[模板]-树链剖分

必要前驱知识点

  1. 链式向前星
  2. dfs序
  3. 线段树(区间)

    相关博客

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    相关题目以及代码

  • luogu-P3384

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    // Author : Wqr_
    // Time : 19/09/16
    // luogu 3384
    #include <bits/stdc++.h>
    #define iofuck std::ios::sync_with_stdio(false), cin.tie(0), cout.tie(0)
    #define INF 0x3f3f3f3f
    #define nl (nc << 1)
    #define nr (nc << 1 | 1)
    using namespace std;
    typedef long long ll;
    const ll nmax = 1e5 + 10;
    const ll nmax2 = 2e5 + 10;
    ll n, m, r, mod;
    ll w[nmax], wt[nmax];
    /*******************向前星***************/
    ll head[nmax], e = 0;
    struct edge {
    ll next, to;
    } eg[nmax2];
    void add(ll u, ll v) {
    eg[e].to = v;
    eg[e].next = head[u];
    head[u] = e++;
    }
    /****************线段树****************/
    struct sgt {
    struct node {
    ll val, l, r, lz;
    node() { lz = val = 0;}
    ll len() { return r - l + 1; }
    ll mid() { return (l + r) / 2; }
    } ns[nmax * 4];
    void pushup(ll nc) {
    ns[nc].val = (ns[nr].val + ns[nl].val) % mod;
    }
    void pushdown(ll nc) {
    node &lson = ns[nl];
    node &rson = ns[nr];
    node &cur = ns[nc];
    lson.lz += cur.lz;
    rson.lz += cur.lz;
    lson.val += cur.lz * lson.len();
    rson.val += cur.lz * rson.len();
    lson.val %= mod;
    rson.val %= mod;
    cur.lz = 0;
    }
    void pr(ll nc){
    node &cur = ns[nc];
    if(cur.l == cur.r){
    cout << cur.val << " ";
    return ;
    }
    if(cur.lz) pushdown(nc);
    pr(nl);
    pr(nr);
    }
    void build(ll nc, ll l, ll r) {
    node &cur = ns[nc];
    cur.l = l;
    cur.r = r;
    if (l == r) {
    cur.val = wt[l] % mod;
    return;
    }
    build(nl, l, cur.mid());
    build(nr, cur.mid() + 1, r);
    pushup(nc);
    }
    void update(ll nc, ll L, ll R, ll C) {
    node &cur = ns[nc];
    if (L <= cur.l && cur.r <= R) {
    cur.lz += C;
    cur.val += C * cur.len();
    return;
    }
    if (cur.lz) pushdown(nc);
    if (L <= cur.mid()) update(nl, L, R, C);
    if (R > cur.mid()) update(nr, L, R, C);
    pushup(nc);
    }
    ll query(ll nc, ll L, ll R) {
    node &cur = ns[nc];
    ll ret = 0;
    if (L <= cur.l && cur.r <= R) {
    ret += cur.val;
    ret %= mod;
    return ret;
    }
    if (cur.lz) pushdown(nc);
    if (L <= cur.mid()) ret += query(nl, L, R);
    if (R > cur.mid()) ret += query(nr, L, R);
    ret %= mod;
    return ret;
    }
    };
    /**************树链穮分**************/
    struct qtree {
    sgt tr;
    ll idcnt;
    qtree(){ idcnt = 0; }
    struct node {
    ll deep, fa, id, top, son, siz;
    } ns[nmax];
    void init(ll root) {
    dfs1(root, 0, 1);
    dfs2(root, root);
    tr.build(1, 1, n);
    }
    void dfs1(ll x, ll f, ll deep) {
    node &cur = ns[x];
    cur.deep = deep;
    cur.fa = f;
    cur.siz = 1;
    ll maxson = -1;
    for (ll i = head[x]; i != -1; i = eg[i].next) {
    ll y = eg[i].to;
    if (y == f) continue;
    dfs1(y, x, deep + 1);
    cur.siz += ns[y].siz;
    if (ns[y].siz > maxson) {
    cur.son = y;
    maxson = ns[y].siz;
    }
    }
    }
    void dfs2(ll x, ll topf) {
    node &cur = ns[x];
    cur.id = ++idcnt;
    wt[cur.id] = w[x];
    cur.top = topf;
    if (!cur.son) return;
    dfs2(cur.son, topf);
    for (ll i = head[x]; i != -1; i = eg[i].next) {
    ll y = eg[i].to;
    if (y == cur.fa || y == cur.son) continue;
    dfs2(y, y);
    }
    }
    void add_by_way(ll x, ll y, ll C) {
    C %= mod;
    while (ns[x].top != ns[y].top) {
    if (ns[ns[x].top].deep < ns[ns[y].top].deep)
    swap(x, y);
    tr.update(1, ns[ns[x].top].id, ns[x].id, C);
    x = ns[ns[x].top].fa;
    }
    if(ns[x].deep > ns[y].deep) swap(x, y);
    tr.update(1, ns[x].id, ns[y].id, C);
    }
    ll que_by_way(ll x, ll y) {
    ll ans = 0;
    while (ns[x].top != ns[y].top) {
    if (ns[ns[x].top].deep < ns[ns[y].top].deep)
    swap(x, y);
    ans += tr.query(1, ns[ns[x].top].id, ns[x].id);
    ans %= mod;
    x = ns[ns[x].top].fa;
    }
    if(ns[x].deep > ns[y].deep) swap(x, y);
    ans += tr.query(1, ns[x].id, ns[y].id);
    ans %= mod;
    return ans;
    }
    void add_by_tree(ll x, ll C) {
    tr.update(1, ns[x].id, ns[x].id + ns[x].siz - 1, C);
    }
    ll que_by_tree(ll x) {
    return tr.query(1, ns[x].id, ns[x].id + ns[x].siz - 1) % mod;
    }
    }qt;
    int main() {
    iofuck;
    #ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
    #endif
    memset(head, -1, sizeof(head));
    cin >> n >> m >> r >> mod;
    for (ll i = 1; i <= n; i++) {
    cin >> w[i];
    }
    ll u, v;
    for (ll i = 0; i < n - 1; i++) {
    cin >> u >> v;
    add(u, v);
    add(v, u);
    }
    qt.init(r);
    ll x, y, z;
    ll com;
    for(int i = 0; i < m; i++){
    cin >> com;
    if (com == 1) {
    cin >> x >> y >> z;
    qt.add_by_way(x, y, z);
    } else if (com == 2) {
    cin >> x >> y;
    cout << qt.que_by_way(x, y) << endl;
    } else if (com == 3) {
    cin >> x >> y;
    qt.add_by_tree(x, y);
    } else if (com == 4) {
    cin >> x;
    cout << qt.que_by_tree(x) << endl;
    }
    }
    return 0;
    }
  • luogu-P2590

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    // Author : Wqr_
    // Time : 19/09/17
    #include<bits/stdc++.h>
    #define iofuck std::ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
    #define INF 0x3f3f3f3f
    #define nl (nc << 1)
    #define nr (nc << 1 | 1)
    using namespace std;
    typedef long long ll;
    const int nmax = 3e5 + 50;
    int n, q, head[nmax], e = 0, w[nmax], wt[nmax];
    struct edge {
    int next, to;
    }eg[nmax * 2];
    void add(int u, int v){
    eg[e].to = v;
    eg[e].next = head[u];
    head[u] = e++;
    }
    struct sgt{
    struct node{
    int vmax, vsum, l, r;
    node(){vmax = vsum = 0;}
    int len() {return l - r + 1;}
    int mid() {return (l + r) / 2;}
    }ns[nmax * 4];
    void pushup(int nc){
    ns[nc].vmax = max(ns[nl].vmax, ns[nr].vmax);
    ns[nc].vsum = ns[nl].vsum + ns[nr].vsum;
    }
    void pr(int nc){
    node &cur = ns[nc];
    if(cur.l == cur.r){
    cout << cur.vmax << " ";
    return ;
    }
    pr(nl);
    pr(nr);
    }
    void build(int nc, int l, int r){
    node &cur = ns[nc];
    cur.l = l;
    cur.r = r;
    if(l == r){
    cur.vmax = cur.vsum = wt[l];
    return ;
    }
    build(nl, l, cur.mid());
    build(nr, cur.mid() + 1, r);
    pushup(nc);
    }
    void update(int nc, int L, int C){
    node &cur = ns[nc];
    if(cur.l == cur.r){
    cur.vsum = cur.vmax = C;
    return ;
    }
    if(L <= cur.mid()) update(nl, L, C);
    if(L > cur.mid()) update(nr, L, C);
    pushup(nc);
    }
    int query_max(int nc, int L, int R){
    node &cur = ns[nc];
    int ret = -INF;
    if(L <= cur.l && cur.r <= R){
    ret = max(ret, cur.vmax);
    return ret;
    }
    if(L <= cur.mid()) ret = max(ret, query_max(nl, L, R));
    if(R > cur.mid()) ret = max(ret, query_max(nr, L, R));
    return ret;
    }
    int query_sum(int nc, int L, int R){
    node &cur = ns[nc];
    int ret = 0;
    if(L <= cur.l && cur.r <= R){
    ret += cur.vsum;
    return ret;
    }
    if(L <= cur.mid()) ret += query_sum(nl, L, R);
    if(R > cur.mid()) ret += query_sum(nr, L, R);
    return ret;
    }
    };
    struct qtree{
    struct node{
    int deep, fa, id, top, son, siz;
    } ns[nmax];
    sgt sss;
    int idcnt;
    qtree() {
    idcnt = 0;
    }
    void init(){
    dfs1(1, 0, 1);
    dfs2(1, 1);
    sss.build(1, 1, n);
    }
    void dfs1(int x, int f, int deep) {
    node &cur = ns[x];
    cur.deep = deep;
    cur.fa = f;
    cur.siz = 1;
    int maxson = -1;
    for (int i = head[x]; i != -1; i = eg[i].next) {
    int y = eg[i].to;
    if (y == f) continue;
    dfs1(y, x, deep + 1);
    cur.siz += ns[y].siz;
    if (ns[y].siz > maxson) {
    cur.son = y;
    maxson = ns[y].siz;
    }
    }
    }
    void dfs2(int x, int topf) {
    node &cur = ns[x];
    cur.id = ++idcnt;
    wt[cur.id] = w[x];
    cur.top = topf;
    if (!cur.son) return;
    dfs2(cur.son, topf);
    for (int i = head[x]; i != -1; i = eg[i].next) {
    int y = eg[i].to;
    if (y == cur.fa || y == cur.son) continue;
    dfs2(y, y);
    }
    }
    void change(int nc, int C){
    sss.update(1, ns[nc].id, C);
    }
    int quemax(int x, int y){
    int ans = -INF;
    while (ns[x].top != ns[y].top) {
    if (ns[ns[x].top].deep < ns[ns[y].top].deep)
    swap(x, y);
    ans = max(ans, sss.query_max(1, ns[ns[x].top].id, ns[x].id));
    x = ns[ns[x].top].fa;
    }
    if(ns[x].deep > ns[y].deep) swap(x, y);
    ans = max(ans, sss.query_max(1, ns[x].id, ns[y].id));
    return ans;
    }
    int quesum(int x, int y){
    int ans = 0;
    while (ns[x].top != ns[y].top) {
    if (ns[ns[x].top].deep < ns[ns[y].top].deep)
    swap(x, y);
    ans += sss.query_sum(1, ns[ns[x].top].id, ns[x].id);
    x = ns[ns[x].top].fa;
    }
    if(ns[x].deep > ns[y].deep) swap(x, y);
    ans += sss.query_sum(1, ns[x].id, ns[y].id);
    return ans;
    }
    void test(){
    sss.pr(1);
    cout << endl;
    }
    }qt;
    int main(){
    iofuck;
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    #endif
    memset(head, -1, sizeof(head));
    cin >> n;
    int u, v;
    for(int i = 0; i < n-1; i++){
    cin >> u >> v;
    add(u, v);
    add(v, u);
    }
    for(int i = 1; i <= n; i++){
    cin >> w[i];
    }
    qt.init();
    //qt.test();
    cin >> q;
    string ope;
    int x, y;
    while(q--){
    cin >> ope >> x >> y;
    if(ope[1] == 'H') qt.change(x, y);
    if(ope[1] == 'M') cout << qt.quemax(x, y) << endl;
    if(ope[1] == 'S') cout << qt.quesum(x, y) << endl;
    }
    return 0;
    }