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  • 2019 ICPC Asia Nanjing Regional F. Paper Grading (字典树DFS序+带修主席树)

    题目链接:https://nanti.jisuanke.com/t/42400

    题意:给一个模式串集合,序号1~n,有T个操作,或者是交换序号,或者是查询模式串集合中序号在L到R之 间的字符串有多少个和目标串公共前缀长度大于等于K。
    —————————————————————————————————
    对模式串集合建字典树,则与目标串(LCP)大于等K的字符串,都在以目标串第(K)个字符所在的结点为根的子树中,每个模式串插入字典树的过程中记录序号,修改时交换序号,询问就相于在子树中询问有多少结点的序号在(L)(R)之间。
    涉及到子树,容易想到建立(DFS)序,再用数据结构维护
    但是不建议在字典树的(DFS)序上用数据结构维护,因为可能出现两个一样的模式串,但是序号不一样,可能会覆盖之前的序号(个人观点,我写的时候是遇到了这种问题,可能写法问题)
    所以可以用一个数组(h[i]),表示序号为(i)的字符串在字典树中的编号为(h[i]),对(h)使用数据结构维护,需要支持单点修改(交换视为两次单点修改)和查询区间([L,R])(h[i])的值在范围([in[x],out[x]])中的数量((x)为目标串第(K)字符在字典树中的结点编号)

    #include <bits/stdc++.h>
    using namespace std;
    const int maxn = 200010;
    int ptov[maxn], tv[maxn];
    /************************************************************/
    struct Trie
    {
        int trie[maxn][26], tot = 0;
        int ins(char s[])
        {
            int len = strlen(s);
            int root = 0;
            for (int i = 0; i < len; i++)
            {
                int id = s[i] - 'a';
                if (trie[root][id] == 0)
                    trie[root][id] = ++tot;
                root = trie[root][id];
            }
            return root;
        }
        int fin(int k, char s[])
        {
            int root = 0;
            for (int i = 0; i < k; i++)
            {
                int id = s[i] - 'a';
                if (trie[root][id] == 0)
                    return -1;
                root = trie[root][id];
            }
            return root;
        }
    } t;
    /************************************************************/
    int in[maxn], out[maxn];
    int tim = 0;
    void dfs(int x)
    {
        in[x] = ++tim;
        for (int i = 0; i < 26; i++)
        {
            if (t.trie[x][i] == 0)
                continue;
            dfs(t.trie[x][i]);
        }
        out[x] = tim;
    }
    /************************************************************/
    int T[maxn], S[maxn], L[maxn * 150], R[maxn * 150], sum[maxn * 150];
    int h[maxn];
    int ul[maxn], ur[maxn];
    int tot, num, n, m;
    
    struct node
    {
        int l, r, k;
        bool flag;
    } Q[maxn << 1];
    
    void build(int &rt, int l, int r)
    {
        rt = ++tot;
        sum[rt] = 0;
        if (l == r)
            return;
        int mid = (l + r) >> 1;
        build(L[rt], l, mid);
        build(R[rt], mid + 1, r);
    }
    
    void update(int &rt, int pre, int l, int r, int x, int val)
    {
        rt = ++tot;
        L[rt] = L[pre];
        R[rt] = R[pre];
        sum[rt] = sum[pre] + val;
        if (l == r)
            return;
        int mid = (l + r) >> 1;
        if (x <= mid)
            update(L[rt], L[pre], l, mid, x, val);
        else
            update(R[rt], R[pre], mid + 1, r, x, val);
    }
    
    int lowbit(int x) { return x & (-x); }
    
    void add(int x, int val)
    {
        int res = lower_bound(h + 1, h + 1 + num, ptov[x]) - h;
        while (x <= n)
        {
            update(S[x], S[x], 1, num, res, val);
            x += lowbit(x);
        }
    }
    
    int Sum(int x, int flag)
    {
        int res = 0;
        while (x > 0)
        {
            if (flag == 1)
                res += sum[L[ur[x]]];
            else if (flag == 2)
                res += sum[L[ul[x]]];
            else if (flag == 3)
                res += sum[ur[x]];
            else
                res += sum[ul[x]];
            x -= lowbit(x);
        }
        return res;
    }
    int query(int s, int e, int ts, int te, int l, int r, int k)
    {
        if (l == r)
            return Sum(e, 3) - Sum(s, 4) + sum[te] - sum[ts];
        int mid = (l + r) >> 1;
        int res = Sum(e, 1) - Sum(s, 2) + sum[L[te]] - sum[L[ts]];
        if (k <= mid)
        {
            for (int i = e; i; i -= lowbit(i))
                ur[i] = L[ur[i]];
            for (int i = s; i; i -= lowbit(i))
                ul[i] = L[ul[i]];
            return query(s, e, L[ts], L[te], l, mid, k);
        }
        else
        {
            for (int i = e; i; i -= lowbit(i))
                ur[i] = R[ur[i]];
            for (int i = s; i; i -= lowbit(i))
                ul[i] = R[ul[i]];
            return res + query(s, e, R[ts], R[te], mid + 1, r, k);
        }
    }
    /************************************************************/
    char s[maxn];
    int main()
    {
        scanf("%d%d", &n, &m);
        for (int i = 1; i <= n; i++)
        {
            scanf("%s", s);
            ptov[i] = t.ins(s);
        }
        dfs(0);
        for (int i = 1; i <= n; i++)
        {
            ptov[i] = in[ptov[i]];
            h[i] = ptov[i];
            tv[i] = ptov[i];
        }
        int q = 0;
        for (int i = 1; i <= m; i++)
        {
            int opt;
            scanf("%d", &opt);
            if (opt == 2) //询问
            {
                scanf("%s%d%d%d", s, &Q[q].k, &Q[q].l, &Q[q].r);
                Q[q].k = t.fin(Q[q].k, s);
                Q[q].flag = true;
                q++;
            }
            else //修改
            {
                int tl, tr;
                scanf("%d%d", &tl, &tr);
                Q[q].l = tl;
                Q[q].r = tv[tr];
                Q[q].flag = false;
                q++;
    
                Q[q].l = tr;
                Q[q].r = tv[tl];
                Q[q].flag = false;
                q++;
    
                swap(tv[tl], tv[tr]);
            }
        }
        sort(h + 1, h + 1 + n);
        num = unique(h + 1, h + 1 + n) - h - 1;
        tot = 0;
        build(T[0], 1, num);
        for (int i = 1; i <= n; i++)
            update(T[i], T[i - 1], 1, num, lower_bound(h + 1, h + 1 + num, ptov[i]) - h, 1);
        for (int i = 1; i <= n; i++)
            S[i] = T[0];
        for (int i = 0; i < q; i++)
        {
            if (Q[i].flag)
            {
                if (Q[i].k == -1)
                    puts("0");
                else if (Q[i].k == 0)
                    printf("%d
    ", Q[i].r - Q[i].l + 1);
                else
                {
                    int tin = lower_bound(h + 1, h + 1 + num, in[Q[i].k]) - h;
                    auto tout = lower_bound(h + 1, h + 1 + num, out[Q[i].k]);
                    for (int j = Q[i].r; j; j -= lowbit(j))
                        ur[j] = S[j];
                    for (int j = Q[i].l - 1; j; j -= lowbit(j))
                        ul[j] = S[j];
                    int ans1 = query(Q[i].l - 1, Q[i].r, T[Q[i].l - 1], T[Q[i].r], 1, num, tout - h);
                    if (tin == 1)
                    {
                        if (*tout == out[Q[i].k])
                            printf("%d
    ", ans1);
                        else
                            printf("%d
    ", ans1 - 1);
                        continue;
                    }
                    for (int j = Q[i].r; j; j -= lowbit(j))
                        ur[j] = S[j];
                    for (int j = Q[i].l - 1; j; j -= lowbit(j))
                        ul[j] = S[j];
                    int ans2 = query(Q[i].l - 1, Q[i].r, T[Q[i].l - 1], T[Q[i].r], 1, num, tin - 1);
                    if (*tout == out[Q[i].k])
                        printf("%d
    ", ans1 - ans2);
                    else
                        printf("%d
    ", ans1 - 1 - ans2);
                }
            }
            else
            {
                add(Q[i].l, -1);
                ptov[Q[i].l] = Q[i].r;
                add(Q[i].l, 1);
            }
        }
        return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/Zeronera/p/11997580.html
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