可持久化trie(BZOJ5338: [TJOI2018]xor)

题面

BZOJ

Sol

显然是要维护一个区域的 \(trie\) 树，然后贪心
区间 \(trie\) 树？？？
可持久化 \(trie\) 树？？？
直接参考主席树表示出区间的方法建立 \(trie\) 树，然后做差就好了
巨简单

# include <bits/stdc++.h>
# define IL inline
# define RG register
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;

IL int Input(){
    RG int x = 0, z = 1; RG char c = getchar();
    for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
    for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
    return x * z;
}

const int maxn(1e5 + 5);
const int pw(1 << 30);

int n, q, first[maxn], cnt, val[maxn], dfn[maxn], idx, id[maxn];
int size[maxn], son[maxn], top[maxn], deep[maxn], fa[maxn];

struct Edge{
    int to, next;
} edge[maxn << 1];

struct Trie{
    int ch[2][maxn * 32], rt[maxn], tot, sz[maxn * 32];

    IL void Modify(RG int &x, RG int v, RG int d){
        ch[0][++tot] = ch[0][x], ch[1][tot] = ch[1][x];
        sz[tot] = sz[x] + 1, x = tot;
        if(!d) return;
        Modify(ch[bool(d & v)][x], v, d >> 1);
    }


    IL int Query1(RG int a, RG int b, RG int v, RG int dep){
        if(!a || !dep) return 0;
        RG int f = bool(dep & v) ^ 1, s = sz[ch[f][a]] - sz[ch[f][b]];
        if(s) return Query1(ch[f][a], ch[f][b], v, dep >> 1) + dep;
        f ^= 1;
        return Query1(ch[f][a], ch[f][b], v, dep >> 1);
    }
    
    IL int Query2(RG int a, RG int b, RG int c, RG int d, RG int v, RG int dep){
        if(!(a + b) || !dep) return 0;
        RG int f = bool(dep & v) ^ 1, s = sz[ch[f][a]] + sz[ch[f][b]] - sz[ch[f][c]] - sz[ch[f][d]];
        if(s) return Query2(ch[f][a], ch[f][b], ch[f][c], ch[f][d], v, dep >> 1) + dep;
        f ^= 1;
        return Query2(ch[f][a], ch[f][b], ch[f][c], ch[f][d], v, dep >> 1);
    }
} tree1, tree2;

IL void Add(RG int u, RG int v){
    edge[cnt] = (Edge){v, first[u]}, first[u] = cnt++;
}

IL void Dfs1(RG int u, RG int ff){
    size[u] = 1, tree1.rt[u] = tree1.rt[ff];
    tree1.Modify(tree1.rt[u], val[u], pw);
    for(RG int e = first[u]; e != -1; e = edge[e].next){
        RG int v = edge[e].to;
        if(v != ff){
            deep[v] = deep[u] + 1, fa[v] = u;
            Dfs1(v, u);
            size[u] += size[v];
            if(size[v] > size[son[u]]) son[u] = v;
        }
    }
}

IL void Dfs2(RG int u, RG int tp){
    dfn[u] = ++idx, id[idx] = u, top[u] = tp;
    if(son[u]) Dfs2(son[u], tp);
    for(RG int e = first[u]; e != -1; e = edge[e].next)
        if(!dfn[edge[e].to]) Dfs2(edge[e].to, edge[e].to);
}

IL int LCA(RG int u, RG int v){
    while(top[u] ^ top[v])
        deep[top[u]] > deep[top[v]] ? u = fa[top[u]] : v = fa[top[v]];
    return deep[u] > deep[v] ? v : u;
}

int main(){
    n = Input(), q = Input();
    for(RG int i = 1; i <= n; ++i) val[i] = Input(), first[i] = -1;
    for(RG int i = 1; i < n; ++i){
        RG int u = Input(), v = Input();
        Add(u, v), Add(v, u);
    }
    Dfs1(1, 0), Dfs2(1, 0);
    for(RG int i = 1; i <= n; ++i){
        tree2.rt[i] = tree2.rt[i - 1];
        tree2.Modify(tree2.rt[i], val[id[i]], pw);
    }
    for(RG int i = 1; i <= q; ++i)
        if(Input() == 1){
            RG int u = Input(), v = Input();
            printf("%d\n", tree2.Query1(tree2.rt[dfn[u] + size[u] - 1], tree2.rt[dfn[u] - 1], v, pw));
        }
        else{
            RG int u = Input(), v = Input(), x = Input(), lca = LCA(u, v);
            printf("%d\n", tree1.Query2(tree1.rt[u], tree1.rt[v], tree1.rt[lca], tree1.rt[fa[lca]], x, pw));
        }
    return 0;
}