zoj2112

来源：互联网发布：古罗马下水道知乎编辑：程序博客网时间：2024/06/11 00:16
树状数组套主席树
好像没有什么特别的地方，就是要注意卡空间。
先处理出初始序列的主席树 O(N∗log(N+M))
然后用树状数组记录修改 O(M∗logN∗log(N+M))
时间复杂度/空间复杂度:
O((N+M∗logN)∗log(N+M))
#include <cstdio>#include <cstdlib>#include <cstring>#include <cmath>#include <ctime>#include <string>#include <map>#include <vector>#include <stack>#include <queue>#include <utility>#include <iostream>#include <algorithm>#define lowbit(x) ((x)&(-x))#define REP(__i,__start,__end) for(int __i = (__start); __i <= (__end); __i++)#define REPt(__i,__start) for(int __i = (__start); __i > 0; __i -= lowbit(__i))template<class Num>void read(Num &x){    char c; int flag = 1;    while((c = getchar()) < '0' || c > '9')        if(c == '-') flag *= -1;    x = c - '0';    while((c = getchar()) >= '0' && c <= '9')        x = (x<<3) + (x<<1) + (c-'0');    x *= flag;    return;}template<class Num>void write(Num x){    if(x < 0) putchar('-'), x = -x;    static char s[20];int sl = 0;    while(x) s[sl++] = x%10 + '0',x /= 10;    if(!sl) {putchar('0');return;}    while(sl) putchar(s[--sl]);}const int maxn = 5e4+5,maxm = 1e4+5, logN = 40, size = 2e6;int n, m;struct TreeNode{    int l, r, cnt;}Emp, S[size];int tot, root[maxn<<1], a[maxn];struct vetor{#define begin() (__arr + 1)#define end() (__arr + __len + 1)    int *__arr, __len;    void set(int size)    {        __len = 0, __arr = (int*)malloc(sizeof(int)*size);    }    void push_back(int x)    {        __arr[++__len] = x;    }    int size()    {        return __len;    }    void unique()    {        std::sort(begin(),end());        __len = std::unique(begin(),end()) - begin();    }    int find(int x)    {        return std::lower_bound(begin(), end(), x)-begin()+1;    }    int get(int x)    {        return __arr[x];    }    int count()    {        int ret = 0;#define Lcnt(x) S[S[x].l].cnt               REP(i, 1, __len) ret += Lcnt(__arr[i]);#undef Lcnt                 return ret;    }    void erase()    {        __len = 0;    }    int gain(int x)    {        erase(), push_back(root[n + x]);        REPt(i, x) push_back(root[i]);    }    void move(int tp)    {        if(tp)  REP(i, 1, __len) __arr[i] = S[__arr[i]].r;        else    REP(i, 1, __len) __arr[i] = S[__arr[i]].l;    }#undef begin#undef end}arr, Tl, Tr;int NewNode(){    S[++tot] = Emp;    return tot;}int TreeAdd(int now,int ll,int rr,int k,int val){    int ret = NewNode();    if(ll == rr)        S[ret].cnt = S[now].cnt + val;    else    {        int mid = (ll + rr) >> 1;        if(k <= mid)        {            S[ret].l = TreeAdd(S[now].l, ll, mid, k, val);            S[ret].r = S[now].r, S[ret].cnt = S[S[ret].l].cnt + S[S[ret].r].cnt;                    }        else        {            S[ret].r = TreeAdd(S[now].r, mid + 1, rr, k, val);            S[ret].l = S[now].l, S[ret].cnt = S[S[ret].l].cnt + S[S[ret].r].cnt;                    }       }    return ret;}void ArrayAdd(int x,int ts,int val){    while(x <= n)    {        root[x] = TreeAdd(root[x], 1, arr.size(), ts, val);        x += lowbit(x);    }}int Build(int ll,int rr){    int ret = NewNode();    if(ll != rr)    {        int mid = (ll + rr) >> 1;        S[ret].l = Build(ll, mid);        S[ret].r = Build(mid + 1, rr);    }    return ret;}void PreWork(){    root[0] = Build(1, arr.size());    REP(i, 1, n) root[i] = root[0];    REP(i, 1, n) root[n+i] = TreeAdd(root[n+i-1], 1, arr.size(), arr.find(a[i]), 1);    }struct operator_import{    int type, i, j, t;    void scan()    {        char c[3];        scanf("%s",c), type = (c[0] == 'C');        if(type)            read(i), read(t), arr.push_back(t);        else            read(i), read(j), read(t);    }    int query(int l,int r,int k)    {        int ll = 1, rr = arr.size();        Tl.gain(l-1), Tr.gain(r);        while(ll != rr)        {            int mid = (ll + rr)>>1, cnt = 0;            cnt += Tr.count(), cnt -= Tl.count();            if(k <= cnt)                Tl.move(0), Tr.move(0), rr = mid;            else                k -= cnt, Tl.move(1), Tr.move(1), ll = mid + 1;        }        return ll;    }    void solve()    {        if(type)        {            ArrayAdd(i, arr.find(a[i]), -1);            ArrayAdd(i, arr.find(t), 1), a[i] = t;        }        else            write(arr.get(query(i, j, t))),puts("");            }}op[maxm];int main(){    int T;#ifndef ONLINE_JUDGE    freopen("zoj2112.in","r",stdin);    freopen("zoj2112.out","w",stdout);#endif    arr.set(maxn + maxm), Tl.set(logN), Tr.set(logN);    std::cin >> T;    while(T--)    {        tot = 0, arr.erase();        std::cin >> n >> m;        REP(i, 1, n) read(a[i]), arr.push_back(a[i]);        REP(i, 1, m) op[i].scan();        arr.unique(), PreWork();        REP(i, 1, m) op[i].solve();    }#ifndef ONLINE_JUDGE    fclose(stdin);    fclose(stdout);#endif    return 0;}
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