{"id":991477,"date":"2024-12-27T08:28:57","date_gmt":"2024-12-27T00:28:57","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/991477.html"},"modified":"2024-12-27T08:28:59","modified_gmt":"2024-12-27T00:28:59","slug":"python%e5%a6%82%e4%bd%95%e8%ae%a1%e7%ae%97%e7%bb%84%e5%90%88%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/991477.html","title":{"rendered":"python\u5982\u4f55\u8ba1\u7b97\u7ec4\u5408\u6570"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25065747\/ba37bac8-7665-4f82-9288-69d49d4ad7c1.webp\" alt=\"python\u5982\u4f55\u8ba1\u7b97\u7ec4\u5408\u6570\" \/><\/p>\n<p><p> <strong>\u5728Python\u4e2d\u8ba1\u7b97\u7ec4\u5408\u6570\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528math\u5e93\u4e2d\u7684comb\u51fd\u6570\u3001\u4f7f\u7528\u81ea\u5b9a\u4e49\u51fd\u6570\u5b9e\u73b0\u9012\u5f52\u8ba1\u7b97\u3001\u5229\u7528\u516c\u5f0f\u7ed3\u5408\u5faa\u73af\u4e09\u79cd\u65b9\u5f0f\u6765\u5b9e\u73b0\u3002<\/strong>\u5176\u4e2d\uff0c\u6700\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u6cd5\u662f\u4f7f\u7528math\u5e93\u4e2d\u7684comb\u51fd\u6570\uff0c\u56e0\u4e3a\u5b83\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5185\u7f6e\u7684\u3001\u4f18\u5316\u7684\u7ec4\u5408\u6570\u8ba1\u7b97\u3002\u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e09\u79cd\u65b9\u6cd5\u3002<\/p>\n<\/p>\n<p><p>\u4e00\u3001\u4f7f\u7528math\u5e93\u4e2d\u7684comb\u51fd\u6570<\/p>\n<\/p>\n<p><p>Python\u7684math\u5e93\u81ea3.8\u7248\u672c\u5f00\u59cb\u5f15\u5165\u4e86\u4e00\u4e2a\u65b0\u7684\u51fd\u6570comb\uff0c\u53ef\u4ee5\u7528\u4e8e\u8ba1\u7b97\u7ec4\u5408\u6570\u3002\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u65b9\u4fbf\u7684\u51fd\u6570\uff0c\u56e0\u4e3a\u5b83\u76f4\u63a5\u63d0\u4f9b\u4e86\u7ec4\u5408\u6570\u8ba1\u7b97\u7684\u529f\u80fd\uff0c\u4f7f\u7528\u8d77\u6765\u975e\u5e38\u7b80\u5355\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import math<\/p>\n<p>def calculate_combination_math(n, k):<\/p>\n<p>    return math.comb(n, k)<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>n = 5<\/p>\n<p>k = 2<\/p>\n<p>print(f&quot;\u7ec4\u5408\u6570C({n}, {k}) =&quot;, calculate_combination_math(n, k))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca<\/strong>\uff1amath.comb(n, k)\u51fd\u6570\u8fd4\u56de\u4ecen\u4e2a\u5143\u7d20\u4e2d\u9009\u53d6k\u4e2a\u5143\u7d20\u7684\u7ec4\u5408\u6570\uff0c\u4e0d\u9700\u8981\u989d\u5916\u7684\u5b9e\u73b0\uff0c\u53ea\u9700\u8c03\u7528\u5373\u53ef\u3002\u8be5\u51fd\u6570\u4f7f\u7528\u4e86\u5185\u90e8\u4f18\u5316\u7b97\u6cd5\uff0c\u6548\u7387\u8f83\u9ad8\u3002<\/p>\n<\/p>\n<p><p>\u4e8c\u3001\u4f7f\u7528\u9012\u5f52\u5b9e\u73b0\u7ec4\u5408\u6570<\/p>\n<\/p>\n<p><p>\u9012\u5f52\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u7f16\u7a0b\u601d\u60f3\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u89e3\u51b3\u8bb8\u591a\u6570\u5b66\u95ee\u9898\uff0c\u5305\u62ec\u7ec4\u5408\u6570\u8ba1\u7b97\u3002\u9012\u5f52\u5b9e\u73b0\u7ec4\u5408\u6570\u7684\u5173\u952e\u5728\u4e8e\u7406\u89e3\u7ec4\u5408\u6570\u7684\u9012\u5f52\u516c\u5f0f\uff1aC(n, k) = C(n-1, k-1) + C(n-1, k)\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def calculate_combination_recursive(n, k):<\/p>\n<p>    if k == 0 or k == n:<\/p>\n<p>        return 1<\/p>\n<p>    return calculate_combination_recursive(n-1, k-1) + calculate_combination_recursive(n-1, k)<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>n = 5<\/p>\n<p>k = 2<\/p>\n<p>print(f&quot;\u7ec4\u5408\u6570C({n}, {k}) =&quot;, calculate_combination_recursive(n, k))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca<\/strong>\uff1a\u5728\u9012\u5f52\u5b9e\u73b0\u4e2d\uff0c\u57fa\u4f8b\uff08base case\uff09\u662f\u5f53k\u7b49\u4e8e0\u6216k\u7b49\u4e8en\u65f6\uff0c\u7ec4\u5408\u6570\u4e3a1\u3002\u5426\u5219\uff0c\u9012\u5f52\u8c03\u7528\u81ea\u8eab\u6765\u8ba1\u7b97\u7ec4\u5408\u6570\u3002<\/p>\n<\/p>\n<p><p>\u4e09\u3001\u4f7f\u7528\u516c\u5f0f\u7ed3\u5408\u5faa\u73af<\/p>\n<\/p>\n<p><p>\u7ec4\u5408\u6570\u7684\u516c\u5f0f\u4e3aC(n, k) = n! \/ (k! * (n-k)!)\uff0c\u56e0\u6b64\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u9636\u4e58\u6765\u5f97\u5230\u7ec4\u5408\u6570\u3002Python\u63d0\u4f9b\u4e86\u4e00\u4e2a\u51fd\u6570math.factorial\u6765\u8ba1\u7b97\u9636\u4e58\uff0c\u53ef\u4ee5\u5229\u7528\u8fd9\u4e2a\u51fd\u6570\u5b9e\u73b0\u7ec4\u5408\u6570\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import math<\/p>\n<p>def calculate_combination_factorial(n, k):<\/p>\n<p>    return math.factorial(n) \/\/ (math.factorial(k) * math.factorial(n - k))<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>n = 5<\/p>\n<p>k = 2<\/p>\n<p>print(f&quot;\u7ec4\u5408\u6570C({n}, {k}) =&quot;, calculate_combination_factorial(n, k))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca<\/strong>\uff1a\u5728\u8fd9\u4e2a\u5b9e\u73b0\u4e2d\uff0c\u9996\u5148\u8ba1\u7b97n\u7684\u9636\u4e58\uff0c\u7136\u540e\u8ba1\u7b97k\u7684\u9636\u4e58\u548c(n-k)\u7684\u9636\u4e58\uff0c\u6700\u540e\u4f7f\u7528\u516c\u5f0f\u8ba1\u7b97\u7ec4\u5408\u6570\u3002\u8fd9\u91cc\u4f7f\u7528\u4e86\u6574\u6570\u9664\u6cd5\uff08\/\/\uff09\uff0c\u56e0\u4e3a\u7ec4\u5408\u6570\u603b\u662f\u6574\u6570\u3002<\/p>\n<\/p>\n<p><p>\u56db\u3001\u4f18\u5316\u5faa\u73af\u8ba1\u7b97\u7ec4\u5408\u6570<\/p>\n<\/p>\n<p><p>\u5728\u5904\u7406\u5927\u6570\u65f6\uff0c\u4f7f\u7528\u9636\u4e58\u7684\u65b9\u5f0f\u53ef\u80fd\u5bfc\u81f4\u6570\u503c\u6ea2\u51fa\uff0c\u56e0\u6b64\u53ef\u4ee5\u4f7f\u7528\u4f18\u5316\u7684\u5faa\u73af\u8ba1\u7b97\u65b9\u6cd5\u3002\u8fd9\u79cd\u65b9\u6cd5\u901a\u8fc7\u9010\u6b65\u76f8\u4e58\u548c\u9010\u6b65\u76f8\u9664\u6765\u907f\u514d\u8ba1\u7b97\u5927\u6570\u9636\u4e58\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def calculate_combination_optimized(n, k):<\/p>\n<p>    if k &gt; n - k:<\/p>\n<p>        k = n - k  # \u4f7f\u7528\u5bf9\u79f0\u6027\u8d28C(n, k) = C(n, n-k)<\/p>\n<p>    c = 1<\/p>\n<p>    for i in range(k):<\/p>\n<p>        c = c * (n - i) \/\/ (i + 1)<\/p>\n<p>    return c<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>n = 5<\/p>\n<p>k = 2<\/p>\n<p>print(f&quot;\u7ec4\u5408\u6570C({n}, {k}) =&quot;, calculate_combination_optimized(n, k))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca<\/strong>\uff1a\u901a\u8fc7\u5bf9\u79f0\u6027\u8d28\uff0c\u53ef\u4ee5\u51cf\u5c11\u8ba1\u7b97\u7684\u6b21\u6570\u3002\u5f53k &gt; n-k\u65f6\uff0c\u8ba1\u7b97C(n, n-k)\u6bd4\u8ba1\u7b97C(n, k)\u66f4\u9ad8\u6548\u3002\u5728\u5faa\u73af\u4e2d\uff0c\u9010\u6b65\u76f8\u4e58\u5e76\u76f8\u9664\uff0c\u907f\u514d\u4e86\u8ba1\u7b97\u5927\u6570\u9636\u4e58\u3002<\/p>\n<\/p>\n<p><p>\u4e94\u3001\u52a8\u6001\u89c4\u5212\u65b9\u6cd5<\/p>\n<\/p>\n<p><p>\u52a8\u6001\u89c4\u5212\u662f\u4e00\u79cd\u6709\u6548\u7684\u89e3\u51b3\u7ec4\u5408\u6570\u8ba1\u7b97\u7684\u65b9\u5f0f\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u9700\u8981\u591a\u6b21\u8ba1\u7b97\u7ec4\u5408\u6570\u7684\u573a\u666f\u3002\u901a\u8fc7\u6784\u5efa\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4\uff0c\u9010\u6b65\u586b\u5145\u6bcf\u4e2a\u7ec4\u5408\u6570\u7684\u503c\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def calculate_combination_dp(n, k):<\/p>\n<p>    C = [[0 for _ in range(k + 1)] for _ in range(n + 1)]<\/p>\n<p>    for i in range(n + 1):<\/p>\n<p>        for j in range(min(i, k) + 1):<\/p>\n<p>            if j == 0 or j == i:<\/p>\n<p>                C[i][j] = 1<\/p>\n<p>            else:<\/p>\n<p>                C[i][j] = C[i-1][j-1] + C[i-1][j]<\/p>\n<p>    return C[n][k]<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>n = 5<\/p>\n<p>k = 2<\/p>\n<p>print(f&quot;\u7ec4\u5408\u6570C({n}, {k}) =&quot;, calculate_combination_dp(n, k))<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca<\/strong>\uff1a\u52a8\u6001\u89c4\u5212\u65b9\u6cd5\u901a\u8fc7\u6784\u5efa\u4e00\u4e2a\u4e8c\u7ef4\u6570\u7ec4C\uff0c\u9010\u6b65\u586b\u5145\u7ec4\u5408\u6570\u7684\u503c\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u5143\u7d20C[i][j]\uff0c\u6839\u636e\u9012\u63a8\u516c\u5f0fC(i, j) = C(i-1, j-1) + C(i-1, j)\u8fdb\u884c\u586b\u5145\u3002<\/p>\n<\/p>\n<p><p>\u516d\u3001\u603b\u7ed3<\/p>\n<\/p>\n<p><p>\u7ec4\u5408\u6570\u8ba1\u7b97\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u6570\u5b66\u95ee\u9898\uff0c\u53ef\u4ee5\u901a\u8fc7\u591a\u79cd\u65b9\u6cd5\u5728Python\u4e2d\u5b9e\u73b0\u3002\u4ece\u76f4\u63a5\u4f7f\u7528\u5185\u7f6e\u51fd\u6570\u5230\u9012\u5f52\u3001\u52a8\u6001\u89c4\u5212\uff0c\u6bcf\u79cd\u65b9\u6cd5\u90fd\u6709\u5176\u9002\u7528\u7684\u573a\u666f\u3002\u5bf9\u4e8e\u6027\u80fd\u8981\u6c42\u8f83\u9ad8\u7684\u573a\u666f\uff0c\u5efa\u8bae\u4f7f\u7528\u5185\u7f6e\u7684math.comb\u51fd\u6570\u6216\u4f18\u5316\u7684\u5faa\u73af\u8ba1\u7b97\u65b9\u6cd5\u3002\u5bf9\u4e8e\u9700\u8981\u7406\u89e3\u7ec4\u5408\u6570\u9012\u5f52\u6027\u8d28\u7684\u573a\u666f\uff0c\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u5b9e\u73b0\uff0c\u800c\u52a8\u6001\u89c4\u5212\u5219\u9002\u7528\u4e8e\u9700\u8981\u91cd\u590d\u8ba1\u7b97\u7684\u573a\u666f\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u5728Python\u4e2d\u8ba1\u7b97\u7ec4\u5408\u6570\uff1f<\/strong><br \/>\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528<code>math<\/code>\u6a21\u5757\u4e2d\u7684<code>comb<\/code>\u51fd\u6570\u6765\u8ba1\u7b97\u7ec4\u5408\u6570\u3002\u7ec4\u5408\u6570\u662f\u6307\u4ecen\u4e2a\u5143\u7d20\u4e2d\u9009\u53d6r\u4e2a\u5143\u7d20\u7684\u4e0d\u540c\u9009\u62e9\u65b9\u5f0f\uff0c\u516c\u5f0f\u4e3aC(n, r) = n! \/ (r! * (n &#8211; r)!)\u3002\u4f7f\u7528<code>math.comb(n, r)<\/code>\u53ef\u4ee5\u76f4\u63a5\u5f97\u5230\u7ed3\u679c\u3002\u4f8b\u5982\uff0c<code>import math; result = math.comb(5, 2)<\/code>\u5c06\u8fd4\u56de10\u3002<\/p>\n<p><strong>\u5728Python\u4e2d\u53ef\u4ee5\u4f7f\u7528\u54ea\u4e9b\u65b9\u6cd5\u8ba1\u7b97\u7ec4\u5408\u6570\uff1f<\/strong><br \/>\u9664\u4e86\u4f7f\u7528<code>math.comb<\/code>\uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u81ea\u5b9a\u4e49\u51fd\u6570\u6765\u8ba1\u7b97\u7ec4\u5408\u6570\u3002\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u6216\u8005\u5faa\u73af\u6765\u5b9e\u73b0\u3002\u4f8b\u5982\uff0c\u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570<code>comb(n, r)<\/code>\uff0c\u4f7f\u7528\u5faa\u73af\u8ba1\u7b97n\u7684\u9636\u4e58\uff0c\u5e76\u6839\u636e\u7ec4\u5408\u6570\u516c\u5f0f\u8fd4\u56de\u7ed3\u679c\u3002\u8fd9\u79cd\u65b9\u5f0f\u9002\u5408\u4e8e\u5bf9\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\u6709\u66f4\u9ad8\u81ea\u5b9a\u4e49\u9700\u6c42\u7684\u573a\u666f\u3002<\/p>\n<p><strong>\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u6709\u54ea\u4e9b\u573a\u666f\uff1f<\/strong><br \/>\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6982\u7387\u8bba\u3001\u7edf\u8ba1\u5b66\u53ca\u5404\u7c7b\u6e38\u620f\u548c\u51b3\u7b56\u5206\u6790\u4e2d\u3002\u4f8b\u5982\uff0c\u5728\u5f69\u7968\u6e38\u620f\u4e2d\uff0c\u8ba1\u7b97\u4e2d\u5956\u7684\u53ef\u80fd\u6027\uff1b\u5728\u9009\u4e3e\u4e2d\uff0c\u5206\u6790\u4e0d\u540c\u5019\u9009\u4eba\u7ec4\u5408\u7684\u6982\u7387\uff1b\u5728\u751f\u7269\u7edf\u8ba1\u4e2d\uff0c\u7814\u7a76\u57fa\u56e0\u7ec4\u5408\u7684\u53ef\u80fd\u6027\u3002\u8fd9\u4e9b\u573a\u666f\u90fd\u9700\u8981\u51c6\u786e\u8ba1\u7b97\u7ec4\u5408\u6570\u4ee5\u8fdb\u884c\u540e\u7eed\u5206\u6790\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\u8ba1\u7b97\u7ec4\u5408\u6570\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528math\u5e93\u4e2d\u7684comb\u51fd\u6570\u3001\u4f7f\u7528\u81ea\u5b9a\u4e49\u51fd\u6570\u5b9e\u73b0\u9012\u5f52\u8ba1\u7b97\u3001\u5229\u7528\u516c\u5f0f\u7ed3\u5408\u5faa\u73af [&hellip;]","protected":false},"author":3,"featured_media":991485,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/991477"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=991477"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/991477\/revisions"}],"predecessor-version":[{"id":991486,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/991477\/revisions\/991486"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/991485"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=991477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=991477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=991477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}