{"id":10007076,"date":"2023-01-13T13:18:34","date_gmt":"2023-01-13T05:18:34","guid":{"rendered":"https:\/\/ityet.com\/?p=10007076"},"modified":"2023-01-13T13:18:34","modified_gmt":"2023-01-13T05:18:34","slug":"%e6%9d%a8%e8%be%89%e4%b8%89%e8%a7%92%e7%9a%845%e4%b8%aa%e7%89%b9%e6%80%a7%ef%bc%8c%e4%b8%80%e4%b8%aa%e6%af%94%e4%b8%80%e4%b8%aa%e7%89%9b%e7%9a%ae%ef%bc%81","status":"publish","type":"post","link":"https:\/\/itmax.cn\/?p=10007076","title":{"rendered":"\u6768\u8f89\u4e09\u89d2\u76845\u4e2a\u7279\u6027\uff0c\u4e00\u4e2a\u6bd4\u4e00\u4e2a\u725b\u76ae\uff01"},"content":{"rendered":"<p>\u4f5c\u8005\uff1a\u5c0f\u5085\u54e5 <br \/>\u535a\u5ba2\uff1a<a href=\"https:\/\/link.segmentfault.com\/?enc=3vGpXW972oxp9SjB40ouoQ%3D%3D.r48dzHt3ZlOOYCrHY5FO9Px%2FzLoxH8xs9iVv2CoMqUo%3D\" rel=\"nofollow\">https:\/\/bugstack.cn<\/a><\/p>\n<blockquote><p>\u6c89\u6dc0\u3001\u5206\u4eab\u3001\u6210\u957f\uff0c\u8ba9\u81ea\u5df1\u548c\u4ed6\u4eba\u90fd\u80fd\u6709\u6240\u6536\u83b7\uff01\ud83d\ude04<\/p><\/blockquote>\n<h2>\u4e00\u3001\u524d\u8a00<\/h2>\n<pre><code>\u6768\u8f89\u4e09\u89d2\u7684\u5386\u53f2<\/code><\/pre>\n<p>\u6768\u8f89\u4e09\u89d2\u6309\u7167\u6768\u8f89\u4e8e1261\u5e74\u6240\u7f16\u5199\u7684\u300a\u8be6\u89e3\u4e5d\u7ae0\u7b97\u6cd5\u300b\u4e00\u4e66\uff0c\u91cc\u9762\u6709\u4e00\u5f20\u56fe\u7247\uff0c\u4ecb\u7ecd\u6b64\u79cd\u7b97\u6cd5\u6765\u81ea\u4e8e\u53e6\u5916\u4e00\u4e2a\u6570\u5b66\u5bb6\u8d3e\u5baa\u6240\u7f16\u5199\u7684\u300a\u91ca\u9501\u7b97\u4e66\u300b\u4e00\u4e66\uff0c\u4f46\u8fd9\u672c\u4e66\u65e9\u5df2\u5931\u4f20\u65e0\u4ece\u8003\u8bc1\u3002\u4f46\u53ef\u4ee5\u80af\u5b9a\u7684\u662f\u8fd9\u4e00\u56fe\u5f62\u7684\u53d1\u73b0\u6211\u56fd\u4e0d\u8fdf\u4e8e1200\u5e74\u5de6\u53f3\u3002\u5728\u6b27\u6d32\uff0c\u8fd9\u56fe\u5f62\u79f0\u4e3a&#8221;\u5df4\u65af\u52a0(Pascal)\u4e09\u89d2&#8221;\u3002\u56e0\u4e3a\u4e00\u822c\u90fd\u8ba4\u4e3a\u8fd9\u662f\u5df4\u65af\u52a0\u57281654\u5e74\u53d1\u660e\u7684\u3002\u5176\u5b9e\u5728\u5df4\u65af\u52a0\u4e4b\u524d\u5df2\u7ecf\u6709\u8bb8\u591a\u4eba\u666e\u53ca\u8fc7\uff0c\u6700\u65e9\u662f\u5fb7\u56fd\u4eba\u963f\u5339\u7eb3\u65af(Pertrus APianus)\uff0c\u4ed6\u66fe\u7ecf\u628a\u8fd9\u4e2a\u56fe\u5f62\u523b\u57281527\u5e74\u8457\u7684\u4e00\u672c\u7b97\u672f\u4e66\u5c01\u9762\u4e0a\u3002\u4f46\u65e0\u8bba\u5982\u4f55\uff0c\u6768\u8f89\u4e09\u89d2\u7684\u53d1\u73b0\uff0c\u5728\u6211\u56fd\u6bd4\u5728\u6b27\u6d32\u81f3\u5c11\u8981\u65e9300\u5e74\u5149\u666f\u3002<\/p>\n<p>\u6b64\u5916\u6768\u8f89\u4e09\u89d2\u539f\u6765\u7684\u540d\u5b57\u4e5f\u4e0d\u662f\u4e09\u89d2\uff0c\u800c\u662f\u53eb\u505a<strong>\u5f00\u65b9\u4f5c\u6cd5\u672c\u6e90<\/strong>\uff0c\u540e\u6765\u4e5f\u6709\u4eba\u79f0\u4e3a<strong>\u4e58\u6cd5\u6c42\u5ec9\u56fe<\/strong>\u3002\u56e0\u4e3a\u8fd9\u4e9b\u540d\u79f0\u5b9e\u5728\u592a\u53e4\u5965\u4e86\u4e9b\uff0c\u6240\u4ee5\u540e\u6765\u7b80\u79f0\u4e3a\u201c\u4e09\u89d2\u201d\u3002<\/p>\n<p>\u5728\u5c0f\u5085\u54e5\u5b66\u4e60\u6768\u8f89\u4e09\u89d2\u7684\u8fc7\u7a0b\u4e2d\uff0c\u627e\u5230\u4e86\u4e00\u672c\u5927\u6570\u5b66\u5bb6\u534e\u7f57\u5e9a\u7684PDF[\u300a\u4ece\u6768\u8f89\u4e09\u89d2\u8c08\u8d77 &#8211; \u534e\u7f57\u5e9a\u300b]()\u3002\u2014\u2014 \u8fd9\u4e9b\u6570\u5b66\u771f\u7684\u975e\u5e38\u91cd\u8981\uff0c\u6bcf\u6bcf\u6620\u5c04\u5230\u7a0b\u5e8f\u4e2d\u90fd\u662f\u4e00\u6bb5\u628afor\u5faa\u73af\u4f18\u5316\u6210\u7b97\u6cd5\u7684\u4f53\u73b0\uff0c\u63d0\u9ad8\u6267\u884c\u6548\u7387\u3002<\/p>\n<h2>\u4e8c\u3001\u6768\u8f89\u4e09\u89d2\u6784\u9020<\/h2>\n<p>\u5728\u5f00\u59cb\u5206\u4eab\u6768\u8f89\u4e09\u89d2\u7684\u7279\u6027\u548c\u4ee3\u7801\u5b9e\u73b0\u524d\uff0c\u6211\u4eec\u5148\u6765\u4e86\u89e3\u4e0b\u6768\u8f89\u4e09\u89d2\u7684\u7ed3\u6784\u6784\u9020\u3002<\/p>\n<p>\u200b    <img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000043330031\" alt=\"img\" title=\"img\" loading=\"lazy\"><\/p>\n<p>\u6768\u8f89\u4e09\u89d2\u7684\u7ed3\u6784\u548c\u89c4\u5f8b\u975e\u5e38\u7b80\u5355\uff0c\u9664\u53bb\u6bcf\u6b21\u4e24\u8fb9\u76841\uff0c\u4e2d\u95f4\u7684\u6570\u5b57\u90fd\u662f\u4e0a\u9762\u4e24\u4e2a\u6570\u5b57\u7684\u548c\u3002\u5982\u56fe\u793a\u610f\u7684\u4e09\u89d2\u533a\u57df\u3002\u4f46\u4e5f\u5c31\u662f\u5982\u6b64\u7b80\u5355\u7684\u7ed3\u6784\uff0c\u5374\u6709\u7740\u8bf8\u591a\u7684\u6570\u5b66\u903b\u8f91\u4f53\u73b0\u3002\u5305\u62ec\u6211\u4eec\u8ba1\u7b97\u7684\u4e8c\u9879\u5f0f\u3001N\u9009X\u7684\u79cd\u6570\u8fd8\u6709\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7b49\uff0c\u90fd\u53ef\u4ee5\u5728\u6768\u8f89\u4e09\u89d2\u4e2d\u4f53\u73b0\u51fa\u6765\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u6765\u770b\u770b\u8fd9\u4e9b\u7279\u6027\u3002<\/p>\n<h2>\u4e09\u3001\u6768\u8f89\u4e09\u89d2\u7279\u6027<\/h2>\n<p>\u4e3a\u4e86\u65b9\u4fbf\u5b66\u4e60\u6768\u8f89\u4e09\u89d2\u7684\u6570\u5b66\u903b\u8f91\u7279\u6027\uff0c\u6211\u4eec\u628a\u5b83\u6309\u5de6\u5bf9\u9f50\u65b9\u5f0f\u8fdb\u884c\u6392\u5217\u3002<\/p>\n<pre><code>[1]\n[1,1]\n[1,2,1]\n[1,3,3,1]\n[1,4,6,4,1]\n[1,5,10,10,5,1]\n[1,6,15,20,15,6,1]\n[1,7,21,35,35,21,7,1]\n[1,8,28,56,70,56,28,8,1]<\/code><\/pre>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u5c31\u4ee5\u8fd9\u7ec4\u6768\u8f89\u4e09\u89d2\u6570\u5217\uff0c\u6765\u5c55\u793a\u5b83\u7684\u6570\u5b66\u903b\u8f91\u7279\u6027\u3002\u5173\u4e8e\u6768\u8f89\u4e09\u89d2\u7684Java\u4ee3\u7801\u653e\u5df2\u5230\u4e0b\u6587\u4e2d\uff0c\u8bfb\u8005\u53ef\u4ee5\u67e5\u9605\u3002<\/p>\n<h3>1. \u4e8c\u9879\u5f0f\u5c55\u5f00<\/h3>\n<p>\u5927\u5bb6\u5728\u4e0a\u5b66\u9636\u6bb5\u4e00\u5b9a\u5b66\u4e60\u8fc7\u4e8c\u9879\u5f0f\u5c55\u5f00\uff0c\u4f8b\u5982\uff1a<code>(x+y)^2 = x^2 + 2xy + y^2<\/code> \u5176\u5b9e\u8fd9\u4e2a\u5c55\u5f00\u7684\u6570\u5b66\u903b\u8f91\u5728\u6768\u8f89\u4e09\u89d2\u4e2d\u53ef\u4ee5\u975e\u5e38\u597d\u7684\u5c55\u793a\u51fa\u6765\u3002<\/p>\n<p>\u200b    <img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000043330032\" alt=\"img\" title=\"img\" loading=\"lazy\"><\/p>\n<ul>\n<li>\u4efb\u610f\u4e00\u4e2a\u4e8c\u9879\u5f0f\u5c55\u5f00\u540e\u7684\u6570\u5b57\u4e58\u79ef\uff0c\u90fd\u53ef\u4ee5\u6620\u5c04\u5230\u6768\u8f89\u4e09\u89d2\u5bf9\u5e94\u7684\u4e2d\u7684\u6570\u5b57\u3002<\/li>\n<li>\u4e8c\u9879\u5f0f\u5c55\u5f00\u516c\u5f0f\u662f\u7528\u6765\u8ba1\u7b97\u7ed9\u5b9a\u4e8c\u9879\u5f0f\u7684\u6307\u6570\u5e42\u7684\u5c55\u5f00\u5f0f\u7684\u516c\u5f0f\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u4e8c\u9879\u5f0f (x + y)n\uff0c\u4e8c\u9879\u5f0f\u5c55\u5f00\u516c\u5f0f\u4e3a\uff1a<code>(x + y)^n = x^n + nx^{n-1}y + n(n-1)x^{n-2}y^2 + ... + y^n<\/code> \u8fd9\u4e2a\u516c\u5f0f\u4e5f\u6b63\u597d\u7b26\u5408\u6768\u8f89\u4e09\u89d2\u7684\u6570\u5b57\u503c\u3002<\/li>\n<\/ul>\n<h3>2. \u7ec4\u5408\u6570<\/h3>\n<p>\u7ec4\u5408\u6570\u662f\u6570\u5b66\u4e2d\u5b9a\u4e49\u7684\u4e00\u79cd\u6570\u5b66\u6982\u5ff5\uff0c\u7528\u4e8e\u8ba1\u7b97\u6709\u591a\u5c11\u79cd\u9009\u62e9\u53ef\u4ee5\u4ece\u4e00\u7ec4\u7269\u54c1\u4e2d\u9009\u62e9\u51fa\u82e5\u5e72\u7684\u7269\u54c1\u3002\u6bd4\u5982\u4f60\u65e9\u4e0a\u67095\u79cd\u6c34\u679c\u53ef\u4ee5\u5403\uff0c\u4f46\u4f60\u5403\u4e0d\u4e86\u90a3\u4e48\u591a\uff0c\u8ba9\u4f605\u79cd\u6c34\u679c\u4e2d\u90092\u4e2a\uff0c\u770b\u770b\u6709\u591a\u5c11\u79cd\u9009\u62e9\u3002\u901a\u8fc7\u4f7f\u7528\u516c\u5f0f c(n,k) = n!\/k!(n-k)! \u53ef\u4ee5\u8ba1\u7b97\u51fa\uff0c5\u90092\u670910\u79cd\u9009\u62e9\u3002<\/p>\n<p>\u90a3\u4e48\u8fd9\u6837\u4e00\u4e2a\u8ba1\u7b97\u4e5f\u662f\u53ef\u4ee5\u4f53\u73b0\u5728\u6768\u8f89\u4e09\u89d2\u4e2d\u7684\u3002<\/p>\n<p>\u200b    <img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000043330033\" alt=\"img\" title=\"img\" loading=\"lazy\"><\/p>\n<ul>\n<li>5\u90092\uff0c\u5728\u6768\u8f89\u4e09\u89d2\u4e2d\u53ef\u4ee5\u627e\u5230\u7b2c5\u884c\u7684\u7b2c2\u5217\uff0c\u7ed3\u679c\u662f10\u3002\u6309\u7167\u8fd9\u4e2a\u89c4\u5f8b\uff0c5\u90093=10\u30015\u90094=5<\/li>\n<\/ul>\n<h3>3. \u6590\u6ce2\u90a3\u5951\u6570\u5217<\/h3>\n<p>\u6590\u6ce2\u90a3\u5951\u6570\u5217\u51fa\u73b0\u5728\u5370\u5ea6\u6570\u5b66\u4e2d\uff0c\u4e0e\u68b5\u6587\u97f5\u5f8b\u6709\u5173\u3002\u5728\u68b5\u8bed\u8bd7\u6b4c\u4f20\u7edf\u4e2d\uff0c\u4eba\u4eec\u5bf9\u5217\u4e3e\u6240\u6709\u6301\u7eed\u65f6\u95f4\u4e3a 2 \u5355\u4f4d\u7684\u957f (L) \u97f3\u8282\u4e0e 1 \u5355\u4f4d\u6301\u7eed\u65f6\u95f4\u7684\u77ed (S) \u97f3\u8282\u5e76\u5217\u7684\u6a21\u5f0f\u5f88\u611f\u5174\u8da3\u3002\u5173\u4e8e\u66f4\u591a\u6590\u6ce2\u90a3\u5951\u66f4\u591a\u77e5\u8bc6\u53ef\u4ee5\u9605\u8bfb\u5c0f\u5085\u54e5\u7684\uff1a<a href=\"https:\/\/link.segmentfault.com\/?enc=WY%2FSA7xwBCSWJPlFOEfIOA%3D%3D.VjwgVLX5KHYNHorgmfRNBaitD40v5oto8KHWYYojpnIyp%2BhLiRdFHGgf%2BmP10JjFpcAw6bghG5jOztdKjwlZpm8bRmPX2o2n973fY8cx1tw%3D\" rel=\"nofollow\">\u300a\u7a0b\u5e8f\u5458\u6570\u5b66\uff1a\u6590\u6ce2\u90a3\u5951\u300b\u2014\u2014 \u4e3a\u4ec0\u4e48\u4e0d\u80fd\u7528\u6590\u6ce2\u90a3\u5951\u6563\u5217\uff0c\u505a\u6570\u636e\u5e93\u8def\u7531\u7b97\u6cd5\uff1f<\/a><\/p>\n<p>\u6590\u6ce2\u90a3\u5951\u6570\u5217\u53ef\u4ee5\u7531\u9012\u5f52\u5173\u7cfb\u5b9a\u4e49\uff1a<code>F0 = 0\uff0cF1 = 1\uff0cFn = Fn-1 + Fn-2<\/code><\/p>\n<table>\n<thead>\n<tr>\n<th align=\"center\">F0<\/th>\n<th align=\"center\">F1<\/th>\n<th align=\"center\">F2<\/th>\n<th align=\"center\">F3<\/th>\n<th align=\"center\">F4<\/th>\n<th align=\"center\">F5<\/th>\n<th align=\"center\">F6<\/th>\n<th align=\"center\">F7<\/th>\n<th align=\"center\">F8<\/th>\n<th align=\"center\">F9<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td align=\"center\">0<\/td>\n<td align=\"center\">1<\/td>\n<td align=\"center\">1<\/td>\n<td align=\"center\">2<\/td>\n<td align=\"center\">3<\/td>\n<td align=\"center\">5<\/td>\n<td align=\"center\">8<\/td>\n<td align=\"center\">13<\/td>\n<td align=\"center\">21<\/td>\n<td align=\"center\">34<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u800c\u8fd9\u6837\u4e00\u4e2a\u6709\u89c4\u5f8b\u7684\u6590\u6ce2\u90a3\u5951\u6570\u5217\u5728\u6768\u8f89\u4e09\u89d2\u4e2d\u4e5f\u662f\u6709\u6240\u4f53\u73b0\u7684\u3002<\/p>\n<p>\u200b    <img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000043330034\" alt=\"img\" title=\"img\" loading=\"lazy\"><\/p>\n<ul>\n<li>\u628a\u659c\u5bf9\u89d2\u7684\u6570\u5b57\u505a\u52a0\u548c\uff0c\u4f1a\u5f97\u5230\u4e00\u7ec4\u6590\u6ce2\u90a3\u5951\u6570\u5217\uff1b1\u30011\u30012\u30013\u30015\u30018\u300113\u300115\u300133<\/li>\n<\/ul>\n<h3>4. \u6b21\u65b9\u6570<\/h3>\n<p>\u5728\u6768\u8f89\u4e09\u89d2\u4e2d\u8fd8\u6709\u4e00\u4e2a\u975e\u5e38\u6709\u610f\u601d\u7684\u7279\u6027\uff0c\u5c31\u662f\u67092\u7684\u6b21\u65b9\u548c11\u6b21\u65b9\u6570\u3002<\/p>\n<p><strong>2\u6b21\u65b9<\/strong><\/p>\n<p>\u200b    <img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000043330035\" alt=\"img\" title=\"img\" loading=\"lazy\"><\/p>\n<p>&#8211; \u6768\u8f89\u4e09\u89d2\u6bcf\u4e00\u884c\u7684\u6570\u5b57\u52a0\u548c\uff0c\u6b63\u597d\u76842\u76840\u6b21\u65b9\u30011\u6b21\u65b9..n\u6b21\u65b9<\/p>\n<p><strong>11\u6b21\u65b9<\/strong><\/p>\n<p>\u200b    <img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000043330036\" alt=\"img\" title=\"img\" loading=\"lazy\"><\/p>\n<ul>\n<li>\u53e6\u5916\u4e00\u4e2a\u662f11\u7684\u6b21\u5e42\uff0c\u4f8b\u598211\u76842\u6b21\u5e42\u7684\u7ed3\u679c\u6b63\u597d\u662f121\u8fd9\u4e00\u6392\u6570\u5b57\u7684\u7ec4\u5408\u3002\u5982\u679c\u662f11\u76845\u6b21\u5e42\uff0c\u4e2d\u95f4\u6709\u8fde\u7eed\u768410\uff0c\u5219\u662f\u628a\u540e\u4e00\u4f4d\u5411\u524d\u4e00\u4f4d\u8fdb\u4f4d\u4e00\u4e0b\u3002<\/li>\n<\/ul>\n<h3>5. \u5e73\u65b9\u6570<\/h3>\n<p>\u200b    <img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000043330037\" alt=\"img\" title=\"img\" loading=\"lazy\"><\/p>\n<ul>\n<li>\u5728\u6768\u8f89\u4e09\u89d2\u4e2d\u8fd8\u6709\u4e00\u4e2a\u5e73\u65b9\u6570\u7684\u89c4\u5f8b\u4f53\u73b0\u3002\u6bd4\u59823\u7684\u5e73\u65b9\u6b63\u597d\u662f\u53f3\u4fa73+6\u7684\u7ed3\u679c\u30024\u7684\u5e73\u65b9\u662f\u53f3\u4fa76+10\u7684\u7ed3\u679c\u3002<\/li>\n<\/ul>\n<h2>\u56db\u3001\u6768\u8f89\u4e09\u89d2\u5b9e\u73b0<\/h2>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u5b9e\u73b0\u4e0b\u6768\u8f89\u4e09\u89d2\uff1b<\/p>\n<pre><code>public HashMap&lt;Integer, Integer&gt; pascalTriangle(int lineNumber) {\n    HashMap&lt;Integer, Integer&gt; currentLine = new HashMap&lt;&gt;();\n    currentLine.put(0, 1);\n    int currentLineSize = lineNumber + 1;\n    for (int numberIdx = 1; numberIdx &lt; currentLineSize; numberIdx += 1) {\n        \/*\n         * https:\/\/github.com\/trekhleb\/javascript-algorithms\/blob\/master\/src\/algorithms\/math\/pascal-triangle\/pascalTriangle.js\n         * \u7b2ci\u884c\u53f7\u4e2d\u7684\u7b2c -th \u4e2a\u6761\u76eelineNumber\u662f Binomial CoefficientC(lineNumber, i)\u5e76\u4e14\u6240\u6709\u884c\u90fd\u4ee5 value \u5f00\u59341\u3002\u8fd9\u4e2a\u601d\u8def\u662fC(lineNumber, i)\u4f7f\u7528C(lineNumber, i-1). \u5b83\u53ef\u4ee5O(1)\u4f7f\u7528\u4ee5\u4e0b\u65b9\u6cd5\u53ca\u65f6\u8ba1\u7b97\uff1a\n         * C(lineNumber, i)   = lineNumber! \/ ((lineNumber - i)! * i!)\n         * C(lineNumber, i - 1) = lineNumber! \/ ((lineNumber - i + 1)! * (i - 1)!)\n         *\n         * \u4ece\u4ee5\u4e0a\u4e24\u4e2a\u8868\u8fbe\u5f0f\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4e0b\u9762\u7684\u8868\u8fbe\u5f0f\uff1aC(lineNumber, i) = C(lineNumber, i - 1) * (lineNumber - i + 1) \/ i\n         * \u6240\u4ee5C(lineNumber, i)\u53ef\u4ee5\u4eceC(lineNumber, i - 1)\u65f6\u95f4\u4e0a\u7b97\u51fa\u6765O(1)\n         *\/\n        currentLine.put(numberIdx, ((null == currentLine.get(numberIdx - 1) ? 0 : currentLine.get(numberIdx - 1)) * (lineNumber - numberIdx + 1)) \/ numberIdx);\n    }\n    return currentLine;\n}<\/code><\/pre>\n<p><strong>\u5355\u5143\u6d4b\u8bd5<\/strong><\/p>\n<pre><code>@Test\npublic void test_PascalTriangle() {\n    PascalTriangle pascalTriangle = new PascalTriangle();\n    for (int i = 0; i &lt;= 10; i++) {\n        HashMap&lt;Integer, Integer&gt; currentLineMap = pascalTriangle.pascalTriangle(i);\n        System.out.println(JSON.toJSONString(currentLineMap.values()));\n    }\n}\n\n[1]\n[1,1]\n[1,2,1]\n[1,3,3,1]\n[1,4,6,4,1]\n[1,5,10,10,5,1]\n[1,6,15,20,15,6,1]\n[1,7,21,35,35,21,7,1]\n[1,8,28,56,70,56,28,8,1]\n[1,9,36,84,126,126,84,36,9,1]\n[1,10,45,120,210,252,210,120,45,10,1]<\/code><\/pre>\n<ul>\n<li>\u8fd9\u6837\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4e00\u7ec4\u6768\u8f89\u4e09\u89d2\u6570\u5217\u4e86\u3002<\/li>\n<\/ul>\n<h2>\u4e94\u3001\u5e38\u89c1\u9762\u8bd5\u9898<\/h2>\n<ul>\n<li>\u6768\u8f89\u4e09\u89d2\u6709\u54ea\u4e9b\u7528\u9014\uff1f<\/li>\n<li>\u7528\u4ee3\u7801\u5b9e\u73b0\u4e0b\u6768\u8f89\u4e09\u89d2\u3002\u2014\u2014 \u5728LeetCode\u4e2d\u4e5f\u6709\u8fd9\u6837\u7684\u9898\u76ee<\/li>\n<\/ul>\n<p><a href=\"https:\/\/segmentfault.com\/a\/1190000043330029\">https:\/\/segmentfault.com\/a\/1190000043330029<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4f5c\u8005\uff1a\u5c0f\u5085\u54e5 \u535a\u5ba2\uff1ahttps:\/\/bugstack.cn \u6c89\u6dc0\u3001\u5206\u4eab\u3001\u6210\u957f\uff0c\u8ba9\u81ea\u5df1\u548c\u4ed6\u4eba\u90fd\u80fd\u6709\u6240\u6536\u83b7\uff01\ud83d\ude04 \u4e00 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[4],"tags":[],"class_list":["post-10007076","post","type-post","status-publish","format-standard","hentry","category-share"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/itmax.cn\/index.php?rest_route=\/wp\/v2\/posts\/10007076","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/itmax.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/itmax.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/itmax.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/itmax.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10007076"}],"version-history":[{"count":0,"href":"https:\/\/itmax.cn\/index.php?rest_route=\/wp\/v2\/posts\/10007076\/revisions"}],"wp:attachment":[{"href":"https:\/\/itmax.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10007076"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/itmax.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10007076"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/itmax.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10007076"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}