{"id":104,"date":"2024-12-12T09:43:40","date_gmt":"2024-12-12T09:43:40","guid":{"rendered":"https:\/\/www.infomega.ro\/a10a\/?page_id=104"},"modified":"2024-12-12T09:50:40","modified_gmt":"2024-12-12T09:50:40","slug":"m2-l3-info-numere-prime-variabila-logica","status":"publish","type":"page","link":"https:\/\/www.infomega.ro\/a10a\/info\/m2-info\/m2-l3-info-numere-prime-variabila-logica\/","title":{"rendered":"M2 L3 info Numere prime, variabil\u0103 logic\u0103"},"content":{"rendered":"\n<p>\u00cen limbajele de programare C\/C++ deoarece nu au fost prev\u0103zute de la \u00eenceput cu variabile logice de tipul \u201eadev\u0103rat\u201d sau \u201efals\u201d putem folosi \u00een acest scop o variabil\u0103 de tip \u00eentreg \u00een care dac\u0103 avem valoarea 0(zero) spunem c\u0103 are valoarea logic\u0103 \u201efals\u201d iar dac\u0103 avem orice valoare diferit\u0103 de 0(zero) spunem c\u0103 are valoarea logic\u0103 \u201eadev\u0103rat\u201d.<\/p>\n\n\n\n<p>Un num\u0103r prim este un num\u0103r \u00eentreg pozitiv care nu are divizori proprii. Programul de mai jos verific\u0103 dac\u0103 un num\u0103r \u00eentreg citit de la tastatur\u0103 este prim.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;iostream&gt;\n\nint main() {\n    using namespace std;\n\n    int nr;\n    cout &lt;&lt; \"Introduceti un numar intreg: \";\n    cin &gt;&gt; nr;\n\n    if (nr &lt; 2) {\n        cout &lt;&lt; nr &lt;&lt; \" numarul trebuie sa fie mai mare sau egal cu 2\" &lt;&lt; endl;\n    } else {\n        int ePrim = 1; \/\/ 1 pentru prim, 0 pentru neprim\n        int d = 2;\n        while (d &lt;= nr\/2) {\n            if (nr % d == 0) {\n                ePrim = 0; \/\/ Gasit un divizor, deci nu e prim\n                break;\n            }\n            ++d;\n        }\n\n        if (ePrim) {\n            cout &lt;&lt; nr &lt;&lt; \" este un numar prim.\" &lt;&lt; endl;\n        } else {\n            cout &lt;&lt; nr &lt;&lt; \" nu este un numar prim.\" &lt;&lt; endl;\n        }\n    }\n\n    return 0;\n}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Explica\u021bie:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Input<\/strong>: Programul solicit\u0103 utilizatorului s\u0103 introduc\u0103 un num\u0103r \u00eentreg.<\/li>\n\n\n\n<li><strong>Cazurile speciale<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Dac\u0103 num\u0103rul este mai mic dec\u00e2t 2, este direct declarat ca neprim (deoarece numerele prime sunt definite doar pentru valori mai mari sau egale cu 2).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Verificarea primalit\u0103\u021bii<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Folose\u0219te un <code>int<\/code> numit <code>ePrim<\/code>, ini\u021bializat cu valoarea 1 (consider\u0103m num\u0103rul prim la \u00eenceput).<\/li>\n\n\n\n<li>Bucla <code>while<\/code> verific\u0103 divizibilitatea num\u0103rului cu to\u021bi divizorii de la 2 p\u00e2n\u0103 la r\u0103d\u0103cina p\u0103trat\u0103 a num\u0103rului.<\/li>\n\n\n\n<li>Dac\u0103 este g\u0103sit un divizor, <code>ePrim<\/code> devine 0 \u0219i bucla se opre\u0219te.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Output<\/strong>: La final, \u00een func\u021bie de valoarea lui <code>ePrim<\/code>, se afi\u0219eaz\u0103 dac\u0103 num\u0103rul este prim sau nu.<\/li>\n<\/ol>\n\n\n\n<p>Hai s\u0103 analiz\u0103m codul linie cu linie:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1.<\/strong> <code>#include &lt;iostream&gt;<\/code><\/h3>\n\n\n\n<p>Aceast\u0103 linie include biblioteca standard C++ care permite intrarea \u0219i ie\u0219irea de date prin <code>cin<\/code> (pentru citire) \u0219i <code>cout<\/code> (pentru afi\u0219are).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2.<\/strong> <code>int main()<\/code><\/h3>\n\n\n\n<p>Punctul de intrare al programului. Toate instruc\u021biunile care urmeaz\u0103 vor fi executate de la aceast\u0103 func\u021bie.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>3.<\/strong> <code>using namespace std;<\/code><\/h3>\n\n\n\n<p>Aceast\u0103 linie permite utilizarea elementelor din namespace-ul <code>std<\/code> f\u0103r\u0103 a scrie explicit prefixul <code>std::<\/code>. De exemplu, putem scrie <code>cin<\/code> \u0219i <code>cout<\/code> \u00een loc de <code>std::cin<\/code> \u0219i <code>std::cout<\/code>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>4.<\/strong> <code>int nr;<\/code><\/h3>\n\n\n\n<p>Declar\u0103 o variabil\u0103 de tip \u00eentreg, numit\u0103 <code>nr<\/code>, care va stoca num\u0103rul introdus de utilizator.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>5.<\/strong> <code>cout &lt;&lt; \"Introduceti un numar intreg: \";<\/code><\/h3>\n\n\n\n<p>Afi\u0219eaz\u0103 mesajul pe ecran, cer\u00e2nd utilizatorului s\u0103 introduc\u0103 un num\u0103r \u00eentreg.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>6.<\/strong> <code>cin &gt;&gt; nr;<\/code><\/h3>\n\n\n\n<p>Cite\u0219te un num\u0103r \u00eentreg de la tastatur\u0103 \u0219i \u00eel stocheaz\u0103 \u00een variabila <code>nr<\/code>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>7.<\/strong> <code>if (nr &lt; 2) {<\/code><\/h3>\n\n\n\n<p>Aceast\u0103 condi\u021bie verific\u0103 dac\u0103 num\u0103rul introdus este mai mic dec\u00e2t 2. Numerele mai mici de 2 (cum ar fi 1, 0, sau numere negative) nu sunt prime, deci programul va afi\u0219a un mesaj corespunz\u0103tor.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>8.<\/strong> <code>cout &lt;&lt; nr &lt;&lt; \" numarul trebuie sa fie mai mare sau egal cu 2\" &lt;&lt; endl;<\/code><\/h3>\n\n\n\n<p>Dac\u0103 num\u0103rul este mai mic dec\u00e2t 2, acest mesaj este afi\u0219at, iar programul se termin\u0103 pentru acel caz.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>9.<\/strong> <code>} else {<\/code><\/h3>\n\n\n\n<p>Dac\u0103 num\u0103rul este mai mare sau egal cu 2, se trece la blocul <code>else<\/code>, unde programul verific\u0103 dac\u0103 num\u0103rul este prim.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>10.<\/strong> <code>int ePrim = 1;<\/code><\/h3>\n\n\n\n<p>Aceasta este o variabil\u0103 de tip \u00eentreg folosit\u0103 pentru a determina dac\u0103 num\u0103rul este prim:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Valoarea <code>1<\/code> \u00eenseamn\u0103 c\u0103 num\u0103rul este considerat prim p\u00e2n\u0103 la proba contrarie.<\/li>\n\n\n\n<li>Valoarea <code>0<\/code> indic\u0103 faptul c\u0103 num\u0103rul <strong>nu<\/strong> este prim (are divizori).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>11.<\/strong> <code>int d = 2;<\/code><\/h3>\n\n\n\n<p>Aceasta este o variabil\u0103 care reprezint\u0103 un poten\u021bial divizor al num\u0103rului. Ini\u021bial, \u00eencepe de la 2, cel mai mic divizor posibil al unui num\u0103r mai mare dec\u00e2t 1.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>12.<\/strong> <code>while (d &lt;= nr \/ 2) {<\/code><\/h3>\n\n\n\n<p>Bucla <code>while<\/code> verific\u0103 dac\u0103 exist\u0103 vreun divizor \u00eentre <code>2<\/code> \u0219i <code>nr \/ 2<\/code> (inclusiv). Numerele mai mari dec\u00e2t <code>nr \/ 2<\/code> nu trebuie verificate, deoarece, dac\u0103 exist\u0103 un divizor, acesta este mai mic sau egal cu jum\u0103tatea num\u0103rului.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>13.<\/strong> <code>if (nr % d == 0) {<\/code><\/h3>\n\n\n\n<p>Aceast\u0103 condi\u021bie verific\u0103 dac\u0103 <code>nr<\/code> este divizibil cu <code>d<\/code>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dac\u0103 restul \u00eemp\u0103r\u021birii (<code>nr % d<\/code>) este <code>0<\/code>, \u00eenseamn\u0103 c\u0103 <code>d<\/code> este un divizor al lui <code>nr<\/code>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>14.<\/strong> <code>ePrim = 0;<\/code><\/h3>\n\n\n\n<p>Dac\u0103 s-a g\u0103sit un divizor, se seteaz\u0103 variabila <code>ePrim<\/code> la <code>0<\/code>, indic\u00e2nd c\u0103 num\u0103rul nu este prim.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>15.<\/strong> <code>break;<\/code><\/h3>\n\n\n\n<p>Iese imediat din bucla <code>while<\/code>, deoarece num\u0103rul nu mai trebuie verificat \u00een continuare \u2013 \u0219tim deja c\u0103 nu este prim.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>16.<\/strong> <code>++d;<\/code><\/h3>\n\n\n\n<p>Incrementarea variabilei <code>d<\/code> pentru a verifica urm\u0103torul posibil divizor.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>17.<\/strong> <code>if (ePrim) {<\/code><\/h3>\n\n\n\n<p>Dup\u0103 ce bucla se termin\u0103, se verific\u0103 valoarea lui <code>ePrim<\/code>. Dac\u0103 este \u00eenc\u0103 <code>1<\/code>, \u00eenseamn\u0103 c\u0103 num\u0103rul nu a avut divizori \u0219i este prim.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>18.<\/strong> <code>cout &lt;&lt; nr &lt;&lt; \" este un numar prim.\" &lt;&lt; endl;<\/code><\/h3>\n\n\n\n<p>Dac\u0103 <code>ePrim<\/code> este <code>1<\/code>, afi\u0219eaz\u0103 c\u0103 num\u0103rul este prim.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>19.<\/strong> <code>} else {<\/code><\/h3>\n\n\n\n<p>Dac\u0103 <code>ePrim<\/code> este <code>0<\/code>, \u00eenseamn\u0103 c\u0103 num\u0103rul nu este prim.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>20.<\/strong> <code>cout &lt;&lt; nr &lt;&lt; \" nu este un numar prim.\" &lt;&lt; endl;<\/code><\/h3>\n\n\n\n<p>Afi\u0219eaz\u0103 c\u0103 num\u0103rul nu este prim.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>21.<\/strong> <code>return 0;<\/code><\/h3>\n\n\n\n<p>Finalul func\u021biei <code>main<\/code>. Programul returneaz\u0103 <code>0<\/code>, indic\u00e2nd c\u0103 s-a terminat cu succes.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Exemplu de rulare<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Intrare:<\/h4>\n\n\n\n<p><code>Introduce\u021bi un num\u0103r \u00eentreg: 7<\/code><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Ie\u0219ire:<\/h4>\n\n\n\n<p><code>7 este un num\u0103r prim.<\/code><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Intrare:<\/h4>\n\n\n\n<p><code>Introduce\u021bi un num\u0103r \u00eentreg: 4<\/code><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Ie\u0219ire:<\/h4>\n\n\n\n<p><code>4 nu este un num\u0103r prim.<\/code><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Tem\u0103<\/h2>\n\n\n\n<p>S\u0103 se modifice programul de mai sus astfel \u00eenc\u00e2t s\u0103 afi\u0219eze toate numerele prime mai mici dec\u00e2t un num\u0103r \u00eentreg n citit de la tastatur\u0103.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Rezolvarea temei: <\/h2>\n\n\n\n<p><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;iostream>\nusing namespace std;\n\nint main() {\n    int n;\n    cout &lt;&lt; \"Introduceti un numar intreg: \";\n    cin >> n;\n\n    if (n &lt; 2) {\n        cout &lt;&lt; \"Nu exista numere prime mai mici decat \" &lt;&lt; n &lt;&lt; \".\" &lt;&lt; endl;\n    } else {\n        int numar = 2; \/\/ \u00cencepem de la primul num\u0103r prim\n        while (numar &lt;= n) {\n            int ePrim = 1; \/\/ Presupunem c\u0103 num\u0103rul este prim\n            int d = 2; \/\/ Divizorul \u00eencepe de la 2\n\n            \/\/ Verific\u0103m dac\u0103 num\u0103rul este prim\n            while (d &lt;= numar \/ 2) {\n                if (numar % d == 0) {\n                    ePrim = 0; \/\/ Dac\u0103 exist\u0103 un divizor, nu este prim\n                    break;\n                }\n                ++d;\n            }\n\n            \/\/ Dac\u0103 num\u0103rul este prim, \u00eel afi\u0219\u0103m\n            if (ePrim) {\n                cout &lt;&lt; numar &lt;&lt; \" \";\n            }\n\n            ++numar; \/\/ Trecem la urm\u0103torul num\u0103r\n        }\n        cout &lt;&lt; endl; \/\/ Linie nou\u0103 la final\n    }\n\n    return 0;\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u00cen limbajele de programare C\/C++ deoarece nu au fost prev\u0103zute de la \u00eenceput cu variabile logice de tipul \u201eadev\u0103rat\u201d sau \u201efals\u201d putem folosi \u00een acest scop o variabil\u0103 de tip \u00eentreg \u00een care dac\u0103 avem valoarea 0(zero) spunem c\u0103 are valoarea logic\u0103 \u201efals\u201d iar dac\u0103 avem orice valoare diferit\u0103 de 0(zero) spunem c\u0103 are valoarea [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":37,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_FSMCFIC_featured_image_caption":"","_FSMCFIC_featured_image_nocaption":"","_FSMCFIC_featured_image_hide":"","footnotes":""},"class_list":["post-104","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - 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