SGU 101.Domino (Euler path)

Find Euler path ... Direct DFS, Time complexity O (N)

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#include <cstdio>#include <cstring>#include <algorithm>#include <stack>using namespace std;#define X (i) Edge[i].first#define Y (i) Edge[i].secondtypedef pair<int, int> PII;const int MAXN = ten;const int MAXM = 109;const int n = 7;struct Edge {int to, F, Id;edge* Next;} E[MAXM << 1], *pt = E, *HEAD[MAXN]; void Addedge (int u, int v, int Id, int f) {pt->to = v;pt->f = F;pt->id = Id;pt->next = Head[u];Head[u] = pt++;} inline edge* Rev (edge* e) {return E + ((e-e) ^ 1);}PII EDGE[MAXM];int N, CNT[MAXN], PAR[MAXN];stack<pii> S;int Find (int x) {return x = = Par[x]? x:par[x] = Find (par[x]);}bool Chk () {int c = 0;for (int i = 0; i < n; i++)if ((Cnt[i] & 1) && ++c > 2) return false;for (int i = 0; i < n; i++) par[i] = i;for (int i = 0; i < N; i++)Par[find (X (i))] = Find (Y (i));C =-1;for (int i = 0; i < n; i++) if (Cnt[i]) {if (!~c)C = par[i];else if (par[i]! = c)return false;}return true;}void Euler (int x) {For (edge*&e = head[x]; e;) if (e->f) {int F = e->f, t = e->to, Id = e->id;e->f = Rev (e)->f = 0;e = e->next;Euler (t);S.push (Make_pair (Id, F));} elsee = e->next;}int main () {scanf ("%d", &n);memset (CNT, 0, sizeof CNT);for (int i = 0; i < N; i++) {scanf ("%d%d", &x (i), &y (i));cnt[x (i)]++;cnt[y (i)]++;Addedge (X (i), Y (i), I, 1);Addedge (Y (i), X (i), I,-1);}if (!chk ()) {puts ("No solution");return 0;}for (int i = 0; i < n; i++) if (Cnt[i] & 1) {Euler (i);While (! S.empty ()) {PII p = s.top (); S.pop ();printf ("%d%c\n", ++p.first, P.second! = 1? '-': ' + ');}return 0;}for (int i = 0; i < n; i++) if (Cnt[i]) {Euler (i);While (! S.empty ()) {PII p = s.top (); S.pop ();printf ("%d%c\n", ++p.first, P.second! = 1? '-': ' + ');}return 0;}return 0;}

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101. Domino

Time limit per test:0.25 sec.
Memory limit per test:4096 KB

Dominoes–game played with small, rectangular blocks of wood or other material, each identified by a number of dots, or P IPs, on it face. The blocks usually is called bones, dominoes, or pieces and sometimes men, stones, or even cards.
The face of each piece are divided, by a line or ridge, into and squares, each of the which are marked as would be a pair of dic E...

The principle in nearly all modern dominoes games are to match one end of a piece to another so is identically or recipro Cally numbered.

Encyclopædia BRITANNICA

Given a set of domino pieces where each side are marked with the digits from 0 to 6. Your task is to arrange pieces in a line such the, that they touch through equal marked sides. It's possible to rotate pieces changing left and right side.

Input

The first line of the input contains a single integer N (1≤ n ≤100) representing the total number of P Ieces in the domino set. The following N lines describe pieces. Each piece was represented on a separate line in a form of the digits from 0 to 6 separated by a space.

Output

Write "No Solution" if it is the impossible to arrange them described. If It is a possible, write any of the. Pieces must is written in left-to-right order. Every of N lines must contains number of current Domino piece and sign "+" or "-" (first means so you don't rotate that pi ECE, and second if you rotate it).

Sample Input

Sample Output

SGU 101.Domino (Euler path)