[BZOJ 3651] 네트워크 통신 [Link - Cut Tree]

/* Pigonometry */
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <map>
#include <utility>

using namespace std;

typedef pair<int, int> pii;

const int maxn = 8005, maxc = 101, maxs = 100000;

int n, m, c;

map<pii, int> com;

int sta[maxs], top;

struct _lct {
	int son[maxn][2], pre[maxn], deg[maxn];
	bool rev[maxn];

	void init() {
		for(int i = 0; i < maxn; i++) son[i][0] = son[i][1] = pre[i] = deg[i] = 0;
	}

	bool isroot(int x) {
		return son[pre[x]][0] != x && son[pre[x]][1] != x;
	}

	void pushdown(int x) {
		if(rev[x]) {
			int l = son[x][0], r = son[x][1];
			rev[l] ^= 1; rev[r] ^= 1;
			swap(son[l][0], son[l][1]); swap(son[r][0], son[r][1]);
			rev[x] = 0;
		}
	}

	void rotate(int x) {
		int y = pre[x], z = pre[y], type = son[y][1] == x;
		pre[son[y][type] = son[x][!type]] = y;
		pre[x] = z;
		if(!isroot(y)) son[z][son[z][1] == y] = x;
		pre[son[x][!type] = y] = x;
	}

	void maintain(int x) {
		top = 0;
		for(sta[++top] = x; !isroot(x); x = pre[x]) sta[++top] = pre[x];
		for(; top; pushdown(sta[top--]));
	}

	void splay(int x) {
		maintain(x);
		while(!isroot(x)) {
			int y = pre[x], z = pre[y];
			if(isroot(y)) rotate(x);
			else if(son[y][1] == x ^ son[z][1] == y) rotate(x), rotate(x);
			else rotate(y), rotate(x);
		}
	}

	void access(int x) {
		for(int y = 0; x; x = pre[y = x]) {
			splay(x);
			son[x][1] = y;
		}
	}

	void makeroot(int x) {
		access(x); splay(x); rev[x] ^= 1;
		swap(son[x][0], son[x][1]);
	}

	void link(int x, int y) {
		makeroot(x); pre[x] = y;
		deg[x]++; deg[y]++;
	}

	void cut(int x, int y) {
		makeroot(x); access(y); splay(y);
		deg[x]--; deg[y]--;
		son[y][0] = pre[x] = 0;
	}

	int findroot(int x) {
		access(x); splay(x);
		for(; son[x][0]; x = son[x][0]);
		return x;
	}
	
	bool check(int x, int y) {
		return findroot(x) == findroot(y);
	}
} lct[maxc];

inline int iread() {
	int f = 1, x = 0; char ch = getchar();
	for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;
	for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
	return f * x;
}

int main() {
	n = iread(); m = iread(); c = iread(); int T = iread();
	for(int i = 1; i <= c; i++) lct[i].init();

	for(int i = 1; i <= m; i++) {
		int u = iread(), v = iread(), w = iread();
		lct[w].link(u, v);
		com[pii(u, v)] = com[pii(v, u)] = w;
	}

	while(T--) {
		int u = iread(), v = iread(), w = iread();
		int tmp = com[pii(u, v)];
		if(tmp == 0) printf("No such cable.
");
		else if(tmp == w) printf("Already owned.
");
		else if(lct[w].deg[u] == 2 || lct[w].deg[v] == 2) printf("Forbidden: monopoly.
");
		else if(lct[w].check(u, v)) printf("Forbidden: redundant.
");
		else {
			lct[tmp].cut(u, v);
			com[pii(u, v)] = com[pii(v, u)] = w;
			lct[w].link(u, v);
			printf("Sold.
");
		}
	}

	return 0;
}