{"id":65,"date":"2025-08-14T03:45:09","date_gmt":"2025-08-13T19:45:09","guid":{"rendered":"http:\/\/thebugmuxi.xyz\/?p=65"},"modified":"2025-08-14T03:45:10","modified_gmt":"2025-08-13T19:45:10","slug":"%e9%a2%98%e7%9b%ae-2706-%e8%93%9d%e6%a1%a5%e6%9d%af2022%e5%b9%b4%e7%ac%ac%e5%8d%81%e4%b8%89%e5%b1%8a%e7%a0%94%e7%a9%b6%e7%94%9f%e7%bb%84%e5%86%b3%e8%b5%9b%e7%9c%9f%e9%a2%98-%e5%85%ad%e5%85%ad","status":"publish","type":"post","link":"https:\/\/www.thebugmuxi.xyz\/index.php\/2025\/08\/14\/%e9%a2%98%e7%9b%ae-2706-%e8%93%9d%e6%a1%a5%e6%9d%af2022%e5%b9%b4%e7%ac%ac%e5%8d%81%e4%b8%89%e5%b1%8a%e7%a0%94%e7%a9%b6%e7%94%9f%e7%bb%84%e5%86%b3%e8%b5%9b%e7%9c%9f%e9%a2%98-%e5%85%ad%e5%85%ad\/","title":{"rendered":"\u9898\u76ee 2706:\u00a0\u84dd\u6865\u676f2022\u5e74\u7b2c\u5341\u4e09\u5c4a\u7814\u7a76\u751f\u7ec4\u51b3\u8d5b\u771f\u9898-\u516d\u516d\u5927\u987a"},"content":{"rendered":"\n<p>python\u89e3\u6cd5\u7b54\u6848\u4ec5\u6b64\u4e00\u4efd<\/p>\n\n\n\n<p>\u8981\u89e3\u51b3\u6570\u5217 B \u524d n \u9879\u548c\u7684\u95ee\u9898\uff0c\u6838\u5fc3\u662f\u901a\u8fc7\u6570\u5b66\u516c\u5f0f\u63a8\u5bfc\u7b80\u5316\u8ba1\u7b97\uff0c\u907f\u514d\u9010\u4f4d\u6a21\u62df\u7684\u4f4e\u6548\u64cd\u4f5c\u3002\u4ee5\u4e0b\u662f\u9ad8\u6548\u4e14\u7b26\u5408\u65f6\u95f4\/\u5185\u5b58\u9650\u5236\u7684\u89e3\u51b3\u65b9\u6848\uff1a<\/p>\n\n\n\n<p>\u6570\u5b66\u63a8\u5bfc\uff08\u5173\u952e\uff09<\/p>\n\n\n\n<p>\u26a0\ufe0f\u7531\u4e8e\u6587\u672c\u7684\u5c40\u9650\u6027\u63a8\u5bfc\u8fc7\u7a0b\u4f1a\u5728\u6700\u540e\u9644\u4e0a\u624b\u5199\u7b97\u5f0f\u26a0\ufe0f<\/p>\n\n\n\n<p>1.\u00a0\u6570\u5217 A \u7684\u901a\u9879\uff1a<br>a_i \u662f\u7531 i \u4e2a 6 \u7ec4\u6210\u7684\u6570<\/p>\n\n\n\n<p>\u200b2.\u00a0\u6570\u5217 B \u7684\u901a\u9879\uff1a<br>b_i = a_i^2 \uff0c\u4ee3\u5165 a_i <\/p>\n\n\n\n<p>3.\u00a0\u524d n \u9879\u548c S_n \uff1a<br>\u5bf9 b_i \u6c42\u548c\uff0c\u5229\u7528\u7b49\u6bd4\u6570\u5217\u6c42\u548c\u516c\u5f0f\u5316\u7b80\uff1b\u5206\u522b\u8ba1\u7b97\u4e09\u4e2a\u6c42\u548c\u9879<br>\u200b\u6700\u540e\u4ee3\u5165\u540e\u901a\u5206\u5316\u7b80<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1. \u6784\u9020\u5927\u6570\u5b57\u7b26\u4e32<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>term1<\/strong>\uff1a\u8868\u793a\u00a0<code>(100^(n+1) - 100)\/99<\/code>\n<ul class=\"wp-block-list\">\n<li>\u5b57\u7b26\u4e32\u5f62\u5f0f\uff1a<code>\"10\"<\/code>\u00a0\u91cd\u590d\u00a0<code>n<\/code>\u00a0\u6b21 +\u00a0<code>\"0\"<\/code><\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a<code>n=1<\/code>\u00a0\u2192\u00a0<code>\"100\"<\/code>,\u00a0<code>n=2<\/code>\u00a0\u2192\u00a0<code>\"10100\"<\/code><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>term2<\/strong>\uff1a\u8868\u793a\u00a0<code>2*(10^(n+1)-10)\/9<\/code>\n<ul class=\"wp-block-list\">\n<li>\u5b57\u7b26\u4e32\u5f62\u5f0f\uff1a<code>\"2\"<\/code>\u00a0\u91cd\u590d\u00a0<code>n<\/code>\u00a0\u6b21 +\u00a0<code>\"0\"<\/code><\/li>\n\n\n\n<li>\u793a\u4f8b\uff1a<code>n=1<\/code>\u00a0\u2192\u00a0<code>\"20\"<\/code>,\u00a0<code>n=2<\/code>\u00a0\u2192\u00a0<code>\"220\"<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2. \u5b57\u7b26\u4e32\u51cf\u6cd5 (<code>subtract<\/code>\u51fd\u6570)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u529f\u80fd<\/strong>\uff1a\u8ba1\u7b97\u00a0<code>term1 - term2<\/code><\/li>\n\n\n\n<li><strong>\u5b9e\u73b0\u539f\u7406<\/strong>\uff1a\n<ol start=\"1\" class=\"wp-block-list\">\n<li>\u5bf9\u9f50\u4f4d\u6570\uff1a\u5728\u8f83\u77ed\u6570\u5b57\u524d\u88650<\/li>\n\n\n\n<li><strong>\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d<\/strong>\u9010\u4f4d\u76f8\u51cf<\/li>\n\n\n\n<li>\u5904\u7406\u501f\u4f4d\uff1a\u82e5\u5f53\u524d\u4f4d\u4e0d\u591f\u51cf\uff0c\u5411\u9ad8\u4f4d\u501f1\uff08+10\uff09<\/li>\n\n\n\n<li>\u79fb\u9664\u7ed3\u679c\u7684\u524d\u5bfc\u96f6<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>\u793a\u4f8b<\/strong>\uff1a<code>subtract(\"100\", \"20\")<\/code><\/li>\n<\/ul>\n\n\n<pre>100\n-20\n---\n 80  \/\/ \u9010\u4f4d\u8ba1\u7b97\uff1a0-0=0, 0-2\u501f\u4f4d\u219210-2=8, 1-0-\u501f\u4f4d=0<\/pre>\n\n\n<h4 class=\"wp-block-heading\">3. \u5b57\u7b26\u4e32\u52a0\u6cd5 (<code>add<\/code>\u51fd\u6570)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u529f\u80fd<\/strong>\uff1a\u5c06\u51cf\u6cd5\u7ed3\u679c\u52a0\u4e0a\u00a0<code>n<\/code><\/li>\n\n\n\n<li><strong>\u5b9e\u73b0\u539f\u7406<\/strong>\uff1a\n<ol start=\"1\" class=\"wp-block-list\">\n<li>\u5bf9\u9f50\u4f4d\u6570\uff1a\u5728\u8f83\u77ed\u6570\u5b57\u524d\u88650<\/li>\n\n\n\n<li><strong>\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d<\/strong>\u9010\u4f4d\u76f8\u52a0<\/li>\n\n\n\n<li>\u5904\u7406\u8fdb\u4f4d\uff1a\u548c\u226510\u65f6\u8fdb\u4f4d<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>\u793a\u4f8b<\/strong>\uff1a<code>add(\"80\", \"1\")<\/code><\/li>\n<\/ul>\n\n\n<pre> 80\n+ 01\n----\n 81  \/\/ 0+1=1, 8+0=8<\/pre>\n\n\n<h4 class=\"wp-block-heading\">4. \u5b57\u7b26\u4e32\u4e58\u4ee54 (<code>multiply4<\/code>\u51fd\u6570)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u529f\u80fd<\/strong>\uff1a\u5c06\u52a0\u6cd5\u7ed3\u679c\u4e58\u4ee54<\/li>\n\n\n\n<li><strong>\u5b9e\u73b0\u539f\u7406<\/strong>\uff1a\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u4ece\u4f4e\u4f4d\u5230\u9ad8\u4f4d<\/strong>\u9010\u4f4d\u4e58\u4ee54<\/li>\n\n\n\n<li>\u5904\u7406\u8fdb\u4f4d\uff1a\u4e58\u79ef\u226510\u65f6\u8fdb\u4f4d<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>\u793a\u4f8b<\/strong>\uff1a<code>multiply4(\"81\")<\/code><\/li>\n<\/ul>\n\n\n<pre>81 \u00d7 4\uff1a\n  1\u00d74 = 4 \u2192 \u51994\n  8\u00d74 = 32 \u2192 \u51992\uff0c\u8fdb\u4f4d3 \u2192 \u6700\u7ec8324<\/pre>\n\n\n<h4 class=\"wp-block-heading\">5. \u5b57\u7b26\u4e32\u9664\u4ee59 (<code>divide9<\/code>\u51fd\u6570)<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u529f\u80fd<\/strong>\uff1a\u5c06\u4e58\u6cd5\u7ed3\u679c\u9664\u4ee59<\/li>\n\n\n\n<li><strong>\u5b9e\u73b0\u539f\u7406<\/strong>\uff1a\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u4ece\u9ad8\u4f4d\u5230\u4f4e\u4f4d<\/strong>\u9010\u4f4d\u5904\u7406<\/li>\n\n\n\n<li>\u5f53\u524d\u503c = \u4f59\u6570\u00d710 + \u5f53\u524d\u4f4d\u6570\u5b57<\/li>\n\n\n\n<li>\u5546 = \u5f53\u524d\u503c \/\/ 9<\/li>\n\n\n\n<li>\u4f59\u6570 = \u5f53\u524d\u503c % 9<\/li>\n\n\n\n<li>\u8df3\u8fc7\u5546\u7684\u524d\u5bfc\u96f6<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>\u793a\u4f8b<\/strong>\uff1a<code>divide9(\"324\")<\/code><\/li>\n<\/ul>\n\n\n<pre>3 \/\/ 9 = 0 (\u8df3\u8fc7)\n32 \/\/ 9 = 3 \u2192 \u4f59\u65705\n54 \/\/ 9 = 6 \u2192 \u554636<\/pre>\n\n\n<p>6. \u5b8c\u6574\u8ba1\u7b97\u6d41\u7a0b<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>n = int(input())\nterm1 = \"10\" * n + \"0\"      # \u6784\u9020term1\nterm2 = \"2\" * n + \"0\"       # \u6784\u9020term2\ndiff = subtract(term1, term2)  # \u5927\u6570\u51cf\u6cd5\nsum_val = add(diff, str(n))    # \u52a0\u4e0an\nproduct = multiply4(sum_val)   # \u4e58\u4ee54\nresult = divide9(product)      # \u9664\u4ee59\nprint(result)<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u5173\u952e\u7f16\u7a0b\u6280\u5de7<\/h3>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u5927\u6570\u8868\u793a<\/strong>\uff1a\u7528\u5b57\u7b26\u4e32\u907f\u514d\u6570\u503c\u6ea2\u51fa<\/li>\n\n\n\n<li><strong>\u9010\u4f4d\u8fd0\u7b97<\/strong>\uff1a\u6a21\u62df\u624b\u5de5\u8ba1\u7b97\u8fc7\u7a0b<\/li>\n\n\n\n<li><strong>\u8fdb\u4f4d\/\u501f\u4f4d\u5904\u7406<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u52a0\u6cd5\/\u4e58\u6cd5\uff1a\u4ece\u4f4e\u4f4d\u5411\u9ad8\u4f4d\u5904\u7406\u8fdb\u4f4d<\/li>\n\n\n\n<li>\u51cf\u6cd5\uff1a\u4ece\u4f4e\u4f4d\u5411\u9ad8\u4f4d\u5904\u7406\u501f\u4f4d<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u524d\u5bfc\u96f6\u5904\u7406<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li>\u51cf\u6cd5\u7ed3\u679c\u9700\u5220\u9664\u524d\u5bfc\u96f6<\/li>\n\n\n\n<li>\u9664\u6cd5\u7ed3\u679c\u9700\u8df3\u8fc7\u524d\u5bfc\u96f6<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u8fb9\u754c\u5904\u7406<\/strong>\uff1a\u7a7a\u7ed3\u679c\u8fd4\u56de&#8221;0&#8243;<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u590d\u6742\u5ea6\u5206\u6790<\/h3>\n\n\n\n<p>\u5b58\u50a8\u4e2d\u95f4\u7ed3\u679c\u7684\u5b57\u7b26\u4e32\u957f\u5ea6\u4e0en\u6210\u6b63\u6bd4<\/p>\n\n\n\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/p>\n\n\n\n<p>\u6240\u6709\u5b57\u7b26\u4e32\u64cd\u4f5c\uff08\u52a0\/\u51cf\/\u4e58\/\u9664\uff09\u5747\u4e0e\u6570\u5b57\u4f4d\u6570\u6210\u7ebf\u6027\u5173\u7cfb<\/p>\n\n\n\n<p>\u6570\u5b57\u6700\u5927\u957f\u5ea6\u7ea6 2n+1<\/p>\n\n\n\n<p>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/p>\n\n\n\n<ul class=\"wp-block-list\"><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b8c\u6574\u7b54\u6848<\/h2>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca wp-block-group-is-layout-flex\">\n\n\n<pre class=\"wp-block-code\"><code>n = int(input())\n\n# \u6784\u9020term1: (100^(n+1) - 100)\/99\uff0c\u5f62\u5f0f\u4e3a\"10\"*n + \"0\"\nterm1 = \"10\" * n + \"0\"\n\n# \u6784\u9020term2: 2*(10^(n+1)-10)\/9\uff0c\u5f62\u5f0f\u4e3a\"2\"*n + \"0\"\nterm2 = \"2\" * n + \"0\"\n\ndef subtract(a, b):\n    \"\"\"\u5b57\u7b26\u4e32\u51cf\u6cd5\uff1a\u8fd4\u56dea - b\uff08\u786e\u4fdda >= b\uff09\"\"\"\n    len_a = len(a)\n    len_b = len(b)\n    # \u8865\u5168b\u7684\u957f\u5ea6\uff0c\u524d\u5bfc\u88650\n    b = '0' * (len_a - len_b) + b\n    result = &#91;]\n    borrow = 0\n    for i in range(len_a - 1, -1, -1):\n        digit_a = int(a&#91;i]) - borrow\n        digit_b = int(b&#91;i])\n        if digit_a &lt; digit_b:\n            digit_a += 10\n            borrow = 1\n        else:\n            borrow = 0\n        result.append(str(digit_a - digit_b))\n    # \u53bb\u9664\u524d\u5bfc0\n    result_str = ''.join(reversed(result)).lstrip('0')\n    return result_str if result_str else '0'\n\n\ndiff = subtract(term1, term2)\n\ndef add(a, b):\n    \"\"\"\u5b57\u7b26\u4e32\u52a0\u6cd5\uff1a\u8fd4\u56dea + b\"\"\"\n    max_len = max(len(a), len(b))\n    a = a.zfill(max_len)\n    b = b.zfill(max_len)\n    result = &#91;]\n    carry = 0\n    for i in range(max_len - 1, -1, -1):\n        total = int(a&#91;i]) + int(b&#91;i]) + carry\n        carry = total \/\/ 10\n        result.append(str(total % 10))\n    if carry:\n        result.append(str(carry))\n    return ''.join(reversed(result))\n\n\nsum_diff_term3 = add(diff, str(n))\n\ndef multiply4(s):\n    \"\"\"\u5b57\u7b26\u4e32\u4e58\u4ee54\"\"\"\n    result = &#91;]\n    carry = 0\n    for c in reversed(s):\n        product = int(c) * 4 + carry\n        carry = product \/\/ 10\n        result.append(str(product % 10))\n    if carry:\n        result.append(str(carry))\n    return ''.join(reversed(result))\n\n\nproduct = multiply4(sum_diff_term3)\n\ndef divide9(s):\n    \"\"\"\u5b57\u7b26\u4e32\u9664\u4ee59\uff08\u7ed3\u679c\u4e3a\u6574\u6570\uff09\"\"\"\n    result = &#91;]\n    remainder = 0\n    for c in s:\n        num = remainder * 10 + int(c)\n        q = num \/\/ 9\n        remainder = num % 9\n        if q == 0 and not result:  # \u8df3\u8fc7\u524d\u5bfc0\n            continue\n        result.append(str(q))\n    return ''.join(result) if result else '0'\n\n\nprint(divide9(product))\n\n\n\n<\/code><\/pre>\n\n\n\n<p><\/p>\n<\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.https:\/\/www.thebugmuxi.xyz\/wp-content\/uploads\/2025\/08\/\u5fae\u4fe1\u56fe\u7247_20250814034302_270-1-768x1024.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"1024\" data-original=\"https:\/\/www.https:\/\/www.thebugmuxi.xyz\/wp-content\/uploads\/2025\/08\/\u5fae\u4fe1\u56fe\u7247_20250814034302_270-1-768x1024.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-67\"  sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>python\u89e3\u6cd5\u7b54\u6848\u4ec5\u6b64\u4e00\u4efd \u8981\u89e3\u51b3\u6570\u5217 B \u524d n \u9879\u548c\u7684\u95ee\u9898\uff0c\u6838\u5fc3\u662f\u901a\u8fc7\u6570\u5b66\u516c\u5f0f\u63a8\u5bfc\u7b80\u5316\u8ba1\u7b97\uff0c\u907f\u514d\u9010\u4f4d\u6a21\u62df [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":17,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[8,9],"class_list":["post-65","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-leam","tag-8","tag-9"],"_links":{"self":[{"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/posts\/65","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=65"}],"version-history":[{"count":1,"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/posts\/65\/revisions"}],"predecessor-version":[{"id":68,"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/posts\/65\/revisions\/68"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/media\/17"}],"wp:attachment":[{"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=65"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=65"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.thebugmuxi.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=65"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}