• HDU5286 wyh2000 and sequence【分块 均摊复杂度】


    HDU5286 wyh2000 and sequence

    题意:

    给出长为(N)的序列(A_1,A_2,A_3,cdots,A_n)(q)次询问,每次询问给出区间([L,R]),假设区间内出现过的数为(C_1,C_2,cdots,C_k),出现的次数分别为(B_1,B_2,cdots,B_k),输出(sum_{i=1}^{k}C_i^{B_i} % 1000000007),要求在线

    题解:

    如果不要求在线,直接用莫队很快就能解决,现在要求在线,还是考虑把序列分块,预处理出所有连续的块的答案,和到第(i)块为止,各个数出现的次数的前缀和
    对于每次查询,如果在一个块内,就直接暴力查询
    否则对于在两端非整块的元素,记录元素大小和出现次数,将这些元素带来的贡献计算一下即可

    有点卡常

    //#pragma GCC optimize("O3")
    //#pragma comment(linker, "/STACK:1024000000,1024000000")
    #include<bits/stdc++.h>
    using namespace std;
    function<void(void)> ____ = [](){ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);};
    const int MOD = 1e9+7;
    const int MAXN = 5e4+7;
    const int SQT = 240;
    int n,q,m,sqt,A[MAXN],pre[SQT][MAXN],pos[MAXN],belong[MAXN],l[SQT],r[SQT],la;
    int ans[SQT][SQT],num[MAXN];
    vector<int> vec,cnt,pw[MAXN];
    void divide(){
        sqt = pow(n,0.5);
        m = n / sqt + (n%sqt?1:0);
        for(int i = 1; i <= n; i++) belong[i] = (i-1) / sqt + 1;
        for(int i = 1; i <= m; i++) l[i] = (i-1) * sqt + 1, r[i] = i * sqt;
        r[m] = n;
    }
    void gao(){
        int L, R;
        scanf("%d %d",&L,&R);
        L = (L^la)%n+1; R = (R^la)%n+1;
        if(L>R) L ^= R ^= L ^= R;
        int lp = belong[L], rp = belong[R];
        if(lp==rp){
            int ret = 0;
            for(int i = L; i <= R; i++) num[pos[i]] = 0;
            for(int i = L; i <= R; i++){
                ret = ret - pw[pos[i]][num[pos[i]]];
                ret = ret + pw[pos[i]][++num[pos[i]]];
                if(ret<0) ret += MOD;
                if(ret>=MOD) ret -= MOD;
            }
            printf("%d
    ",la=ret);
        }
        else{
            vector<int> arr;
            for(int i = L; i <= r[lp]; i++){
                num[pos[i]] = 0;
                arr.push_back(pos[i]);
            }
            for(int i = l[rp]; i <= R; i++){
                num[pos[i]] = 0;
                arr.push_back(pos[i]);
            }
            sort(arr.begin(),arr.end()); arr.erase(unique(arr.begin(),arr.end()),arr.end());
            for(int i = L; i <= r[lp]; i++) num[pos[i]]++;
            for(int i = l[rp]; i <= R; i++) num[pos[i]]++;
            lp++, rp--;
            int ret = ans[lp][rp];
            for(int i = 0; i < (int)arr.size(); i++){
                ret = ret - pw[arr[i]][pre[rp][arr[i]]-pre[lp-1][arr[i]]];
                ret = ret + pw[arr[i]][pre[rp][arr[i]]-pre[lp-1][arr[i]]+num[arr[i]]];
                if(ret<0) ret += MOD;
                if(ret>=MOD) ret -= MOD;            
            }
            printf("%d
    ",la=ret);
        }
    }
    void solve(){
        scanf("%d %d",&n,&q);
        vec.clear();
        for(int i = 1; i <= n; i++){
            scanf("%d",&A[i]);
            vec.push_back(A[i]);
        }
        sort(vec.begin(),vec.end()); vec.erase(unique(vec.begin(),vec.end()),vec.end());
        for(int i = 1; i <= n; i++) pos[i] = lower_bound(vec.begin(),vec.end(),A[i]) - vec.begin();
        divide();
        for(int i = 1; i <= m; i++) for(int j = 0; j < (int)vec.size(); j++) pre[i][j] = 0;
        for(int i = 1; i <= n; i++) pre[belong[i]][pos[i]]++;
        for(int i = 1; i <= m; i++) for(int j = 0; j < (int)vec.size(); j++) pre[i][j] += pre[i-1][j];
        cnt.resize(vec.size());
        for(int i = 0; i < (int)vec.size(); i++) cnt[i] = 0;
        for(int i = 1; i <= n; i++) cnt[pos[i]]++;
        for(int i = 0; i < (int)vec.size(); i++){
            pw[i].resize(cnt[i]+1);
            pw[i][0] = 1; for(int j = 1; j <= cnt[i]; j++) pw[i][j] = 1ll * pw[i][j-1] * vec[i] % MOD;
            pw[i][0] = 0;
        }
        for(int i = 1; i <= m; i++){
            memset(num,0,sizeof(num));
            int p = l[i] - 1, ret = 0;
            for(int j = i; j <= m; j++){
                while(p<r[j]){
                    p++;
                    ret -= pw[pos[p]][num[pos[p]]];
                    ret += pw[pos[p]][++num[pos[p]]];
                    if(ret<0) ret += MOD;
                    if(ret>=MOD) ret -= MOD;
                }
                ans[i][j] = ret;
            }
        }
        la = 0;
        while(q--) gao();
        for(int i = 0; i < (int)vec.size(); i++) pw[i].clear();
    }
    int main(){
        int T;
        for(scanf("%d",&T); T; T--) solve();
        return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/kikokiko/p/12894815.html
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