Bit Array C++


Problem Statement :


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. a .


Input Format

Four space separated integers on a single line,
N, S , P , and Q respectively.

Output Format

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

Constraints

   1 <=  N  <= 10^8
   0 <=  S, P, Q  <= 2^31


Solution :



title-img 


                            Solution in C :

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

unsigned long long mask[40000000];

unsigned insert(unsigned x) {
    unsigned res = (mask[x >> 6] & (1ULL << (x & 0x3F))) == 0;
    mask[x >> 6] |= 1ULL << (x & 0x3F);
    return res;
}

int main() {
    unsigned N, S, P, Q;
    cin >> N >> S >> P >> Q;
    unsigned x = S;
    unsigned ans = 0;
    ans += insert(x);
    for (unsigned i = 1; i < N; i++) {
        x = (1LL * x * P + Q) % 2147483648;
        ans += insert(x);
    }
    cout << ans << endl;
    return 0;
}








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