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March 14, 2026 10:40
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teorema-fundamentala-arit.cpp
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| /*Teorema fundamentala a aritmeticii | |
| orice numar poate sa fie descompus in produs de factori primi | |
| 10 = 2^1 * 5^1 | |
| 11 = 11^1 | |
| 12 = 2^2 * 3 | |
| 1 = 2^0 * 3^0 * 5^0 = | |
| 14 = 2 * 7 | |
| 10 = 2 * 5 | |
| */ | |
| #include <iostream> | |
| #include <vector> | |
| using namespace std; | |
| vector<pair<int,int>> decompuneInFactoriPrimi( int n ) { | |
| vector<pair<int, int>> factori; | |
| int divisor = 2; | |
| //n = 100 | |
| while( n > 1 ) { | |
| int count = 0; | |
| while(n % divisor == 0) {//5%5 = 1 rest 0 | |
| n /= divisor; //n = 1 | |
| count++;//2 | |
| } | |
| if(count > 0) {//2>0 | |
| factori.push_back({divisor, count});//in vectorul factori facem push la perechea {5,2} | |
| } | |
| divisor++;//divisor 5 | |
| //optimizare: verificam doar pana la radical din n | |
| if(divisor * divisor > n) { | |
| if(n > 1) { | |
| factori.push_back({n,1}); | |
| } | |
| break; | |
| } | |
| } | |
| return factori; //({2,2},{5,2}) | |
| } | |
| int main() { | |
| int n; | |
| cout<<"Numar="; | |
| cin>>n; | |
| if(n <= 1) { | |
| cout<<"Numarul trebuie sa fie mai mare decat 1!"; | |
| return 0; | |
| } | |
| auto factori = decompuneInFactoriPrimi(n); | |
| //n = 100 | |
| //factori = descompuneInFactoriPrimi(100) | |
| //100 = 2^2 * 5^2 | |
| //output: ({2,2},{5,2}) | |
| cout<<"Descompunerea in factori primi este: "; | |
| for(int i = 0; i < factori.size(); i++) { | |
| cout<<factori[i].first <<"^"<<factori[i].second; //{2-first,3-second}{8-first,9-second} | |
| if(i < factori.size() - 1) { | |
| cout<<" * "; | |
| } | |
| } | |
| cout<<endl; | |
| } |
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