50 lines
1.2 KiB
C++
50 lines
1.2 KiB
C++
/*
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Counting Fractions
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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.
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If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get:
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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
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It can be seen that there are 21 elements in this set.
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How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?
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*/
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#include <bits/stdc++.h>
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using namespace std;
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const int MAX = 1000000;
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int main(){
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cout << "Hello this is Patrick" << endl;
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auto start = chrono::high_resolution_clock::now();
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vector<int> phi(MAX + 1);
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for(int i = 2; i <= MAX; ++i){
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phi[i] = i;
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}
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long long sum = 0;
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for(int i = 2; i <= MAX; ++i){
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if(phi[i] == i){
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for(int j = i; j <= MAX; j += i){
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phi[j] = phi[j] / i * (i - 1);
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}
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}
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sum += phi[i];
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}
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cout << sum << endl;
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auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
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cout << (float)duration.count()/1000 << endl;
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return 0;
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}
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