Menci

眉眼如初,岁月如故

在那无法确定的未来
只愿真心如现在一般清澈


「SDOI2014」旅行 - 树链剖分

给一棵树,每个点有其初始颜色和权值,每次修改一个点的颜色或权值,查询路径上颜色与起点相同点权值的和或最大值。

链接

BZOJ 3531

题解

树链剖分,对每种颜色单独建立线段树,线段树动态开点、删点,时间复杂度与空间复杂度均为 O(nlogn) O(n \log n) 级别。

代码

#include <cstdio>
#include <algorithm>
#include <stack>

const int MAXN = 1e5;
const int MAXQ = 1e5;
const int MAXC = 1e5;

struct SegmentTree {
    int l, r, mid;
    SegmentTree *lc, *rc;
    int max, sum;

    SegmentTree(const int l, const int r) : l(l), r(r), mid(l + (r - l) / 2), lc(NULL), rc(NULL), max(0), sum(0) {}

    void update(const int pos, const int val) {
        if (l != r) {
            SegmentTree *&c = pos <= mid ? lc : rc;
            if (!c) c = (pos <= mid) ? new SegmentTree(l, mid) : new SegmentTree(mid + 1, r);
            c->update(pos, val);
            if (val == 0 && !c->lc && !c->rc) delete c, c = NULL;
            max = sum = 0;
            if (lc) max = std::max(max, lc->max), sum += lc->sum;
            if (rc) max = std::max(max, rc->max), sum += rc->sum;
        } else sum = max = val;
    }

    int querySum(const int l, const int r) {
        if (l > this->r || r < this->l) return 0;
        else if (l <= this->l && r >= this->r) return sum;
        else return (lc ? lc->querySum(l, r) : 0) + (rc ? rc->querySum(l, r) : 0);
    }

    int queryMax(const int l, const int r) {
        if (l > this->r || r < this->l) return 0;
        else if (l <= this->l && r >= this->r) return max;
        else return std::max(lc ? lc->queryMax(l, r) : 0, rc ? rc->queryMax(l, r) : 0);
    }
} *seg[MAXC];

struct Node;
struct Edge;

struct Node {
    Edge *e;
    int d, s, i;
    bool f;
    Node *p, *c, *t;
} N[MAXN];

struct Edge {
    Node *s, *t;
    Edge *next;

    Edge(Node *s, Node *t) : s(s), t(t), next(s->e) {}
};

inline void addEdge(const int s, const int t) {
    N[s].e = new Edge(&N[s], &N[t]);
    N[t].e = new Edge(&N[t], &N[s]);
}

int n, q, f[MAXN], v[MAXN];

inline void cut() {
    std::stack<Node *> s;
    s.push(&N[0]);
    N[0].d = 1;

    while (!s.empty()) {
        Node *v = s.top();
        if (!v->f) {
            v->f = true;
            for (Edge *e = v->e; e; e = e->next) if (!e->t->d) {
                e->t->d = v->d + 1;
                e->t->p = v;
                s.push(e->t);
            }
        } else {
            v->s = 1;
            for (Edge *e = v->e; e; e = e->next) if (e->t->p == v) {
                v->s += e->t->s;
                if (!v->c || v->c->s < e->t->s) v->c = e->t;
            }
            s.pop();
        }
    }

    s.push(&N[0]);
    int i = 0;
    while (!s.empty()) {
        Node *v = s.top();
        if (v->f) {
            v->f = false;
            v->i = i++;
            if (!v->p || v != v->p->c) v->t = v;
            else v->t = v->p->t;
            for (Edge *e = v->e; e; e = e->next) if (e->t->p == v && e->t != v->c) s.push(e->t);
            if (v->c) s.push(v->c);
        } else s.pop();
    }
}

inline int querySum(const int u, const int v, SegmentTree *seg) {
    Node *a = &N[u], *b = &N[v];
    int ans = 0;
    while (a->t != b->t) {
        if (a->t->d < b->t->d) std::swap(a, b);
        ans += seg->querySum(a->t->i, a->i);
        a = a->t->p;
    }
    if (a->d > b->d) std::swap(a, b);
    return ans + seg->querySum(a->i, b->i);
}

inline int queryMax(const int u, const int v, SegmentTree *seg) {
    Node *a = &N[u], *b = &N[v];
    int ans = 0;
    while (a->t != b->t) {
        if (a->t->d < b->t->d) std::swap(a, b);
        ans = std::max(ans, seg->queryMax(a->t->i, a->i));
        a = a->t->p;
    }
    if (a->d > b->d) std::swap(a, b);
    return std::max(ans, seg->queryMax(a->i, b->i));
}

int main() {
    scanf("%d %d", &n, &q);

    for (int i = 0; i < MAXC; i++) seg[i] = new SegmentTree(0, n - 1);
    for (int i = 0; i < n; i++) {
        scanf("%d %d", &v[i], &f[i]);
        f[i]--;
        // printf("seg[%d]->update(%d, %d)\n", f[i], i, v[i]);
        // seg[f[i]]->update(i, v[i]);
    }

    for (int i = 0; i < n - 1; i++) {
        int u, v;
        scanf("%d %d", &u, &v), u--, v--;
        addEdge(u, v);
    }

    cut();

    for (int i = 0; i < n; i++) seg[f[i]]->update(N[i].i, v[i]);

    while (q-- ) {
        char s[3];
        int a, b;
        scanf("%s %d %d", s, &a, &b);

        if (s[1] == 'C') {
            a--, b--;
            seg[f[a]]->update(N[a].i, 0);
            seg[b]->update(N[a].i, v[a]);
            f[a] = b;
        } else if (s[1] == 'W') {
            a--;
            seg[f[a]]->update(N[a].i, b);
            v[a] = b;
        } else if (s[1] == 'S') {
            a--, b--;
            printf("%d\n", querySum(a, b, seg[f[a]]));
        } else if (s[1] == 'M') {
            a--, b--;
            printf("%d\n", queryMax(a, b, seg[f[a]]));
        }
    }

    return 0;
}
comments powered by Disqus