P4312 [COI2009] OTOCI

https://www.luogu.com.cn/record/98474073

Luogu/P4312/P4312.cpp

@@ -0,0 +1,214 @@
+#include <iostream>
+#include <stack>
+#include <string>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 3e4 + 5;
+
+class LinkCutTree {
+  private:
+    struct node {
+        size_t l, r, f;
+        unsigned v, s;
+        bool rev;
+
+        node()
+            : l(0), r(0), f(0), s(0), v(0), rev(false) {}
+
+        node(unsigned _v, size_t _f)
+            : l(0), r(0), f(_f), s(_v), v(_v), rev(false) {}
+
+        size_t &child(unsigned x) {
+            return !x ? l : r;
+        }
+    } tr[N];
+
+    inline void pushup(size_t u) {
+        tr[u].s = tr[tr[u].l].s + tr[u].v + tr[tr[u].r].s;
+    }
+
+    inline void pushdown(const size_t &u) {
+        if (!tr[u].rev) return;
+
+        std::swap(tr[u].l, tr[u].r);
+        tr[tr[u].l].rev = !tr[tr[u].l].rev;
+        tr[tr[u].r].rev = !tr[tr[u].r].rev;
+        tr[u].rev = false;
+    }
+
+    unsigned relation(const size_t &u) {
+        return u == tr[tr[u].f].l ? 0 : 1;
+    }
+
+    bool isRoot(const size_t &u) {
+        return tr[tr[u].f].l != u && tr[tr[u].f].r != u;
+    }
+
+    void rotate(size_t u) {
+        size_t p = tr[u].f;
+        unsigned x = relation(u);
+
+        if (!isRoot(p)) {
+            tr[tr[p].f].child(relation(p)) = u;
+        }
+        tr[u].f = tr[p].f;
+
+        if (tr[u].child(x ^ 1)) {
+            tr[tr[u].child(x ^ 1)].f = p;
+        }
+        tr[p].child(x) = tr[u].child(x ^ 1);
+
+        tr[u].child(x ^ 1) = p;
+        tr[p].f = u;
+
+        pushup(p);
+        pushup(u);
+    }
+
+    void splay(size_t u) {
+        std::stack<size_t> st;
+
+        size_t cur = u;
+        st.push(cur);
+        while (!isRoot(cur)) {
+            st.push(tr[cur].f);
+            cur = tr[cur].f;
+        }
+
+        while (!st.empty()) {
+            pushdown(st.top());
+            st.pop();
+        }
+
+        while (!isRoot(u)) {
+            if (isRoot(tr[u].f)) {
+                rotate(u);
+            } else if (relation(u) == relation(tr[u].f)) {
+                rotate(tr[u].f);
+                rotate(u);
+            } else {
+                rotate(u);
+                rotate(u);
+            }
+        }
+    }
+
+    void access(size_t u) {
+        for (size_t f = 0; u; u = tr[f = u].f) {
+            splay(u);
+            tr[u].r = f;
+            pushup(u);
+        }
+    }
+
+    void makeRoot(const size_t &u) {
+        access(u);
+        splay(u);
+        tr[u].rev = !tr[u].rev;
+    }
+
+    size_t findRoot(size_t u) {
+        access(u);
+        splay(u);
+
+        while (tr[u].l) {
+            u = tr[u].l;
+        }
+
+        return u;
+    }
+
+    void split(const size_t &x, const size_t &y) {
+        makeRoot(x);
+        access(y);
+        splay(y);
+    }
+
+  public:
+    void set(int p, int v) {
+        tr[p].s = tr[p].v = v;
+    }
+
+    unsigned query(int x, int y) {
+        split(x, y);
+
+        return tr[y].s;
+    }
+
+    bool check(int x, int y) {
+        return findRoot(x) == findRoot(y);
+    }
+
+    void link(const int &x, const int &y) {
+        makeRoot(x);
+
+        if (findRoot(y) != x) {
+            tr[x].f = y;
+        }
+    }
+
+    void cut(int x, int y) {
+        split(x, y);
+
+        if (tr[y].l == x) {
+            tr[y].l = 0;
+            tr[x].f = 0;
+        }
+    }
+
+    void change(int p, int v) {
+        access(p);
+        splay(p);
+        tr[p].v = v;
+        pushup(p);
+    }
+} lct;
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n;
+
+    cin >> n;
+
+    for (int i = 1, x; i <= n; i++) {
+        cin >> x;
+
+        lct.set(i, x);
+    }
+
+    int q;
+
+    cin >> q;
+
+    while (q--) {
+        std::string op;
+        int x, y;
+
+        cin >> op >> x >> y;
+
+        if (op == "bridge") {
+            if (lct.check(x, y)) {
+                cout << "no" << endl;
+            } else {
+                lct.link(x, y);
+
+                cout << "yes" << endl;
+            }
+        } else if (op == "penguins") {
+            lct.change(x, y);
+        } else {  // op == "excursion"
+            if (lct.check(x, y)) {
+                cout << lct.query(x, y) << endl;
+            } else {
+                cout << "impossible" << endl;
+            }
+        }
+    }
+
+    return 0;
+}