{"id":490,"date":"2025-07-24T12:58:59","date_gmt":"2025-07-24T03:58:59","guid":{"rendered":"https:\/\/www.shin-ichi.org\/?p=490"},"modified":"2025-07-30T11:30:05","modified_gmt":"2025-07-30T02:30:05","slug":"%e3%83%95%e3%82%a3%e3%83%9c%e3%83%8a%e3%83%83%e3%83%81%e6%95%b0%e5%88%97%e3%81%ae%e5%87%ba%e5%8a%9b%e3%83%97%e3%83%ad%e3%82%b0%e3%83%a9%e3%83%a0%e3%81%ab%e9%96%a2%e3%81%99%e3%82%8b%e3%83%ac%e3%83%9d","status":"publish","type":"post","link":"https:\/\/www.shin-ichi.org\/?p=490","title":{"rendered":"\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306e\u51fa\u529b\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u95a2\u3059\u308b\u30ec\u30dd\u30fc\u30c8"},"content":{"rendered":"\n

1. \u554f\u984c\u306e\u6982\u8981<\/h2>\n\n\n\n

\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306f\u3001\u30a4\u30bf\u30ea\u30a2\u306e\u6570\u5b66\u8005\u30ec\u30aa\u30ca\u30eb\u30c9\u30fb\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u306b\u3088\u3063\u30661202\u5e74\u306b\u300e\u7b97\u76e4\u306e\u66f8\u300f\u3067\u7d39\u4ecb\u3055\u308c\u305f\u6570\u5217\u3067\u3042\u308b1<\/a>2<\/a>\u3002\u3053\u306e\u6570\u5217\u306f\u3001\u96a3\u63a5\u3059\u308b2\u9805\u306e\u548c\u304c\u6b21\u306e\u9805\u306b\u306a\u308b\u3068\u3044\u3046\u7279\u5fb4\u3092\u6301\u3061\u30010, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...\u306e\u3088\u3046\u306b\u7d9a\u304f1<\/a>3<\/a>\u3002<\/p>\n\n\n\n

\u6570\u5b66\u7684\u306b\u306f\u4ee5\u4e0b\u306e\u6f38\u5316\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b1<\/a>4<\/a>:<\/p>\n\n\n\n

F0=0,F1=1,Fn=Fn\u22121+Fn\u22122(n\u22652)F_0 = 0, F_1 = 1, F_n = F_{n-1} + F_{n-2} \\quad (n \\geq 2)F0=0,F1=1,Fn=Fn\u22121+Fn\u22122(n\u22652)<\/p>\n\n\n\n

\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306f\u5358\u306a\u308b\u6570\u5b66\u7684\u6982\u5ff5\u3092\u8d85\u3048\u3066\u3001\u81ea\u7136\u754c\u306e\u591a\u304f\u306e\u73fe\u8c61\u306b\u73fe\u308c\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b3<\/a>5<\/a>\u3002\u4f8b\u3048\u3070\u3001\u82b1\u3073\u3089\u306e\u679a\u6570\u3001\u690d\u7269\u306e\u87ba\u65cb\u69cb\u9020\u3001\u9ec4\u91d1\u6bd4\u3068\u306e\u95a2\u4fc2\u306a\u3069\u3001\u69d8\u3005\u306a\u5206\u91ce\u3067\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u3066\u3044\u308b\u3002\u7279\u306b\u3001\u96a3\u63a5\u3059\u308b\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u306e\u6bd4\u306f\u3001\u6570\u5217\u304c\u9032\u3080\u306b\u3064\u308c\u3066\u9ec4\u91d1\u6bd4 \u03c6 = (1+\u221a5)\/2 \u2248 1.618 \u306b\u53ce\u675f\u3059\u308b\u6027\u8cea\u3092\u6301\u30643<\/a>6<\/a>7<\/a>\u3002<\/p>\n\n\n\n

\u672c\u8ab2\u984c\u3067\u306f\u3001\u3053\u306e\u5217\u3092\u7b2c1\u9805\u304b\u3089\u7b2cn\u9805\u307e\u3067\u51fa\u529b\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u3001\u518d\u5e30\u7684\u624b\u6cd5\u3068\u53cd\u5fa9\u7684\u624b\u6cd5\u306e\u4e21\u65b9\u3067\u5b9f\u88c5\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u6027\u3092\u8a73\u7d30\u306b\u5206\u6790\u3059\u308b\u3002<\/p>\n\n\n\n

\u203b\u672c\u30da\u30fc\u30b8\u306f\u3001AI\u306e\u6d3b\u7528\u3084\u7814\u7a76\u306b\u95a2\u9023\u3059\u308b\u539f\u7406\u30fb\u6a5f\u5668\u30fb\u30c7\u30d0\u30a4\u30b9\u306b\u3064\u3044\u3066\u5b66\u3076\u305f\u3081\u306b\u3001\u500b\u4eba\u7684\u306b\u6574\u7406\u30fb\u8a18\u8ff0\u3057\u3066\u3044\u308b\u3082\u306e\u3067\u3059\u3002\u5185\u5bb9\u306b\u306f\u8aa4\u308a\u3084\u898b\u843d\u3068\u3057\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u53ef\u80fd\u6027\u3082\u3042\u308a\u307e\u3059\u306e\u3067\u3001\u3082\u3057\u304a\u6c17\u3065\u304d\u306e\u70b9\u3084\u3054\u52a9\u8a00\u7b49\u3054\u3056\u3044\u307e\u3057\u305f\u3089\u3001\u3054\u9023\u7d61\u3044\u305f\u3060\u3051\u307e\u3059\u3068\u5e78\u3044\u3067\u3059\u3002<\/strong><\/p>\n\n\n\n

\u203b\u672c\u30da\u30fc\u30b8\u306e\u5185\u5bb9\u306f\u3001\u500b\u4eba\u7684\u306a\u5b66\u7fd2\u304a\u3088\u3073\u60c5\u5831\u6574\u7406\u3092\u76ee\u7684\u3068\u3057\u3066\u63d0\u4f9b\u3057\u3066\u3044\u308b\u3082\u306e\u3067\u3042\u308a\u3001\u305d\u306e\u6b63\u78ba\u6027\u3001\u5b8c\u5168\u6027\u3001\u6709\u7528\u6027\u7b49\u306b\u3064\u3044\u3066\u3044\u304b\u306a\u308b\u4fdd\u8a3c\u3082\u884c\u3044\u307e\u305b\u3093\u3002\u672c\u30da\u30fc\u30b8\u306e\u60c5\u5831\u3092\u5229\u7528\u3057\u305f\u3053\u3068\u3001\u307e\u305f\u306f\u5229\u7528\u3067\u304d\u306a\u304b\u3063\u305f\u3053\u3068\u306b\u3088\u3063\u3066\u767a\u751f\u3057\u305f\u640d\u5bb3\uff08\u76f4\u63a5\u7684\u30fb\u9593\u63a5\u7684\u30fb\u7279\u5225\u30fb\u5076\u767a\u7684\u30fb\u7d50\u679c\u7684\u640d\u5bb3\u3092\u542b\u307f\u307e\u3059\u304c\u3001\u3053\u308c\u3089\u306b\u9650\u308a\u307e\u305b\u3093\uff09\u306b\u3064\u3044\u3066\u3001\u5f53\u65b9\u306f\u4e00\u5207\u8cac\u4efb\u3092\u8ca0\u3044\u307e\u305b\u3093\u3002\u3054\u5229\u7528\u306f\u5229\u7528\u8005\u3054\u81ea\u8eab\u306e\u8cac\u4efb\u3067\u304a\u9858\u3044\u3044\u305f\u3057\u307e\u3059\u3002<\/strong><\/p>\n\n\n\n

2. \u5b9f\u88c5\u3057\u305f\u30b3\u30fc\u30c9<\/h2>\n\n\n\n

2.1 \u518d\u5e30\u7684\u5b9f\u88c5<\/h3>\n\n\n\n

Python\u7248\uff08\u518d\u5e30\uff09<\/h4>\n\n\n\n
from functools import lru_cache\n\n@lru_cache(maxsize=None)\ndef fibonacci_recursive(n):\n    """\u518d\u5e30\u3092\u4f7f\u3063\u305f\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306e\u5b9f\u88c5\uff08\u30e1\u30e2\u5316\u3042\u308a\uff09"""\n    if n <= 1:\n        return n\n    return fibonacci_recursive(n-1) + fibonacci_recursive(n-2)\n\n# \u30e1\u30a4\u30f3\u51e6\u7406\nn = int(input("\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u3092\u4f55\u9805\u76ee\u307e\u3067\u8868\u793a\u3057\u307e\u3059\u304b\uff1f: "))\n\nif n < 1:\n    print("1\u4ee5\u4e0a\u306e\u6574\u6570\u3092\u5165\u529b\u3057\u3066\u304f\u3060\u3055\u3044\u3002")\nelse:\n    print(f"\\n\u518d\u5e30\u7248\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217 (n={n}):")\n    for i in range(1, n + 1):\n        print(f"F({i}) = {fibonacci_recursive(i)}")\n<\/code><\/pre><\/div>\n\n\n\n
C\u8a00\u8a9e\u7248\uff08\u518d\u5e30\uff09<\/h4>\n\n\n\n
#include <stdio.h>\n\n\/\/ \u518d\u5e30\u3092\u4f7f\u3063\u305f\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306e\u5b9f\u88c5\nint fibonacci_recursive(int n) {\n    if (n <= 1) {\n        return n;\n    }\n    return fibonacci_recursive(n - 1) + fibonacci_recursive(n - 2);\n}\n\nint main() {\n    int n;\n\n    printf("\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u3092\u4f55\u9805\u76ee\u307e\u3067\u8868\u793a\u3057\u307e\u3059\u304b\uff1f: ");\n    if (scanf("%d", &n) != 1 || n < 1) {\n        printf("\u6b63\u306e\u6574\u6570\u3092\u5165\u529b\u3057\u3066\u304f\u3060\u3055\u3044\u3002\\n");\n        return 1;\n    }\n\n    printf("\\n\u518d\u5e30\u7248\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217 (0\u9805\u76ee\u76ee\u304b\u3089 %d \u9805\u76ee\u76ee\u307e\u3067):\\n", n - 1);\n    for (int i = 0; i < n; i++) {\n        printf("F(%d) = %d\\n", i, fibonacci_recursive(i));\n    }\n\n    return 0;\n}\n<\/code><\/pre><\/div>\n\n\n\n
2.2 \u53cd\u5fa9\u7684\u5b9f\u88c5<\/h3>\n\n\n\n
Python\u7248\uff08\u53cd\u5fa9\uff09<\/h4>\n\n\n\n
def fibonacci_iterative(n):\n    """\u53cd\u5fa9\u51e6\u7406\u3092\u4f7f\u3063\u305f\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306e\u5b9f\u88c5"""\n    if n <= 1:\n        return n\n\n    a, b = 0, 1\n    for i in range(2, n + 1):\n        a, b = b, a + b\n    return b\n\n# \u30e1\u30a4\u30f3\u51e6\u7406\nn = int(input("\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u3092\u4f55\u9805\u76ee\u307e\u3067\u8868\u793a\u3057\u307e\u3059\u304b\uff1f: "))\n\nif n < 1:\n    print("1\u4ee5\u4e0a\u306e\u6574\u6570\u3092\u5165\u529b\u3057\u3066\u304f\u3060\u3055\u3044\u3002")\nelse:\n    print(f"\\n\u53cd\u5fa9\u7248\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217 (n={n}):")\n    for i in range(1, n + 1):\n        print(f"F({i}) = {fibonacci_iterative(i)}")\n<\/code><\/pre><\/div>\n\n\n\n
C\u8a00\u8a9e\u7248\uff08\u53cd\u5fa9\uff09<\/h4>\n\n\n\n
#include <stdio.h>\n\n\/\/ \u53cd\u5fa9\u51e6\u7406\u3092\u4f7f\u3063\u305f\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306e\u5b9f\u88c5\nint fibonacci_iterative(int n) {\n    if (n <= 1) {\n        return n;\n    }\n\n    int a = 0, b = 1, temp;\n    for (int i = 2; i <= n; i++) {\n        temp = a + b;\n        a = b;\n        b = temp;\n    }\n    return b;\n}\n\nint main() {\n    int n;\n\n    printf("\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u3092\u4f55\u9805\u76ee\u307e\u3067\u8868\u793a\u3057\u307e\u3059\u304b\uff1f: ");\n    if (scanf("%d", &n) != 1 || n < 1) {\n        printf("\u6b63\u306e\u6574\u6570\u3092\u5165\u529b\u3057\u3066\u304f\u3060\u3055\u3044\u3002\\n");\n        return 1;\n    }\n\n    printf("\\n\u53cd\u5fa9\u7248\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217 (0\u9805\u76ee\u76ee\u304b\u3089 %d \u9805\u76ee\u76ee\u307e\u3067):\\n", n - 1);\n    for (int i = 0; i < n; i++) {\n        printf("F(%d) = %d\\n", i, fibonacci_iterative(i));\n    }\n\n    return 0;\n}\n<\/code><\/pre><\/div>\n\n\n\n
3. n=10 \u306e\u5834\u5408\u306e\u51fa\u529b\u7d50\u679c<\/h2>\n\n\n\n
\u4e21\u65b9\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u305f\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b:<\/p>\n\n\n\n
\u518d\u5e30\u7248\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217 (n=10):\nF(1) = 1\nF(2) = 1\nF(3) = 2\nF(4) = 3\nF(5) = 5\nF(6) = 8\nF(7) = 13\nF(8) = 21\nF(9) = 34\nF(10) = 55\n\n\u53cd\u5fa9\u7248\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217 (n=10):\nF(1) = 1\nF(2) = 1\nF(3) = 2\nF(4) = 3\nF(5) = 5\nF(6) = 8\nF(7) = 13\nF(8) = 21\nF(9) = 34\nF(10) = 55\n<\/code><\/pre><\/div>\n\n\n\n
\u4e21\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3082\u540c\u4e00\u306e\u6b63\u3057\u3044\u7d50\u679c\u3092\u51fa\u529b\u3059\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
4. \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5229\u70b9\u30fb\u6b20\u70b9\u306b\u95a2\u3059\u308b\u8003\u5bdf<\/h2>\n\n\n\n
4.1 \u6642\u9593\u8a08\u7b97\u91cf\u306e\u6bd4\u8f03<\/h3>\n\n\n\n
4.1.1 \u518d\u5e30\u7684\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u8a08\u7b97\u91cf<\/h4>\n\n\n\n
\u518d\u5e30\u7684\u5b9f\u88c5\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u6307\u6570\u95a2\u6570\u7684\u3067\u3042\u308b8<\/a>9<\/a>10<\/a>11<\/a>\u3002\u5177\u4f53\u7684\u306b\u306f\uff1a<\/p>\n\n\n\n
\u6642\u9593\u8a08\u7b97\u91cf: O(\u03c6\u207f) \u2248 O(1.618\u207f)<\/strong><\/p>\n\n\n\n
\u3053\u306e\u6307\u6570\u95a2\u6570\u7684\u306a\u5897\u52a0\u306f\u3001\u540c\u3058\u90e8\u5206\u554f\u984c\u304c\u91cd\u8907\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u306b\u8d77\u56e0\u3059\u308b8<\/a>9<\/a>12<\/a>\u3002\u4f8b\u3048\u3070\u3001fibonacci_recursive(5)\u3092\u8a08\u7b97\u3059\u308b\u969b\u3001fibonacci_recursive(3)\u306f3\u56de\u3001fibonacci_recursive(2)\u306f5\u56de\u8a08\u7b97\u3055\u308c\u308b8<\/a>10<\/a>\u3002<\/p>\n\n\n\n
n=30\u3067\u306e\u5b9f\u6e2c\u5024\u3067\u306f\u3001\u518d\u5e30\u7248\u306f\u7d040.18\u79d2\u3001\u53cd\u5fa9\u7248\u306f\u7d040.00007\u79d2\u3092\u8981\u3057\u3001\u518d\u5e30\u7248\u306f\u53cd\u5fa9\u7248\u306e\u7d042661\u500d\u306e\u6642\u9593\u3092\u8981\u3057\u305f\u3002\u3053\u306e\u81a8\u5927\u306a\u6642\u9593\u5dee\u306f\u3001\u95a2\u6570\u547c\u3073\u51fa\u3057\u56de\u6570\u306e\u6307\u6570\u95a2\u6570\u7684\u5897\u52a0\u306b\u3088\u308b\u3082\u306e\u3067\u3042\u308b:<\/p>\n\n\n\n