r\n#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)\r\n#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)\r\n\r\n#define ALL(A) A.begin(), A.end()\r\n#define LLA(A) A.rbegin(), A.rend()\r\n#define CPY(A, B) memcpy(A, B, sizeof(A))\r\n#define INS(A, P, B) A.insert(A.begin() + P, B)\r\n#define ERS(A, P) A.erase(A.begin() + P)\r\n#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())\r\n#define UBD(A, x) (upper_bound(ALL(A), x) - A.begin())\r\n#define CTN(T, x) (T.find(x) != T.end())\r\n#define SZ(A) int((A).size())\r\n#define PB push_back\r\n#define MP(A, B) make_pair(A, B)\r\n#define PTT pair<T, T>\r\n#define Ts *this\r\n#define rTs return Ts\r\n#define fi first\r\n#define se second\r\n#define re real()\r\n#define im imag()\r\n\r\n#define Rush for(int ____T=RD(); ____T--;)\r\n#define Display(A, n, m) {                      \\\r\n  REP(i, n){\t\t                            \\\r\n        REP(j, m-1) cout << A[i][j] << " ";     \\\r\n        cout << A[i][m-1] << endl;\t\t        \\\r\n\t}\t\t\t\t\t\t                    \\\r\n}\r\n#define Display_1(A, n, m) {                    \\\r\n\tREP_1(i, n){\t\t                        \\\r\n        REP_1(j, m-1) cout << A[i][j] << " ";   \\\r\n        cout << A[i][m] << endl;\t\t        \\\r\n\t}\t\t\t\t\t\t                    \\\r\n}\r\n\r\ntypedef long long LL;\r\n\/\/typedef long double DB;\r\ntypedef double DB;\r\ntypedef unsigned uint;\r\ntypedef unsigned long long uLL;\r\n\r\ntypedef vector<int> VI;\r\ntypedef vector<char> VC;\r\ntypedef vector<string> VS;\r\ntypedef vector<LL> VL;\r\ntypedef vector<DB> VF;\r\ntypedef set<int> SI;\r\ntypedef set<string> SS;\r\ntypedef map<int, int> MII;\r\ntypedef map<string, int> MSI;\r\ntypedef pair<int, int> PII;\r\ntypedef pair<LL, LL> PLL;\r\ntypedef vector<PII> VII;\r\ntypedef vector<VI> VVI;\r\ntypedef vector<VII> VVII;\r\n\r\ntemplate<class T> inline T& RD(T &);\r\ntemplate<class T> inline void OT(const T &);\r\n\/\/inline int RD(){int x; return RD(x);}\r\ninline LL RD(){LL x; return RD(x);}\r\ninline DB& RF(DB &);\r\ninline DB RF(){DB x; return RF(x);}\r\ninline char* RS(char *s);\r\ninline char& RC(char &c);\r\ninline char RC();\r\ninline char& RC(char &c){scanf(" %c", &c); return c;}\r\ninline char RC(){char c; return RC(c);}\r\n\/\/inline char& RC(char &c){c = getchar(); return c;}\r\n\/\/inline char RC(){return getchar();}\r\n\r\ntemplate<class T> inline T& RDD(T &);\r\ninline LL RDD(){LL x; return RDD(x);}\r\n\r\ntemplate<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}\r\ntemplate<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}\r\ntemplate<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}\r\ntemplate<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}\r\ntemplate<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}\r\ntemplate<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}\r\ninline char& RC(char &a, char &b){RC(a), RC(b); return a;}\r\ninline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}\r\ninline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}\r\ninline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}\r\ninline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}\r\ninline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}\r\ninline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}\r\ninline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}\r\ninline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}\r\ninline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}\r\ninline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}\r\ninline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}\r\ninline void RS(char *s1, char *s2){RS(s1), RS(s2);}\r\ninline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}\r\ntemplate<class T0,class T1>inline T0& RDD(T0&a, T1&b){RDD(a),RDD(b); return a;}\r\ntemplate<class T0,class T1,class T2>inline T1& RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c); return a;}\r\n\r\ntemplate<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}\r\ntemplate<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}\r\ntemplate<class T> inline void CLR(T &A){A.clear();}\r\n\r\ntemplate<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}\r\ntemplate<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}\r\ntemplate<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}\r\ntemplate<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}\r\ntemplate<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}\r\ntemplate<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}\r\ntemplate<class T> inline void CLR(priority_queue<T> &Q){while (!Q.empty()) Q.pop();}\r\ntemplate<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}\r\ntemplate<class T> inline void CLR(queue<T> &Q){while (!Q.empty()) Q.pop();}\r\n\r\ntemplate<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}\r\ntemplate<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}\r\ntemplate<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}\r\ntemplate<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}\r\ntemplate<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}\r\n\r\ntemplate<class T> inline bool EPT(T &a){return a.empty();}\r\ntemplate<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}\r\ntemplate<class T, class C> inline T& SRT(T &A, C cmp){sort(ALL(A), cmp); return A;}\r\ntemplate<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}\r\ntemplate<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}\r\ntemplate<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}\r\ntemplate<class T, class C> inline T& UNQ(T &A, C cmp){SRT(A, cmp);return UNQQ(A);}\r\n\r\n\r\n\/\/}\r\n\r\n\/** Constant List .. **\/ \/\/{\r\n\r\nconst int MOD = int(1e9) + 7;\r\nconst int INF = 0x3f3f3f3f;\r\nconst LL INFF = 0x3f3f3f3f3f3f3f3fLL;\r\nconst DB EPS = 1e-9;\r\nconst DB OO = 1e20;\r\nconst DB PI = acos(-1.0); \/\/M_PI;\r\n\r\nconst int dx[] = {-1, 1, 0, 0};\r\nconst int dy[] = {0, 0, 1, -1};\r\n\r\n\/\/}\r\n\r\n\/** Add On .. **\/ \/\/{\r\n\/\/ <<= '0. Nichi Joo ., \/\/{\r\n\r\ntemplate<class T> inline bool checkMin(T &a,const T b){return b < a ? a = b, 1 : 0;}\r\ntemplate<class T> inline bool checkMax(T &a,const T b){return a < b ? a = b, 1 : 0;}\r\ntemplate <class T, class C> inline bool checkUpd(T& a, const T b, C c){return c(b,a) ? a = b, 1 : 0;}\r\ntemplate<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}\r\ntemplate<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}\r\ntemplate<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}\r\ntemplate<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}\r\ntemplate<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}\r\ntemplate<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}\r\ntemplate<class T> inline T sqr(T a){return a*a;}\r\ntemplate<class T> inline T cub(T a){return a*a*a;}\r\ntemplate<class T> inline T ceil(T x, T y){return (x - 1) \/ y + 1;}\r\ntemplate<class T> T abs(T x){return x>0?x:-x;}\r\ninline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}\r\ninline int sgn(DB x, DB y){return sgn(x - y);}\r\n\r\ninline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))\/(2*a*b);}\r\ninline DB cot(DB x){return 1.\/tan(x);};\r\ninline DB sec(DB x){return 1.\/cos(x);};\r\ninline DB csc(DB x){return 1.\/sin(x);};\r\n\r\n\/\/}\r\n\/\/ <<= '1. Bitwise Operation ., \/\/{\r\nnamespace BO{\r\n\r\ninline bool _1(int x, int i){return bool(x&1<<i);}\r\ninline bool _1(LL x, int i){return bool(x&1LL<<i);}\r\ninline LL _1(int i){return 1LL<<i;}\r\ninline LL _U(int i){return _1(i) - 1;};\r\n\r\ninline int reverse_bits(int x){\r\n    x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);\r\n    x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);\r\n    x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);\r\n    x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);\r\n    x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);\r\n    return x;\r\n}\r\n\r\ninline LL reverse_bits(LL x){\r\n    x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);\r\n    x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);\r\n    x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);\r\n    x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);\r\n    x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);\r\n    x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);\r\n    return x;\r\n}\r\n\r\ntemplate<class T> inline bool odd(T x){return x&1;}\r\ntemplate<class T> inline bool even(T x){return !odd(x);}\r\ntemplate<class T> inline T low_bit(T x) {return x & -x;}\r\ntemplate<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}\r\ntemplate<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}\r\ntemplate<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}\r\n\r\ninline int clz(int x){return __builtin_clz(x);}\r\ninline int clz(LL x){return __builtin_clzll(x);}\r\ninline int ctz(int x){return __builtin_ctz(x);}\r\ninline int ctz(LL x){return __builtin_ctzll(x);}\r\ninline int lg2(int x){return !x ? -1 : 31 - clz(x);}\r\ninline int lg2(LL x){return !x ? -1 : 63 - clz(x);}\r\ninline int low_idx(int x){return !x ? -1 : ctz(x);}\r\ninline int low_idx(LL x){return !x ? -1 : ctz(x);}\r\ninline int high_idx(int x){return lg2(x);}\r\ninline int high_idx(LL x){return lg2(x);}\r\ninline int parity(int x){return __builtin_parity(x);}\r\ninline int parity(LL x){return __builtin_parityll(x);}\r\ninline int count_bits(int x){return __builtin_popcount(x);}\r\ninline int count_bits(LL x){return __builtin_popcountll(x);}\r\n\r\n} using namespace BO;\/\/}\r\n\r\n\r\n\/\/ <<= '2. Number Theory .,\/\/{\r\nnamespace NT{\r\n\/\/#define gcd __gcd\r\ninline LL gcd(LL a, LL b){return b?gcd(b,a%b):a;}\r\ninline LL lcm(LL a, LL b){return a*b\/gcd(a,b);}\r\n\r\ninline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}\r\ninline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}\r\n\r\n\/* \u6a21\u6570\u4e24\u500d\u521a\u597d\u8d85 int \u65f6\u3002\r\ninline int sum(uint a, int b){a += b; a %= MOD;if (a < 0) a += MOD; return a;}\r\ninline void INC(int &a, int b){a = sum(a, b);}\r\n*\/\r\n\r\ninline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}\r\ninline int dff(int a, int b){a -= b; if (a < 0) a  += MOD; return a;}\r\ninline void MUL(int &a, int b){a = (LL)a * b % MOD;}\r\n\/\/inline int pdt(int a, int b){return (LL)a * b % MOD;}\r\ninline int pdt(int x,int y) {\r\n    int ret; __asm__ __volatile__ ("\\tmull %%ebx\\n\\tdivl %%ecx\\n":"=d"(ret):"a"(x),"b"(y),"c"(MOD));\r\n    return ret;\r\n}\r\n\r\n\r\ninline int gcd(int m, int n, int &x, int &y){\r\n\r\n    x = 1, y = 0; int xx = 0, yy = 1, q;\r\n\r\n    while (1){\r\n        q = m \/ n, m %= n;\r\n        if (!m){x = xx, y = yy; return n;}\r\n        DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));\r\n        q = n \/ m, n %= m;\r\n        if (!n) return m;\r\n        DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));\r\n    }\r\n}\r\n\r\ninline int sum(int a, int b, int c){return sum(a, sum(b, c));}\r\ninline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}\r\ninline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}\r\ninline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}\r\n\r\ninline int pow(int a, LL b){\r\n    int c(1); while (b){\r\n        if (b&1) MUL(c, a);\r\n        MUL(a, a), b >>= 1;\r\n    }\r\n    return c;\r\n}\r\n\r\ntemplate<class T> inline T pow(T a, LL b){\r\n    T c(1); while (b){\r\n        if (b&1) c *= a;\r\n        a *= a, b >>= 1;\r\n    }\r\n    return c;\r\n}\r\n\r\ntemplate<class T> inline T pow(T a, int b){\r\n    return pow(a, (LL)b);\r\n}\r\n\r\ninline int _I(int b){\r\n    int a = MOD, x1 = 0, x2 = 1, q; while (1){\r\n        q = a \/ b, a %= b;\r\n        if (!a) return x2;\r\n        DEC(x1, pdt(q, x2));\r\n\r\n        q = b \/ a, b %= a;\r\n        if (!b) return x1;\r\n        DEC(x2, pdt(q, x1));\r\n    }\r\n}\r\n\r\ninline void DIV(int &a, int b){MUL(a, _I(b));}\r\ninline int qtt(int a, int b){return pdt(a, _I(b));}\r\n\r\nstruct Int{\r\n    int val;\r\n\r\n    operator int() const{return val;}\r\n\r\n    Int(int _val = 0):val(_val){\r\n        val %= MOD; if (val < 0) val += MOD;\r\n    }\r\n    Int(LL _val):val(_val){\r\n        _val %= MOD; if (_val < 0) _val += MOD;\r\n        val = _val;\r\n    }\r\n\r\n    Int& operator +=(const int& rhs){INC(val, rhs);rTs;}\r\n    Int operator +(const int& rhs) const{return sum(val, rhs);}\r\n    Int& operator -=(const int& rhs){DEC(val, rhs);rTs;}\r\n    Int operator -(const int& rhs) const{return dff(val, rhs);}\r\n    Int& operator *=(const int& rhs){MUL(val, rhs);rTs;}\r\n    Int operator *(const int& rhs) const{return pdt(val, rhs);}\r\n    Int& operator \/=(const int& rhs){DIV(val, rhs);rTs;}\r\n    Int operator \/(const int& rhs) const{return qtt(val, rhs);}\r\n    Int operator-()const{return MOD-*this;}\r\n};\r\n\r\n} using namespace NT;\/\/}\r\n\r\n\r\n\/\/}\r\n\r\n\r\n\r\n\/** I\/O Accelerator Interface .. **\/ \/\/{\r\n#define g (c=getchar())\r\n#define d isdigit(g)\r\n#define p x=x*10+c-'0'\r\n#define n x=x*10+'0'-c\r\n#define pp l\/=10,p\r\n#define nn l\/=10,n\r\ntemplate<class T> inline T& RD(T &x){\r\n    char c;while(!d);x=c-'0';while(d)p;\r\n    return x;\r\n}\r\ntemplate<class T> inline T& RDD(T &x){\r\n    char c;while(g,c!='-'&&!isdigit(c));\r\n    if (c=='-'){x='0'-g;while(d)n;}\r\n    else{x=c-'0';while(d)p;}\r\n    return x;\r\n}\r\ninline DB& RF(DB &x){\r\n    \/\/scanf("%lf", &x);\r\n    char c;while(g,c!='-'&&c!='.'&&!isdigit(c));\r\n    if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}\r\n        else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}\r\n    else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}\r\n        else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}\r\n    return x;\r\n}\r\n#undef nn\r\n#undef pp\r\n#undef n\r\n#undef p\r\n#undef d\r\n#undef g\r\ninline char* RS(char *s){\r\n    \/\/gets(s);\r\n    scanf("%s", s);\r\n    return s;\r\n}\r\n\r\nLL last_ans; int Case; template<class T> inline void OT(const T &x){\r\n    \/\/printf("Case #%d: ", ++Case);\r\n    \/\/printf("%lld\\n", x);\r\n    \/\/printf("%I64d\\n", x);\r\n    \/\/printf("%.9f\\n", x);\r\n    printf("%d\\n", x);\r\n    \/\/cout << x << endl;\r\n    \/\/last_ans = x;\r\n}\r\n\r\n\r\n\/\/}\/* .................................................................................................................................. *\/\r\n\r\nconst int N = int(1e5) + 9;\r\n\r\n\r\n\r\n#define ri register int\r\n#define rep(io, st, ed) for(ri io = st; io <= ed; io ++)\r\n#define drep(io, ed, st) for(ri io = ed; io >= st; io --)\r\n\r\nnamespace Chairman_Tree {\r\n#define lx c[0][x]\r\n#define rx c[1][x]\r\n#define ly c[0][y]\r\n#define ry c[1][y]\r\n#define ml ((l+r)>>1)\r\n#define mr (ml+1)\r\n#define lc lx, lv\r\n#define rc rx, lv\r\n    const int NN = 20*N;\r\n    const int LV = 17;\r\n    int c[2][NN], xr[NN]; bool cv[NN]; int tot;\r\n\r\n    int new_node() {\r\n        ++tot;\r\n        return tot;\r\n    }\r\n\r\n    void put_xor(int x, int lv, int v) {\r\n        if (_1(v, lv)) swap(lx, rx);\r\n        xr[x] ^= v;\r\n    }\r\n\r\n    void upd(int x) {\r\n        cv[x] = cv[lx] && cv[rx];\r\n    }\r\n\r\n    void rls(int x, int lv) {\r\n        if (xr[x]) {\r\n            --lv;\r\n            put_xor(rc, xr[x]); put_xor(lc, xr[x]);\r\n            xr[x] = 0;\r\n        }\r\n    }\r\n\r\n    void Init(int &x, int lv, int v) {\r\n        x = new_node();\r\n        if (!~lv) cv[x] = 1;\r\n        else {\r\n            if (_1(v, lv--)) Init(rc, v);\r\n            else Init(lc, v);\r\n        }\r\n    }\r\n\r\n    int Merge(int x, int y, int lv = LV) {\r\n        if (!x || !y) return x | y;\r\n        if (!~lv) {\r\n            cv[x] |= cv[y];\r\n            return x;\r\n        }\r\n        rls(x, lv); rls(y, lv--);\r\n        lx = Merge(lx, ly, lv);\r\n        rx = Merge(rx, ry, lv);\r\n        upd(x);\r\n        return x;\r\n    }\r\n\r\n    int Mex(int x, int lv = LV) {\r\n        if (!x || !~lv) return 0;\r\n        rls(x, lv--);\r\n        return cv[lx] ? _1(lv+1) + Mex(rc) : Mex(lc);\r\n    }\r\n\r\n} using namespace Chairman_Tree;\r\n\r\nVI adj[N]; int rt[N], col[N], sg[N];\r\nint n;\r\n\r\nvoid dfs(int u = 1, int p = -1) {\r\n    int s = 0;\r\n    for (auto v: adj[u]) if (v != p) {\r\n        dfs(v, u); s ^= sg[v];\r\n    }\r\n    if (!col[u]) Init(rt[u], LV, s);\r\n    for (auto v: adj[u]) if (v != p) {\r\n        put_xor(rt[v], LV, s ^ sg[v]);\r\n        rt[u] = Merge(rt[u], rt[v]);\r\n    }\r\n    sg[u] = Mex(rt[u], LV);\r\n}\r\n\r\nVI Z;\r\n\r\nvoid gao(int u = 1, int p = -1, int SG = 0) {\r\n    for (auto v: adj[u]) if (v != p) SG ^= sg[v];\r\n    if (!col[u] && !SG) Z.PB(u);\r\n    for (auto v: adj[u]) if (v != p) gao(v, u, SG^sg[v]);\r\n}\r\n\r\nint main() {\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen("in.txt", "r", stdin);\r\n#endif\r\n\r\n    RD(n); REP_1(i, n) RD(col[i]); DO(n-1) {\r\n        int x, y; RD(x, y);\r\n        adj[x].PB(y); adj[y].PB(x);\r\n    }\r\n    dfs();\r\n    if (sg[1]) {\r\n        gao(); SRT(Z);\r\n        for (auto z: Z) OT(z);\r\n    } else {\r\n        puts("-1");\r\n    }\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
https:\/\/www.spoj.com\/problems\/COT3\/ https:\/\/blog.csdn.net\/huzecong\/article\/details\/9142121 https:\/\/my.oschina.net\/u\/4321213\/blog\/3694105 \u975e\u5e38 nice \u7684\u9898\u76ee… \u540c\u65f6\u8003\u5bdf\u7ec4\u5408\u535a\u5f08\u548c\u7ebf\u6bb5\u6811\u5408\u5e76\u3002\u3002\u3002 \u4e0d\u59a8\u5148\u8003\u8651\u7b80\u5355\u7684\u95ee\u9898\uff0c\u5982\u4f55\u8f93\u51fa\u7b2c\u4e00\u6b65\u7684\u65b9\u6848\u3002 \u6211\u4eec\u679a\u4e3e\u7b2c\u4e00\u6b65\u843d\u5728\u54ea\u91cc\uff0c\u90a3\u4e48\u5f62\u6210\u7684\u9ed1\u94fe\u4f1a\u628a\u539f\u6811\u5212\u5206\u4e3a\u82e5\u5e72\u5b50\u6811\uff0c\u6bcf\u7ec4\u5b50\u6811\u76f8\u4e92\u72ec\u7acb\uff0c\u4e8e\u662f\u53d8\u6210\u6e38\u620f\u7684\u548c\uff0c \u6839\u636e SG \u5b9a\u7406\uff0c\u6211\u4eec\u53ea\u8981\u80fd\u6c42\u51fa\u6bcf\u4e2a\u8282\u70b9\u4e3a\u6839\u7684 sg \u503c\u5373\u53ef\u3002 void gao(int u = 1, int p = -1, int SG = 0) { \/\/ \u9012\u5f52\u8fdb\u6765\u7684 SG \u8868\u793a\u5b50\u6811\u5916\u7684\u6e38\u620f for (auto v: adj[u]) if (v != p) SG ^= sg[v]; \/\/ \u518d xor \u4e0a\u5b50\u6811\u5185\u7684\u6e38\u620f if (!col[u] && !SG) Z.PB(u); for (auto v: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-1758","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-sm","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1758","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=1758"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1758\/revisions"}],"predecessor-version":[{"id":1759,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1758\/revisions\/1759"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=1758"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=1758"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=1758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}