codingcircle » Bit Array

You are given four integers: N, S, P, Q. You will use them in order to create the sequence a with the following pseudo-code.

a[0] = S (modulo 2^31)
for i = 1 to N-1
    a[i] = a[i-1]*P+Q (modulo 2^31)

Your task is to calculate the number of distinct integers in the sequence .

Input Format

Four space separated integers on a single line, , , , and respectively.

Output Format

A single integer that denotes the number of distinct integers in the sequence .

Constraints

1 ≤ N ≤ 10⁸

0 ≤ S,P,Q < 2³¹

Sample Input

3 1 1 1

Sample Output

Explanation

a = [1,2,3]

Hence, there are 3 different integers in the sequence.

Solution Implementation


#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <bitset>
using namespace std;



int main() {
    unsigned long long n,s,p,q,r=0,ans=0,returned,v;
    n=100000000; s=1232077670; p=126810854; q=1536183938; //26
    // n=100000000; s=569099406; p=1607140150; q=823906344; //31
    cin>>n>>s>>p>>q;
    unsigned long long i, a0=s, a=s, ap=0, k=0, kt=0;

    v=pow(2,31);
    // v-=1;
    // cout<<bitset<64>(v)<<endl;
    // v=~v;
    // cout<<bitset<64>(v)<<endl;
    for(i=0; i<n; i++){
        // a=(a*p+q)&v;
        a=(a*p+q);
        a=a%v;
        // cout<<bitset<64>(a)<<" 1 "<<endl;
        // a&=v;
        // cout<<bitset<64>(a)<<endl;
        if((a==a0 || a==ap) && i!=0){
            k=i+1;
            break;
        }
        ap=a;
    }
    if (i==n) k=i;


    cout <<k<<endl;

    return 0;
}

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