CF411H 被遗忘的树 Havel定理 || 网络流

全场只有3个人A的题扔过来当今天的T4.Orz DWX大爷考试时A掉这道题

网络流做法是题解做法，上CF就能看到

但是我们还有其他的方法！

我们有Havel定理的某条推论，既然这是一个树，那么某个子联通块中的点数一定大于边数

然后我们就贪心地选择，用上面的东西来判断是否可选

然后没了

结果考试的时候直接对于10的部分分输出一条链就不会了

Orz 龙哥 rand出60分

结果SDOI3道题和这道神题扔过来4个小时一起做的感觉真是爽

/* ***********************************************Author        :BPM136Created Time  :2016/4/25 17:00:52File Name     :DSF.cpp************************************************ */#include<iostream>#include<cstdio>#include<algorithm>#include<cstdlib>#include<cmath>#include<cstring>#include<iomanip>#include<bitset>#include<queue>#include<ctime>#include<set>#include<map>#include<utility>#include<vector>#include<functional>#include<numeric>#include<memory>#include<iterator>#define LL long long#define DB double#define LB long double#define UL unsigned long#define ULL unsigned long long#define pb push_back#define popb pop_back#define get(a,i) a&(1<<(i-1))#define PAU putchar(32)#define ENT putchar(10)#define clr(a,b) memset(a,b,sizeof(a))#define fo(_i,_a,_b) for(int _i=_a;_i<=_b;_i++)#define fd(_i,_a,_b) for(int _i=_a;_i>=_b;_i--)#define efo(_i,_a) for(int _i=last[_a];_i!=0;_i=e[_i].next)#define file(x) freopen(#x".in","r",stdin),freopen(#x".out","w",stdout)#define filein(x) freopen(#x".in","r",stdin)#define fileout(x) freopen(#x".out","w",stdout)#define mkd(x) freopen(#x".in","w",stdout);#define setlargestack(x) int size=x<<20;char *p=(char*)malloc(size)+size;__asm__("movl %0, %%esp\n" :: "r"(p));#define end system("pause")using namespace std;LL read(){         LL f=1,d=0;char s=getchar();         while (s<48||s>57){if (s==45) f=-1;s=getchar();}         while (s>=48&&s<=57){d=d*10+s-48;s=getchar();}         return f*d;}LL readln(){       LL f=1,d=0;char s=getchar();       while (s<48||s>57){if (s==45) f=-1;s=getchar();}       while (s>=48&&s<=57){d=d*10+s-48;s=getchar();}       while (s!=10) s=getchar();       return f*d;}inline void write(LL x){    if(x==0){putchar(48);return;}if(x<0)putchar(45),x=-x;    int len=0,buf[20];while(x)buf[len++]=x%10,x/=10;    for(int i=len-1;i>=0;i--)putchar(buf[i]+48);return;}inline void writeln(LL x){write(x);ENT;}const int N = 200010;const int M = 7;const int MAX = 45;int cnt[M];int f[N][M];//vector<int> all[MAX];int all[MAX][N];int tail[MAX];int a[MAX][MAX], sz[MAX];int n, m = -1;int tank[M][M][N];int Ans[N][2];int GetNxt() {char s = getchar(); int d = 1;while(s != '?') s = getchar();while(s == '?') {s = getchar();if(s == '?') d ++;}return d;}void init() {//fo(i, 0, MAX-1) all[i].clear();fo(i, 0, MAX - 1) tail[i] = 0;n = read(); //scanf("%d",&n);fo(i, 1, n) {int len = 0, tmp = i;while(tmp > 0) {len ++, tmp /= 10;}len --;all[len][ tail[len]++ ] = i;if(len + 1 > m) m = len + 1;//m = max(m, len + 1);}fo(i, 0, m - 1) sz[i] = tail[i];#define DEBUG2 looksize//fo(i, 0, m - 1) cout<< sz[i] << ' ';cout<<endl;//memset(a,0,sizeof(a));//char s1[MAX], s2[MAX];fo(i, 0, n - 2) {int x = GetNxt(); x --;int y = GetNxt(); y --;tank[x][y][ ++ tank[x][y][0] ] = i;a[x][y] ++;#define DEBUG3 looka//cout<<x<<' '<<y<<endl;}//cout<<endl;}int tmp[MAX], nu;int v, e;bool check() {fo(j, 1, (1 << m) - 1) {nu = 0;fo(i, 0, m - 1)if(j & (1 << i)) {tmp[nu ++] = i;}v = 0, e = 0;fo(i, 0, nu - 1) v += sz[tmp[i]];fo(i, 0, nu - 1) fo(j, 0, nu - 1) {e += a[tmp[i]][tmp[j]];}#define DEBUG1 lookhell with the edge and ver//cout<< e << ' ' << v <<endl;if(e >= v) return 0;}return 1;}void PushAns(int bit1, int bit2, int u, int v) {if(tank[bit1][bit2][0] == 0) swap(bit1, bit2);int G = tank[bit1][bit2][ tank[bit1][bit2][0] -- ];Ans[G][0] = u, Ans[G][1] = v;}void work() {if(check() == 0) {puts("-1");return ;}#define DEBUG4 breakpoint//cerr<<"startwork"<<endl;for(;1;) {int flag = 0;fo(i, 0, m - 1) {fo(j, 0, m - 1) {if(a[i][j] == 0) continue;if(sz[i] > 1) {a[i][j] --, sz[i] --;if(check()) {#define DEBUG5 lookedge1//write(all[i].back()); PAU; writeln(all[j][0]);PushAns(i, j, all[i][ tail[i]-1 ], all[j][0]);tail[i] --, flag = 1;break;}sz[i] ++, a[i][j] ++;}if(sz[j] > 1) {a[i][j] --, sz[j] --;if(check()) {#define DEBUG6 lookedge2//write(all[i][0]); PAU; writeln(all[j].back());PushAns(i, j, all[i][0], all[j][ tail[j]-1 ]);tail[j] --; flag = 1;break;}sz[j] ++, a[i][j] ++;}}if(flag) break;}if(!flag) break;}fo(i, 0, m - 1) fo(j, 0, m - 1) if(a[i][j] > 0) {#define DEBUG7 lookedge3//write(all[i].back()); PAU; writeln(all[j].back());PushAns(i, j, all[i][ tail[i]-1 ], all[j][ tail[j]-1 ]);}fo(i, 0, n - 2) { write(Ans[i][0]); PAU; writeln(Ans[i][1]);}}int main() {file(D);DB tt = clock();init();cerr << clock() - tt <<endl; DB ttt = clock();work();cerr<< clock() - ttt <<endl;cerr<< "Sumtime::" << clock() - tt <<endl;return 0;}