[SDOI 2011] 染色

发表于2017-04-14更新于2020-08-06

题目大意

一个 nn 个节点的树，每个节点有一个权值 cic_i，给出 mm 组操作，每次操作为：

  • C  a  b  cC \; a \; b \; c：把链 a−ba-b 上的节点的权值全部修改为 cc。
  • Q  a  bQ \; a \; b：询问链 a−ba-b 上有几段权值。

1⩽n,  m⩽100,0001 \leqslant n, \; m \leqslant 100,000

0⩽ci⩽1,000,000,0000 \leqslant c_i \leqslant 1,000,000,000

题目链接

【SDOI 2011】染色 - Luogu 2486

题解

树链剖分裸题。

一直懒得做，今天做了之后被各种细节错误坑惨了（代码中所有有 DBG 的地方几乎都是出过错的地方）。。。

代码

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#include <cstdio>
#include <algorithm>
// #define DBG
const int MAXN = 100005;
struct Edge;
struct Chain;
struct Node {
    Edge *e;
    Chain *c;
    Node *fa, *maxChild;
    int size, dfn, deep;
    bool vis;
#ifdef DBG
    int id;
#endif
} N[MAXN];
struct Edge {
    Node *u, *v;
    Edge *next;
    Edge(Node *u, Node *v) : u(u), v(v), next(u->e) {}
};
struct Chain {
    Node *top;
    Chain(Node *top) : top(top) {}
};
void addEdge(int u, int v) {
    N[u].e = new Edge(&N[u], &N[v]);
    N[v].e = new Edge(&N[v], &N[u]);
}
void dfs1(Node *u) {
    u->vis = true;
    u->size = 1;
#ifdef DBG
    printf("dfs1(%d)\n", u->id);
#endif
    for (Edge *e = u->e; e; e = e->next) {
#ifdef DBG
        printf("when dfs1(%d), v: %d\n", u->id, e->v->id);
#endif
        if (e->v->vis) continue;
        e->v->fa = u;
        e->v->deep = u->deep + 1;
        dfs1(e->v);
        u->size += e->v->size;
        if (!u->maxChild || u->maxChild->size < e->v->size) u->maxChild = e->v;
    }
#ifdef DBG
    printf("end dfs1(%d)\n", u->id);
#endif
}
void dfs2(Node *u) {
    static int dfsClock = 0;
    u->dfn = ++dfsClock;
    if (!u->fa || u != u->fa->maxChild) u->c = new Chain(u);
    else u->c = u->fa->c;
    if (u->maxChild) dfs2(u->maxChild);
    for (Edge *e = u->e; e; e = e->next)
        if (e->v->fa == u && e->v != u->maxChild) dfs2(e->v);
}
void split() {
    N[1].deep = 1;
    dfs1(&N[1]);
#ifdef DBG
    puts("after dfs1");
#endif
    dfs2(&N[1]);
}
struct SegT {
    struct Node {
        int l, r, mid;
        Node *lc, *rc;
        int cnt, val, lval, rval, tag;
        Node(int l, int r, Node *lc, Node *rc) : l(l), r(r), lc(lc), rc(rc), cnt(0), val(0), lval(0), rval(0), tag(-1) {}
        void maintain() {
            cnt = lc->cnt + rc->cnt - (lc->rval == rc->lval);
            lval = lc->lval;
            rval = rc->rval;
        }
        void pushDown() {
            if (tag != -1) {
                val = lval = rval = tag;
                cnt = 1;
                if (lc) lc->tag = tag;
                if (rc) rc->tag = tag;
                tag = -1;
            }
        }
        void update(int pos, int v) {
#ifdef DBG
            printf("update(%d) in [%d, %d] to %d\n", pos, l, r, v);
#endif
            pushDown();
            if (l == r) {
                val = lval = rval = v;
                cnt = 1;
                return;
            }
            int mid = l + (r - l) / 2;
            if (pos <= mid) lc->update(pos, v);
            else rc->update(pos, v);
            maintain();
        }
        void update(int l, int r, int v) {
#ifdef DBG
            printf("update[%d, %d] in [%d, %d] to  %d\n", l, r, this->l, this->r, v);
#endif
            pushDown();
            if (r < this->l || this->r < l) return;
            if (l <= this->l && this->r <= r) {
                tag = v;
                pushDown();
                return;
            }
            lc->update(l, r, v);
            rc->update(l, r, v);
            maintain();
        }
        int query(int pos) {
#ifdef DBG
            printf("queryVal in [%d, %d], val = %d\n", l, r, val);
#endif
            pushDown();
            if (l == r) return val;
            int mid = l + (r - l) / 2;
            if (pos <= mid) return lc->query(pos);
            else return rc->query(pos);
        }
        int query(int l, int r) {
#ifdef DBG
            printf("query[%d, %d] in [%d, %d], cnt = %d\n", l, r, this->l, this->r, cnt);
#endif
            pushDown();
            if (r < this->l || this->r < l) return 0;
            if (l <= this->l && this->r <= r) return cnt;
            int res = lc->query(l, r) + rc->query(l, r);
            int mid = this->l + (this->r - this->l) / 2;
            if (l <= mid && mid < r && lc->rval == rc->lval) res--;
            return res;
        }
    } *root;
    SegT() : root(NULL) {}
    static Node *build(int l, int r) {
        if (l == r) return new Node(l, r, NULL, NULL);
        int mid = l + (r - l) / 2;
        return new Node(l, r, build(l, mid), build(mid + 1, r));
    }
    void update(int pos, int v) {
        root->update(pos, v);
    }
    void update(int l, int r, int v) {
        root->update(l, r, v);
    }
    int query(int pos) {
        return root->query(pos);
    }
    int query(int l, int r) {
        return root->query(l, r);
    }
} segT;
int n, m, c[MAXN];
void update(int a, int b, int val) {
    Node *u = &N[a], *v = &N[b];
    while (u->c != v->c) {
        if (u->c->top->deep < v->c->top->deep) std::swap(u, v);
        segT.update(u->c->top->dfn, u->dfn, val);
        u = u->c->top->fa;
    }
    if (u->deep > v->deep) std::swap(u, v);
    segT.update(u->dfn, v->dfn, val);
}
int query(int a, int b) {
    Node *u = &N[a], *v = &N[b];
    int res = 0;
    while (u->c != v->c) {
        if (u->c->top->deep < v->c->top->deep) std::swap(u, v);
        res += segT.query(u->c->top->dfn, u->dfn);
#ifdef DBG
        printf("query(%d, %d), res = %d(before -)\n", a, b, res);
#endif
        if (segT.query(u->c->top->dfn) == segT.query(u->c->top->fa->dfn)) res--;
#ifdef DBG
        printf("query(%d, %d), res = %d\n", a, b, res);
#endif
        u = u->c->top->fa;
    }
    if (u->deep > v->deep) std::swap(u, v);
    res += segT.query(u->dfn, v->dfn);
    return res;
}
int main() {
    scanf("%d %d", &n, &m);
#ifdef DBG
    for (int i = 1; i <= n; i++) N[i].id = i;
#endif
    for (int i = 1; i <= n; i++) scanf("%d", &c[i]);
    for (int i = 1; i < n; i++) {
        int u, v;
        scanf("%d %d", &u, &v);
        addEdge(u, v);
    }
    split();
#ifdef DBG
    puts("after split");
#endif
    segT.root = SegT::build(1, n);
    for (int i = 1; i <= n; i++) segT.update(N[i].dfn, c[i]);
#ifdef DBG
    puts("after build");
#endif
    while (m--) {
#ifdef DBG
        printf("m = %d\n", m);
#endif
        char op[2];
        int a, b;
        scanf("%s %d %d", op, &a, &b);
        if (op[0] == 'C') {
            int c;
            scanf("%d", &c);
            update(a, b, c);
        } else printf("%d\n", query(a, b));
    }
    return 0;
}