UVALive

Jupiter Atacks!

/**
    题意:B,P,L,N,分别表示进制,mod,数组的个数,操作数
    做法:树状数组  欧几里得  每个数加入到数组Tree的数是 B^(L-i)
    用树状数组进行维护前缀和,然后求一段区间的数,除以B^(L-j)
    因为(前缀和/B^(L-j)) 很大不好计算,所以就用乘法逆元 
       (k是a关于p的乘法的逆元) a*k≡1 (mod p) === (a/b)mod p (b关于p的乘法的逆元)
    PS(当我们要求(a/b) mod p的值,且a很大,无法直接求得a/b的值时,我们就要用到乘法逆元。
        我们可以通过求b关于p的乘法逆元k,将a乘上k再模p,即(a*k) mod p。其结果与(a/b) mod p等价。)
**/
#include <iostream>
#include <algorithm>
#include <string.h>
#include <cmath>
#include <stdio.h>
#define maxn 200000 + 10
using namespace std;
long long Tree[maxn];
long long mmap[maxn];   ///逆元
long long _next[maxn];  /// 次方
long long extend_gcd(long long a,long long b,long long &x,long long &y)
{
    if(a == 0 && b == 0) return -1;
    if(b == 0)
    {
        x = 1;
        y = 0;
        return a;
    }
    long long d = extend_gcd(b,a%b,y,x);
    y -= a/b*x;
    return d;
}
long long mod_reverse(long long a,long long n)
{
    long long x,y;
    long long d = extend_gcd(a,n,x,y);
    if(d == 1) return (x%n+n)%n;
    else return -1;
}
long long B,P,L,N;
int lowbit(int x)
{
    return x&(-x);
}
void add(int x, long long value)
{
    for(int i = x; i <= L; i += lowbit(i))
    {
        Tree[i] = ((Tree[i] + value) % P + P) % P;
    }
}
long long getsum(int x)
{
    long long sum =0;
    for(int i=x; i; i -= lowbit(i))
        sum = ((sum + Tree[i])%P + P)%P;
    return sum;
}
int main()
{
    //freopen("in.txt","r",stdin);
    while(~scanf("%lld %lld %lld %lld",&B,&P,&L,&N))
    {
        if(B == 0 && P == 0 && L == 0 &&N == 0) break;
        memset(Tree,0,sizeof(Tree));
        memset(mmap,0,sizeof(mmap));
        memset(_next,0,sizeof(_next));
        int tmp = 1;
        mmap[L] = 1;
        _next[L] = 1;
        for(int i=L-1; i>=1; i--)
        {
            tmp = (tmp *B) %P;
            mmap[i] = mod_reverse(tmp,P);
            _next[i] = tmp;
        }

        int u,v;
        char ch[10];
        for(int i=1; i<=N; i++)
        {
            scanf("%s %d %d",ch,&u,&v);
            //cout<<ch<<" "<<u<<" "<<v<<endl;
            if(ch[0] == 'E')
            {
                long long ans = (getsum(u) - getsum(u-1));
                ans -= v*_next[u];
                add(u,-ans);
            }
            else if(ch[0] == 'H')
            {
                long long ans = ((getsum(v) - getsum(u-1))%P +P)%P;
                //cout<<"ans = "<<ans<<endl;
                ans = (ans *mmap[v])%P;
                printf("%lld
",ans);
            }
        }
        printf("-
");
    }
    return 0;
}
View Code
原文地址:https://www.cnblogs.com/chenyang920/p/4739007.html