C++ Program to find out the distinct elements in a given sequence

Suppose we are given three integer numbers n, x, y, and z. We have to make a sequence from the given integers where the first item of the sequence is (x modulo 2³¹). Other than the first element, other elements in the sequence a_i = (a_(i-1) * y + z) modulo 2³¹ , where 1 ≤ i ≤ n - 1. We have to find out the number of distinct integers in the sequence we made.

So, if the input is like n = 5, x = 1, y = 2, z = 1, then the output will be 5.

The unique values are {1, 3, 7, 15, 31}. So, the answer is 5.

To solve this, we will follow these steps −

MOD := 2^31
Define an array temp
resize the array temp to the value of MOD
p := x mod MOD
temp[p] := true
ans := 1
for initialize i := 1, when i < n, update (increase i by 1), do −
- p := ((p * y) + z) mod MOD
- if temp[p] is true, then −
  - Come out from the loop
- increase ans by 1
- temp[p] := true
return ans

Example

Let us see the following implementation to get better understanding −

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

const long long MOD = 2147483648;

int solve(int n, long long x, long long y, long long z) {
   vector<bool> temp;
   temp.resize(MOD);
   long long p = x % MOD;
      temp[p] = true;
      int ans = 1;
      for (int i = 1; i < n; ++i) {
         p = ((p * y) + z) % MOD;
         if (temp[p])
            break;
         ++ans;
         temp[p] = true;
   }
   return ans;
}

int main() {
cout<< solve(5, 1, 2, 1) <<endl;
return 0;
}