{"id":9975,"date":"2023-10-20T11:20:30","date_gmt":"2023-10-20T11:20:30","guid":{"rendered":"https:\/\/adelnasim.com\/docs\/courses\/cpp-tutorial\/function-part-6-recursion-1\/"},"modified":"2024-04-07T01:19:30","modified_gmt":"2024-04-07T01:19:30","slug":"function-part-6-recursion-part-1","status":"publish","type":"docs","link":"https:\/\/adelnasim.com\/ar\/docs\/courses\/cpp-tutorial\/function-part-6-recursion-part-1\/","title":{"rendered":"\u0627\u0644\u062f\u0651\u0627\u0644\u0651\u0629 (6) - Recursion 1"},"content":{"rendered":"

Recursion \u0647\u064a \u062a\u0642\u0646\u064a\u0629 \u0628\u0631\u0645\u062c\u0629 \u062d\u064a\u062b \u062a\u0633\u062a\u062f\u0639\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0646\u0641\u0633\u0647\u0627 \u0628\u0634\u0643\u0644 \u0645\u0628\u0627\u0634\u0631 \u0623\u0648 \u063a\u064a\u0631 \u0645\u0628\u0627\u0634\u0631. \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0627 \u0644\u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u062a\u0642\u0633\u064a\u0645\u0647\u0627 \u0625\u0644\u0649 \u0645\u0634\u0643\u0644\u0627\u062a \u0623\u0635\u063a\u0631 \u0648\u0623\u0628\u0633\u0637 \u0645\u0646 \u0646\u0641\u0633 \u0627\u0644\u0646\u0648\u0639.<\/p>\n

\u0642\u062f \u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0635\u0639\u0628 \u0641\u0647\u0645 \u0627\u0644\u0640 Recursion \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629\u060c \u0648\u0644\u0643\u0646\u0647\u0627 \u0623\u062f\u0627\u0629 \u0642\u0648\u064a\u0629 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u062d\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0648\u0627\u0633\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a.<\/p>\n

\u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0645\u062b\u0627\u0644 \u0644\u062f\u0627\u0644\u0651\u0629 Recursion \u0628\u0633\u064a\u0637\u0629 \u0641\u064a \u0644\u063a\u0629 C++:<\/p>\n

#include <iostream>\r\nusing namespace std;\r\nvoid f(int n)\r\n{\r\n    if (n < 1)\r\n        return;\r\n    else\r\n        cout << \"round:\" << n << endl;\r\n    f(n - 1);\r\n}\r\n\r\nint main()\r\n{\r\n    f(5);\r\n    return 0;\r\n}\r\n<\/pre>\n
\u0627\u0644\u062f\u0627\u0644\u0629 f(int n)<\/code> \u0647\u064a \u062f\u0627\u0644\u0629 recursive \u062a\u0642\u0648\u0645 \u0628\u0637\u0628\u0627\u0639\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \"round:\" \u0645\u062a\u0628\u0648\u0639\u0629 \u0628\u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0635\u062d\u064a\u062d n<\/code> \u0625\u0644\u0649 \u0634\u0627\u0634\u0629 \u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a n<\/code> \u0645\u0646 \u0627\u0644\u0645\u0631\u0627\u062a.<\/p>\n
\u062a\u0639\u0645\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0633\u062a\u062f\u0639\u0627\u0621 \u0646\u0641\u0633\u0647\u0627 \u0628\u0634\u0643\u0644 \u0645\u062a\u0643\u0631\u0631 \u0644\u0637\u0628\u0627\u0639\u0629 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \"round:\" \u0645\u062a\u0628\u0648\u0639\u0629 \u0628\u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0635\u062d\u064a\u062d n - 1<\/code> \u0625\u0644\u0649 \u0634\u0627\u0634\u0629 \u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a. \u062a\u0633\u062a\u0645\u0631 \u0647\u0630\u0647 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u062d\u062a\u0649 \u062a\u0635\u0628\u062d \u0642\u064a\u0645\u0629 n<\/code> \u0645\u0633\u0627\u0648\u064a\u0629 \u0644\u0644\u0639\u062f\u062f 1\u060c \u0648\u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u062a\u0631\u062c\u0639 \u0627\u0644\u062f\u0627\u0644\u0629.<\/p>\n
\u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a:<\/p>\n
round: 5\r\nround: 4\r\nround: 3\r\nround: 2\r\nround: 1<\/pre>\n
\u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0635\u0639\u0628 \u0642\u0644\u064a\u0644\u064b\u0627 \u0641\u0647\u0645 \u062f\u0648\u0627\u0644 \u0627\u0644\u0640 Recursive \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629\u060c \u0648\u0644\u0643\u0646\u0647\u0627 \u0623\u062f\u0627\u0629 \u0642\u0648\u064a\u0629 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u062d\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0648\u0627\u0633\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a.<\/p>\n
\u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u0627\u0644\u0627\u0646\u062a\u0628\u0627\u0647 \u0625\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u062b\u0644\u0627\u062b\u0629 \u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0640 recursive (\u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629\u060c \u0648\u0627\u0644\u0645\u0646\u0637\u0642\u060c \u0648\u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0641\u0631\u0639\u064a\u0629)\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u0645 \u0648\u0636\u0639 \u0639\u0644\u0627\u0645\u0629 \u0639\u0644\u064a\u0647\u0627 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n
void f(int n)\r\n{\r\n    if (n < 1)\r\n        return; \/\/base case\r\n    else\r\n        cout << \"round:\" << n << endl; \/\/logic\r\n    f(n - 1); \/\/subproblem\r\n}<\/pre>\n
\u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u062b\u0644\u0627\u062b\u0629 \u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0640recursive \u0647\u064a:<\/p>\n
    \n
  • \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629:<\/strong>\u00a0\u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0647\u064a \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629 \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639\u0647\u0627 \u0645\u0628\u0627\u0634\u0631\u0629 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u062f\u0648\u0646 \u0625\u062c\u0631\u0627\u0621 \u0623\u064a \u0627\u0633\u062a\u062f\u0639\u0627\u0621\u0627\u062a \u0645\u062a\u0643\u0631\u0631\u0629. \u0639\u0627\u062f\u0629\u064b \u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u062d\u0627\u0644\u0629 \u0628\u0633\u064a\u0637\u0629 \u064a\u0645\u0643\u0646 \u062d\u0644\u0647\u0627 \u0645\u0628\u0627\u0634\u0631\u0629\u064b.<\/li>\n
  • \u0627\u0644\u0645\u0646\u0637\u0642:<\/strong>\u00a0\u0645\u0646\u0637\u0642 \u062f\u0627\u0644\u0629 \u0627\u0644\u0640 recursive \u0647\u0648 \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0630\u064a \u064a\u062a\u0645 \u062a\u0646\u0641\u064a\u0630\u0647 \u0644\u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0625\u0644\u0649 \u0645\u0634\u0627\u0643\u0644 \u0623\u0635\u063a\u0631 \u0648\u0623\u0628\u0633\u0637 \u0645\u0646 \u0646\u0641\u0633 \u0627\u0644\u0646\u0648\u0639. \u064a\u062a\u0636\u0645\u0646 \u0627\u0644\u0645\u0646\u0637\u0642 \u0639\u0627\u062f\u0629\u064b \u0625\u062c\u0631\u0627\u0621 \u0627\u0633\u062a\u062f\u0639\u0627\u0621\u0627\u062a \u0645\u062a\u0643\u0631\u0631\u0629 \u0644\u0644\u062f\u0627\u0644\u0629 \u0630\u0627\u062a \u0642\u064a\u0645 \u0625\u062f\u062e\u0627\u0644 \u0623\u0635\u063a\u0631.<\/li>\n
  • \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0641\u0631\u0639\u064a\u0629:<\/strong>\u00a0\u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0641\u0631\u0639\u064a\u0629 \u0647\u064a \u0645\u0634\u0643\u0644\u0629 \u0623\u0635\u063a\u0631 \u0648\u0623\u0628\u0633\u0637 \u0645\u0646 \u0646\u0641\u0633 \u0646\u0648\u0639 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629. \u062a\u0639\u0645\u0644 \u062f\u0648\u0627\u0644 \u0627\u0644\u0640 recursive \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u0625\u0644\u0649 \u0645\u0634\u0643\u0644\u0627\u062a \u0641\u0631\u0639\u064a\u0629 \u062b\u0645 \u062d\u0644 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0627\u0644\u0641\u0631\u0639\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0641\u0633 \u062f\u0627\u0644\u0629 \u0627\u0644\u0640 recursive.<\/li>\n<\/ul>\n
    \u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u062f\u0627\u0644\u0629 recursive \u0641\u064a \u0644\u063a\u0629 C++\u200e \u062a\u062d\u0633\u0628 \u0645\u0636\u0631\u0648\u0628 \u0627\u0644\u0631\u0642\u0645:<\/p>\n
    #include <iostream>\r\nusing namespace std;\r\nint fact(int n)\r\n{\r\n    if (n == 0 || n == 1)\r\n        return 1;\r\n    else\r\n        return n*fact(n - 1);\r\n}\r\n\r\nint main()\r\n{\r\n    cout << fact(5) << endl;\r\n    return 0;\r\n}<\/pre>\n
    \n
    \n
    \n
    \u0627\u0644\u062f\u0627\u0644\u0629 fact(int n)<\/code> \u0647\u064a \u062f\u0627\u0644\u0629 recursive \u062a\u062d\u0633\u0628 \u0645\u0636\u0631\u0648\u0628 \u0627\u0644\u0639\u062f\u062f. \u0645\u0636\u0631\u0648\u0628 \u0627\u0644\u0639\u062f\u062f \u0647\u0648 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0627\u0644\u0645\u0648\u062c\u0628\u0629 \u0627\u0644\u0623\u0635\u063a\u0631 \u0645\u0646 \u0623\u0648 \u062a\u0633\u0627\u0648\u064a \u0647\u0630\u0627 \u0627\u0644\u0639\u062f\u062f. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0645\u0636\u0631\u0648\u0628 5 \u0647\u0648 120\u060c \u0644\u0623\u0646 120 \u0647\u0648 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 1\u060c 2\u060c 3\u060c 4\u060c \u06485. \u0644\u0630\u0644\u0643\u060c \u0633\u064a\u0643\u0648\u0646 \u0646\u0627\u062a\u062c \u0628\u0631\u0646\u0627\u0645\u062c\u0646\u0627 120.<\/p>\n
    \u0627\u0644\u062f\u0627\u0644\u0629 fact(int n)<\/code> \u062a\u0639\u0645\u0644 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0633\u062a\u062f\u0639\u0627\u0621 \u0646\u0641\u0633\u0647\u0627 \u0628\u0634\u0643\u0644 \u0645\u062a\u0643\u0631\u0631 \u0644\u062d\u0633\u0627\u0628 \u0645\u0636\u0631\u0648\u0628 \u0627\u0644\u0631\u0642\u0645 \u0648\u0627\u062d\u062f \u0623\u0642\u0644 \u0645\u0646 \u0631\u0642\u0645 \u0627\u0644\u0625\u062f\u062e\u0627\u0644. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0644\u062d\u0633\u0627\u0628 \u0645\u0636\u0631\u0648\u0628 5\u060c \u0633\u062a\u0633\u062a\u062f\u0639\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0646\u0641\u0633\u0647\u0627 \u0623\u0648\u0644\u0627\u064b \u0644\u062d\u0633\u0627\u0628 \u0645\u0636\u0631\u0648\u0628 4. \u0648\u0645\u0646 \u062b\u0645 \u0633\u062a\u0633\u062a\u062f\u0639\u064a \u0646\u0641\u0633\u0647\u0627 \u0644\u062d\u0633\u0627\u0628 \u0645\u0636\u0631\u0648\u0628 3\u060c \u0648\u0647\u0643\u0630\u0627. \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0629\u060c \u0633\u062a\u0635\u0644 \u0627\u0644\u062f\u0627\u0644\u0629 \u0625\u0644\u0649 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629\u060c \u062d\u064a\u062b \u064a\u0643\u0648\u0646 \u0631\u0642\u0645 \u0627\u0644\u0625\u062f\u062e\u0627\u0644 \u0647\u0648 0 \u0623\u0648 1. \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0647\u064a \u062d\u0627\u0644\u0629 \u062e\u0627\u0635\u0629 \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639\u0647\u0627 \u0645\u0628\u0627\u0634\u0631\u0629 \u0641\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u062f\u0648\u0646 \u0625\u062c\u0631\u0627\u0621 \u0623\u064a \u0627\u0633\u062a\u062f\u0639\u0627\u0621\u0627\u062a \u0645\u062a\u0643\u0631\u0631\u0629. \u0645\u0636\u0631\u0648\u0628 0 \u0647\u0648 1 \u0648\u0645\u0636\u0631\u0648\u0628 1 \u0647\u0648 \u0623\u064a\u0636\u064b\u0627 1\u060c \u0644\u0630\u0627 \u062a\u0642\u0648\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0628\u0633\u0627\u0637\u0629 \u0628\u0625\u0631\u062c\u0627\u0639 1 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a.<\/p>\n
    \u0633\u0644\u0633\u0644\u0629 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a<\/h2>\n
    \n
    \n
    \n
    \n
    \n
    \n
    \n
    \u0645\u062a\u0633\u0644\u0633\u0629 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0647\u064a \u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0628\u062d\u064a\u062b \u064a\u0645\u062b\u0644 \u0643\u0644 \u0639\u062f\u062f \u0641\u064a \u0627\u0644\u0633\u0644\u0633\u0629 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0639\u062f\u062f\u064a\u0646 \u0627\u0644\u0633\u0627\u0628\u0642\u064a\u0646 \u0644\u0647 \u0641\u064a \u0627\u0644\u0633\u0644\u0633\u0644\u0629. \u0623\u0648\u0644 \u0639\u062f\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0633\u0644\u0633\u0629 \u0647\u0645\u0627 0 \u0648 1\u060c \u0648\u0643\u0644 \u0639\u062f\u062f \u0644\u0627\u062d\u0642 \u0647\u0648 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0639\u062f\u062f\u064a\u0646 \u0627\u0644\u0633\u0627\u0628\u0642\u064a\u0646.<\/p>\n
    \u0625\u0644\u064a\u0643 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u062d\u062a\u0649 \u0623\u0648\u0644 10 \u0623\u0631\u0642\u0627\u0645:<\/p>\n
    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...<\/pre>\n
    \u064a\u0645\u0643\u0646 \u0625\u0646\u0634\u0627\u0621 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0643\u0631\u0627\u0631 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n
    F(n) = F(n - 1) + F(n - 2)<\/pre>\n
    \u0628\u064a\u0646\u0645\u0627 F(n)<\/code> \u0647\u0648 \u0627\u0644\u0631\u0642\u0645 n \u0641\u064a \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a.<\/p>\n
    \u064a\u062d\u062a\u0648\u064a \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0639\u0644\u0649 \u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0645\u062b\u064a\u0631\u0629 \u0644\u0644\u0627\u0647\u062a\u0645\u0627\u0645. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0646\u0633\u0628\u0629 \u0623\u0631\u0642\u0627\u0645 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0627\u0644\u0645\u062a\u0639\u0627\u0642\u0628\u0629 \u062a\u0642\u062a\u0631\u0628 \u0645\u0646 \u0627\u0644\u0646\u0633\u0628\u0629 \u0627\u0644\u0630\u0647\u0628\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0635\u0628\u062d \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0623\u0643\u0628\u0631. \u0627\u0644\u0646\u0633\u0628\u0629 \u0627\u0644\u0630\u0647\u0628\u064a\u0629 \u0647\u064a \u0631\u0642\u0645 \u063a\u064a\u0631 \u0645\u0646\u0637\u0642\u064a \u064a\u0633\u0627\u0648\u064a \u062a\u0642\u0631\u064a\u0628\u064b\u0627 1.618.<\/p>\n
    \u064a\u0638\u0647\u0631 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647 \u0644\u0646\u0645\u0630\u062c\u0629 \u0646\u0645\u0648 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0623\u0631\u0627\u0646\u0628\u060c \u0627\u0644\u0646\u0645\u0637 \u0627\u0644\u062d\u0644\u0632\u0648\u0646\u064a \u0644\u0644\u0635\u062f\u0641\u0629\u060c \u0648\u0627\u0644\u0646\u0645\u0637 \u0627\u0644\u0645\u062a\u0641\u0631\u0639 \u0644\u0644\u0634\u062c\u0631\u0629.<\/p>\n
    \u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0641\u064a \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u062d\u0642\u064a\u0642\u064a:<\/p>\n
      \n
    • \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u0645\u0627\u0644\u064a\u0629:<\/strong>\u00a0\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0644\u062a\u062d\u062f\u064a\u062f \u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0627\u0644\u062f\u0639\u0645 \u0648\u0627\u0644\u0645\u0642\u0627\u0648\u0645\u0629 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629 \u0644\u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0623\u0633\u0647\u0645.<\/li>\n
    • \u0627\u0644\u0645\u0648\u0633\u064a\u0642\u0649:<\/strong>\u00a0\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0644\u0625\u0646\u0634\u0627\u0621 \u0645\u0642\u0637\u0648\u0639\u0627\u062a \u0645\u0648\u0633\u064a\u0642\u064a\u0629 \u0630\u0627\u062a \u0625\u064a\u0642\u0627\u0639 \u0648\u0628\u0646\u064a\u0629 \u0645\u0645\u062a\u0639\u0629.<\/li>\n
    • \u0627\u0644\u0641\u0646:<\/strong>\u00a0\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0644\u0625\u0646\u0634\u0627\u0621 \u0623\u0639\u0645\u0627\u0644 \u0641\u0646\u064a\u0629 \u0630\u0627\u062a \u062a\u0631\u0643\u064a\u0628\u0629 \u0645\u062a\u0648\u0627\u0632\u0646\u0629 \u0648\u0645\u062a\u0646\u0627\u063a\u0645\u0629.<\/li>\n
    • \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0645\u0639\u0645\u0627\u0631\u064a\u0629:<\/strong>\u00a0\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0644\u062a\u0635\u0645\u064a\u0645 \u0627\u0644\u0645\u0628\u0627\u0646\u064a \u0648\u0627\u0644\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0623\u062e\u0631\u0649 \u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u0645\u0628\u0647\u062c\u0629 \u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u062c\u0645\u0627\u0644\u064a\u0629 \u0648\u0633\u0644\u064a\u0645\u0629 \u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0647\u064a\u0643\u0644\u064a\u0629.<\/li>\n<\/ul>\n
      \u062a\u0633\u0644\u0633\u0644 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0647\u0648 \u062a\u0633\u0644\u0633\u0644 \u0631\u064a\u0627\u0636\u064a \u0631\u0627\u0626\u0639 \u0648\u0645\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0627\u062a \u0648\u0644\u0647 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u062d\u0642\u064a\u0642\u064a.<\/p>\n
      \u0645\u062b\u0627\u0644:<\/strong><\/p>\n
      #include <iostream>\r\nusing namespace std;\r\nint fib(int n)\r\n{\r\n    if (n == 0 || n == 1)\r\n        return n;\r\n    else\r\n        return fib(n - 1) + fib(n - 2);\r\n}\r\n\r\nint main()\r\n{\r\n    cout << fib(3) << endl;\r\n    return 0;\r\n}\r\n<\/pre>\n
      \u0627\u0644\u062f\u0627\u0644\u0629 fib(int n)<\/code> \u064a\u0639\u0645\u0644 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0633\u062a\u062f\u0639\u0627\u0621 \u0646\u0641\u0633\u0647 \u0628\u0634\u0643\u0644 \u0645\u062a\u0643\u0631\u0631 \u0644\u062d\u0633\u0627\u0628 \u0623\u0631\u0642\u0627\u0645 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0644\u0644\u0631\u0642\u0645\u064a\u0646 \u0627\u0644\u0633\u0627\u0628\u0642\u064a\u0646. \u0625\u0630\u0627 \u0643\u0627\u0646 \u0631\u0642\u0645 \u0627\u0644\u0625\u062f\u062e\u0627\u0644 n<\/code> 0 \u0623\u0648 1\u060c \u0641\u0625\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u062a\u0642\u0648\u0645 \u0628\u0628\u0633\u0627\u0637\u0629 \u0628\u0625\u0631\u062c\u0627\u0639 \u0627\u0644\u0631\u0642\u0645\u060c \u0644\u0623\u0646 \u0623\u0648\u0644 \u0631\u0642\u0645\u064a\u0646 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0647\u0645\u0627 0 \u06481. \u0648\u0628\u062e\u0644\u0627\u0641 \u0630\u0644\u0643\u060c \u062a\u0642\u0648\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0625\u0631\u062c\u0627\u0639 \u0645\u062c\u0645\u0648\u0639 \u0623\u0631\u0642\u0627\u0645 \u0641\u064a\u0628\u0648\u0646\u0627\u062a\u0634\u064a \u0644\u0644\u0631\u0642\u0645\u064a\u0646 \u0627\u0644\u0633\u0627\u0628\u0642\u064a\u0646.<\/p>\n
      \u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a:<\/p>\n
      2<\/pre>\n
       <\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"
      Recursion is a programming technique where a function calls itself directly or indirectly. This can be used to solve problems that can be broken down into smaller, simpler problems of the same type. Recursion can be a bit difficult to understand at first, but it is a powerful tool that can be used to solve […]<\/p>","protected":false},"author":3,"featured_media":0,"parent":2744,"menu_order":23,"comment_status":"closed","ping_status":"closed","template":"","doc_tag":[],"class_list":["post-9975","docs","type-docs","status-publish","hentry","no-post-thumbnail"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/docs\/9975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/docs"}],"about":[{"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/types\/docs"}],"author":[{"embeddable":true,"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/comments?post=9975"}],"version-history":[{"count":6,"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/docs\/9975\/revisions"}],"predecessor-version":[{"id":9982,"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/docs\/9975\/revisions\/9982"}],"up":[{"embeddable":true,"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/docs\/2744"}],"wp:attachment":[{"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/media?parent=9975"}],"wp:term":[{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/adelnasim.com\/ar\/wp-json\/wp\/v2\/doc_tag?post=9975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}