HDU 4757 Tree 可持久化trie+lca

题目：

http://acm.hdu.edu.cn/showproblem.php?pid=4757

题意：

给出一棵树，树上的点都有权值，每次给出一组询问x y z，求从x到y路径上的点权值和z异或得到的最大值

思路：

可持久化trie，在其父节点的基础上更新trie。查询的时候，先查询x y的lca，然后查询x到lca路径上点权值和z异或的最大值，然后查询y到lca路径上点权值和z异或的最大值，取两者较大值即可

#include <bits/stdc++.h>using namespace std;const int N = 100000 + 10, INF = 0x3f3f3f3f;int tot, root[N];int son[N*35][2], sum[N*35];int cnt, head[N];int dep[N], p[N][25];int a[N];bool bs[35];int len = 31;struct edge{    int to, next;}g[N*2];void init(){    cnt = 0;    memset(head, -1, sizeof head);    tot = 0;}void add_edge(int v, int u){    g[cnt].to = u, g[cnt].next = head[v], head[v] = cnt++;}void trie_insert(int p, int pre, int &x){    x = ++tot;    son[x][0] = son[pre][0], son[x][1] = son[pre][1];    //memcpy(son[x], son[pre], sizeof(int) * 2);    sum[x] = sum[pre] + 1;    if(! p) return;    trie_insert(p-1, son[pre][bs[p-1]], son[x][bs[p-1]]);}int trie_query(int p, int st, int en){    if(! p) return 0;    if(sum[son[en][bs[p-1]]] > sum[son[st][bs[p-1]]]) return trie_query(p-1, son[st][bs[p-1]], son[en][bs[p-1]]) + (1<<(p-1));    return trie_query(p-1, son[st][1-bs[p-1]], son[en][1-bs[p-1]]);}void dfs(int v, int fa, int d){    dep[v] = d, p[v][0] = fa;    for(int i = len-1; i >= 0; i--) bs[i] = 1 & (a[v] >> i);    trie_insert(len, root[fa], root[v]);    for(int i = head[v]; i != -1; i = g[i].next)    {        int u = g[i].to;        if(u == fa) continue;        dfs(u, v, dep[v] + 1);    }}void lca_init(int n){    for(int j = 1; (1<<j) <= n; j++)        for(int i = 1; i <= n; i++)            p[i][j] = p[p[i][j-1]][j-1];}int LCA(int v, int u){    if(dep[v] < dep[u]) swap(v, u);    int d = dep[v] - dep[u];    for(int i = 0; (d>>i) != 0; i++)        if((d>>i) & 1) v = p[v][i];    if(v == u) return v;    for(int i = 20; i >= 0; i--)        if(p[v][i] != p[u][i]) v = p[v][i], u = p[u][i];    return p[v][0];}int main(){    int n, m;    while(~ scanf("%d%d", &n, &m))    {        init();        for(int i = 1; i <= n; i++) scanf("%d", &a[i]);        for(int i = 1; i <= n-1; i++)        {            int v, u;            scanf("%d%d", &v, &u);            add_edge(v, u); add_edge(u, v);        }        dfs(1, 0, 1);        lca_init(n);        for(int i = 1; i <= m; i++)        {            int x, y, val;            scanf("%d%d%d", &x, &y, &val);            for(int j = len-1; j >= 0; j--) bs[j] = ! (1 & (val >> j));            int lca = LCA(x, y);            int ans = trie_query(len, root[p[lca][0]], root[x]);            ans = max(ans, trie_query(len, root[p[lca][0]], root[y]));            printf("%d\n", ans);        }    }    return 0;}

写了个非递归版的插入和查询，好像快了一些。。。

#include <bits/stdc++.h>using namespace std;const int N = 100000 + 10, INF = 0x3f3f3f3f;int tot, root[N];int son[N*35][2], sum[N*35];int cnt, head[N];int dep[N], p[N][25];int a[N];bool bs[35];int len = 31;struct edge{    int to, next;}g[N*2];void init(){    cnt = 0;    memset(head, -1, sizeof head);    tot = 0;}void add_edge(int v, int u){    g[cnt].to = u, g[cnt].next = head[v], head[v] = cnt++;}//void trie_insert(int p, int pre, int &x)//{//    x = ++tot;//    son[x][0] = son[pre][0], son[x][1] = son[pre][1];//    //memcpy(son[x], son[pre], sizeof(int) * 2);//    sum[x] = sum[pre] + 1;//    if(! p) return;//    trie_insert(p-1, son[pre][bs[p-1]], son[x][bs[p-1]]);//}int trie_insert(int val, int pre){    int x = ++tot, t = x;    for(int i = len-1; i >= 0; i--)    {        son[x][0] = son[pre][0], son[x][1] = son[pre][1];        sum[x] = sum[pre] + 1;        int j = 1 & (val >> i);        son[x][j] = ++tot;        x = son[x][j], pre = son[pre][j];    }    sum[x] = sum[pre] + 1;    return t;}//int trie_query(int p, int st, int en)//{//    if(! p) return 0;//    if(sum[son[en][bs[p-1]]] > sum[son[st][bs[p-1]]]) return trie_query(p-1, son[st][bs[p-1]], son[en][bs[p-1]]) + (1<<(p-1));//    return trie_query(p-1, son[st][1-bs[p-1]], son[en][1-bs[p-1]]);//}void dfs(int v, int fa, int d){    dep[v] = d, p[v][0] = fa;//    for(int i = len-1; i >= 0; i--) bs[i] = 1 & (a[v] >> i);//    trie_insert(len, root[fa], root[v]);    root[v] = trie_insert(a[v], root[fa]);    for(int i = head[v]; i != -1; i = g[i].next)    {        int u = g[i].to;        if(u == fa) continue;        dfs(u, v, dep[v] + 1);    }}void lca_init(int n){    for(int j = 1; (1<<j) <= n; j++)        for(int i = 1; i <= n; i++)            p[i][j] = p[p[i][j-1]][j-1];}int LCA(int v, int u){    if(dep[v] < dep[u]) swap(v, u);    int d = dep[v] - dep[u];    for(int i = 0; (d>>i) != 0; i++)        if((d>>i) & 1) v = p[v][i];    if(v == u) return v;    for(int i = 20; i >= 0; i--)        if(p[v][i] != p[u][i]) v = p[v][i], u = p[u][i];    return p[v][0];}int trie_query(int x, int y, int val){    int lca = LCA(x, y), lca_fa = p[lca][0];    x = root[x], y = root[y], lca = root[lca], lca_fa = root[lca_fa];    int ans = 0;    for(int i = len-1; i >= 0; i--)    {        int j = !(1 & (val >> i));        if(sum[son[x][j]] + sum[son[y][j]] - sum[son[lca][j]] - sum[son[lca_fa][j]] > 0)        {            ans |= (1 << i);            x = son[x][j], y = son[y][j], lca = son[lca][j], lca_fa = son[lca_fa][j];        }        else x = son[x][!j], y = son[y][!j], lca = son[lca][!j], lca_fa = son[lca_fa][!j];    }    return ans;}int main(){    int n, m;    while(~ scanf("%d%d", &n, &m))    {        init();        for(int i = 1; i <= n; i++) scanf("%d", &a[i]);        for(int i = 1; i <= n-1; i++)        {            int v, u;            scanf("%d%d", &v, &u);            add_edge(v, u); add_edge(u, v);        }        dfs(1, 0, 1);        lca_init(n);        for(int i = 1; i <= m; i++)        {            int x, y, val;            scanf("%d%d%d", &x, &y, &val);//            for(int j = len-1; j >= 0; j--) bs[j] = ! (1 & (val >> j));//            int lca = LCA(x, y);//            int ans = trie_query(len, root[p[lca][0]], root[x]);//            ans = max(ans, trie_query(len, root[p[lca][0]], root[y]));            int ans = trie_query(x, y, val);            printf("%d\n", ans);        }    }    return 0;}