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Project Euler #72: Counting fractions (C++)

Question
Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get:
1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
It can be seen that there are 21 elements in this set.
How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?

Answer : 303963552391

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Solution


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#include <cstdio>
#include <iostream>
#include <sstream>
#include <string>
#include <cmath>
#include <cassert>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <deque>
using namespace std;
typedef long long ll;
typedef pair<double, double> dd;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef vector<vii> vvii;


int euler(int x){
    int ans = x;

    for(int i=2;i*i<=x;i++){
        if(x%i == 0){
            while(x%i == 0) x/=i;
            ans = ans - ans/i;
        }
    }
    if(x > 1){
        ans = ans - ans/x;
    }
    return ans;

}

int main(){
    int N = 1e6 + 10;
    vector<ll> v(N, 0);
    v[0] = 2;
    ll ans = 1;
    for(int i=1;i<N;i++){
        ans += euler(i);
        v[i] = ans;
    }

    int t; cin >> t;
    while(t--){
        int d; cin >> d;
        cout << (v[d]-2) << endl;
    }
}
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