{"id":974979,"date":"2024-12-27T06:09:34","date_gmt":"2024-12-26T22:09:34","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/974979.html"},"modified":"2024-12-27T06:09:36","modified_gmt":"2024-12-26T22:09:36","slug":"python%e5%a6%82%e4%bd%95%e7%bc%96%e5%86%99%e7%bb%84%e5%90%88%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/974979.html","title":{"rendered":"python\u5982\u4f55\u7f16\u5199\u7ec4\u5408\u6570"},"content":{"rendered":"

\"python\u5982\u4f55\u7f16\u5199\u7ec4\u5408\u6570\"<\/p>\n

\u5728Python\u4e2d\u7f16\u5199\u7ec4\u5408\u6570\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u6807\u51c6\u5e93\u4e2d\u7684math<\/code>\u6a21\u5757\u6765\u5b9e\u73b0\uff0c\u5176\u4e2dmath.comb<\/code>\u51fd\u6570\u662f\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u4f60\u8fd8\u53ef\u4ee5\u4f7f\u7528itertools<\/code>\u6a21\u5757\u4e2d\u7684combinations<\/code>\u51fd\u6570\u6765\u751f\u6210\u7ec4\u5408\u3002\u4f7f\u7528math.comb<\/code>\u51fd\u6570\u3001\u4f7f\u7528itertools.combinations<\/code>\u51fd\u6570\u3001\u624b\u52a8\u5b9e\u73b0\u7ec4\u5408\u6570\u516c\u5f0f\u3002<\/strong> \u4e0b\u9762\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8fd9\u4e09\u79cd\u65b9\u6cd5\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528 MATH.COMB \u51fd\u6570<\/h2>\n<\/p>\n

Python\u7684math<\/code>\u6a21\u5757\u81ea3.8\u7248\u8d77\u5f15\u5165\u4e86comb<\/code>\u51fd\u6570\uff0c\u7528\u4e8e\u8ba1\u7b97\u7ec4\u5408\u6570\u3002\u7ec4\u5408\u6570\u8868\u793a\u4ecen\u4e2a\u7269\u54c1\u4e2d\u9009\u53d6k\u4e2a\u7269\u54c1\u7684\u7ec4\u5408\u6570\u91cf\uff0c\u6570\u5b66\u4e0a\u8868\u793a\u4e3aC(n, k)\u3002<\/p>\n<\/p>\n

import math<\/p>\n
\u8ba1\u7b97C(n, k)<\/strong><\/h2>\n
n = 5<\/p>\n
k = 3<\/p>\n
combination = math.comb(n, k)<\/p>\n
print(f"C({n}, {k}) = {combination}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
1.1\u3001\u4f18\u70b9<\/h3>\n<\/p>\n
\u4f7f\u7528math.comb<\/code>\u51fd\u6570\u7684\u4e3b\u8981\u4f18\u70b9\u662f\u5176\u7b80\u5355\u6027\u548c\u5185\u7f6e\u7684\u53ef\u9760\u6027\u3002\u5b83\u76f4\u63a5\u8ba1\u7b97\u7ec4\u5408\u6570\uff0c\u907f\u514d\u4e86\u624b\u52a8\u5b9e\u73b0\u53ef\u80fd\u5e26\u6765\u7684\u9519\u8bef\u3002<\/p>\n<\/p>\n
1.2\u3001\u9650\u5236<\/h3>\n<\/p>\n
math.comb<\/code>\u51fd\u6570\u5728\u8ba1\u7b97\u5927\u6570\u65f6\u4e5f\u80fd\u4fdd\u6301\u9ad8\u6548\uff0c\u4f46\u5b83\u9700\u8981Python 3.8\u6216\u66f4\u9ad8\u7248\u672c\u3002\u5982\u679c\u4f60\u4f7f\u7528\u7684\u662f\u8f83\u4f4e\u7248\u672c\u7684Python\uff0c\u9700\u8981\u8003\u8651\u5176\u4ed6\u65b9\u6cd5\u3002<\/p>\n<\/p>\n
\u4e8c\u3001\u4f7f\u7528 ITERTOOLS.COMBINATIONS \u51fd\u6570<\/h2>\n<\/p>\n
itertools<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u4e00\u4e2acombinations<\/code>\u51fd\u6570\uff0c\u53ef\u4ee5\u751f\u6210\u4e00\u4e2a\u8fed\u4ee3\u5668\uff0c\u8fd4\u56de\u8f93\u5165\u53ef\u8fed\u4ee3\u5bf9\u8c61\u7684\u6240\u6709\u7ec4\u5408\u3002<\/p>\n<\/p>\n
import itertools<\/p>\n
\u751f\u6210\u6240\u6709\u7ec4\u5408<\/strong><\/h2>\n
elements = [1, 2, 3, 4, 5]<\/p>\n
k = 3<\/p>\n
combinations = itertools.combinations(elements, k)<\/p>\n
\u6253\u5370\u6240\u6709\u7ec4\u5408<\/strong><\/h2>\n
for combo in combinations:<\/p>\n
    print(combo)<\/p>\n
<\/code><\/pre>\n<\/p>\n
2.1\u3001\u4f18\u70b9<\/h3>\n<\/p>\n
itertools.combinations<\/code>\u4e0d\u4ec5\u8ba1\u7b97\u7ec4\u5408\u6570\uff0c\u8fd8\u751f\u6210\u6240\u6709\u53ef\u80fd\u7684\u7ec4\u5408\uff0c\u8fd9\u5bf9\u4e8e\u9700\u8981\u8bbf\u95ee\u6240\u6709\u7ec4\u5408\u7684\u573a\u666f\u975e\u5e38\u6709\u7528\u3002<\/p>\n<\/p>\n
2.2\u3001\u5e94\u7528\u573a\u666f<\/h3>\n<\/p>\n
\u8fd9\u79cd\u65b9\u6cd5\u9002\u7528\u4e8e\u9700\u8981\u751f\u6210\u7ec4\u5408\u7684\u573a\u666f\uff0c\u4f8b\u5982\uff0c\u5728\u6570\u636e\u5206\u6790\u4e2d\u9700\u8981\u68c0\u67e5\u6570\u636e\u5b50\u96c6\u7684\u60c5\u51b5\u3002<\/p>\n<\/p>\n
\u4e09\u3001\u624b\u52a8\u5b9e\u73b0\u7ec4\u5408\u6570\u516c\u5f0f<\/h2>\n<\/p>\n
\u5982\u679c\u4f60\u9700\u8981\u5728\u4e0d\u4f9d\u8d56\u5916\u90e8\u5e93\u7684\u60c5\u51b5\u4e0b\u8ba1\u7b97\u7ec4\u5408\u6570\uff0c\u53ef\u4ee5\u624b\u52a8\u5b9e\u73b0\u7ec4\u5408\u6570\u516c\u5f0f\u3002\u7ec4\u5408\u6570\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n
[ C(n, k) = \\frac{n!}{k!(n-k)!} ]<\/p>\n<\/p>\n
def factorial(n):<\/p>\n
    if n == 0 or n == 1:<\/p>\n
        return 1<\/p>\n
    else:<\/p>\n
        return n * factorial(n - 1)<\/p>\n
def comb(n, k):<\/p>\n
    return factorial(n) \/\/ (factorial(k) * factorial(n - k))<\/p>\n
\u8ba1\u7b97C(n, k)<\/strong><\/h2>\n
n = 5<\/p>\n
k = 3<\/p>\n
combination = comb(n, k)<\/p>\n
print(f"C({n}, {k}) = {combination}")<\/p>\n
<\/code><\/pre>\n<\/p>\n
3.1\u3001\u4f18\u70b9<\/h3>\n<\/p>\n
\u624b\u52a8\u5b9e\u73b0\u7ec4\u5408\u6570\u516c\u5f0f\u53ef\u4ee5\u5e2e\u52a9\u4f60\u6df1\u5165\u7406\u89e3\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\u539f\u7406\uff0c\u9002\u5408\u5b66\u4e60\u548c\u6559\u5b66\u76ee\u7684\u3002<\/p>\n<\/p>\n
3.2\u3001\u4f18\u5316\u63d0\u793a<\/h3>\n<\/p>\n
\u5728\u5b9e\u73b0\u8fc7\u7a0b\u4e2d\uff0c\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u6216\u8bb0\u5fc6\u5316\u6280\u672f\u6765\u4f18\u5316\u9012\u5f52\u8ba1\u7b97\u7684\u6548\u7387\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u5927\u6570\u65f6\u3002<\/p>\n<\/p>\n
\u56db\u3001\u7ec4\u5408\u6570\u5728\u5b9e\u9645\u4e2d\u7684\u5e94\u7528<\/h2>\n<\/p>\n
\u7ec4\u5408\u6570\u5728\u5f88\u591a\u5b9e\u9645\u95ee\u9898\u4e2d\u90fd\u626e\u6f14\u7740\u91cd\u8981\u89d2\u8272\u3002\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5e38\u89c1\u7684\u5e94\u7528\u573a\u666f\uff1a<\/p>\n<\/p>\n
4.1\u3001\u6982\u7387\u8bba\u548c\u7edf\u8ba1\u5b66<\/h3>\n<\/p>\n
\u7ec4\u5408\u6570\u5728\u6982\u7387\u8bba\u4e2d\u7528\u4e8e\u8ba1\u7b97\u4e8b\u4ef6\u7684\u53ef\u80fd\u6027\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u4ece\u4e00\u526f\u6251\u514b\u724c\u4e2d\u62bd\u53d6\u4e94\u5f20\u724c\u7684\u6240\u6709\u53ef\u80fd\u7ec4\u5408\uff0c\u4ee5\u786e\u5b9a\u83b7\u5f97\u7279\u5b9a\u624b\u724c\u7684\u6982\u7387\u3002<\/p>\n<\/p>\n
4.2\u3001\u7b97\u6cd5\u548c\u6570\u636e\u7ed3\u6784<\/h3>\n<\/p>\n
\u5728\u7b97\u6cd5\u8bbe\u8ba1\u4e2d\uff0c\u7ec4\u5408\u6570\u7528\u4e8e\u89e3\u51b3\u7ec4\u5408\u4f18\u5316\u95ee\u9898\uff0c\u5982\u80cc\u5305\u95ee\u9898\u548c\u65c5\u884c\u5546\u95ee\u9898\u3002\u8fd9\u4e9b\u95ee\u9898\u6d89\u53ca\u5728\u5927\u91cf\u53ef\u80fd\u7ec4\u5408\u4e2d\u9009\u62e9\u6700\u4f73\u7ec4\u5408\u3002<\/p>\n<\/p>\n
4.3\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7684\u7ec4\u5408\u751f\u6210<\/h3>\n<\/p>\n
\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\uff0c\u7ec4\u5408\u751f\u6210\u7528\u4e8e\u751f\u6210\u6d4b\u8bd5\u7528\u4f8b\u6216\u5728\u5bc6\u7801\u5b66\u4e2d\u751f\u6210\u53ef\u80fd\u7684\u5bc6\u94a5\u7ec4\u5408\u3002<\/p>\n<\/p>\n
\u4e94\u3001\u4f18\u5316\u7ec4\u5408\u6570\u8ba1\u7b97\u7684\u9ad8\u7ea7\u6280\u5de7<\/h2>\n<\/p>\n
\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u7ec4\u5408\u6570\u8ba1\u7b97\u53ef\u80fd\u6d89\u53ca\u5927\u6570\u8fd0\u7b97\uff0c\u4ee5\u4e0b\u662f\u4e00\u4e9b\u4f18\u5316\u6280\u5de7\uff1a<\/p>\n<\/p>\n
5.1\u3001\u4f7f\u7528\u5bf9\u79f0\u6027<\/h3>\n<\/p>\n
\u7531\u4e8e\u7ec4\u5408\u6570\u5177\u6709\u5bf9\u79f0\u6027\uff0c\u5373C(n, k) = C(n, n-k)\uff0c\u53ef\u4ee5\u5728k > n\/2\u65f6\u4f7f\u7528C(n, n-k)\u6765\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002<\/p>\n<\/p>\n
5.2\u3001\u52a8\u6001\u89c4\u5212<\/h3>\n<\/p>\n
\u52a8\u6001\u89c4\u5212\u662f\u4e00\u79cd\u4f18\u5316\u9012\u5f52\u8ba1\u7b97\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u7528\u4e8e\u9884\u5148\u8ba1\u7b97\u548c\u5b58\u50a8\u5b50\u95ee\u9898\u7684\u89e3\uff0c\u4ece\u800c\u907f\u514d\u91cd\u590d\u8ba1\u7b97\u3002<\/p>\n<\/p>\n
5.3\u3001\u8fed\u4ee3\u8ba1\u7b97<\/h3>\n<\/p>\n
\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u901a\u8fc7\u8fed\u4ee3\u800c\u4e0d\u662f\u9012\u5f52\u6765\u8ba1\u7b97\u7ec4\u5408\u6570\uff0c\u8fd9\u53ef\u4ee5\u51cf\u5c11\u6808\u6ea2\u51fa\u7684\u98ce\u9669\u548c\u5185\u5b58\u6d88\u8017\u3002<\/p>\n<\/p>\n
\u901a\u8fc7\u4ee5\u4e0a\u51e0\u79cd\u65b9\u6cd5\u548c\u6280\u5de7\uff0c\u4f60\u53ef\u4ee5\u5728Python\u4e2d\u6709\u6548\u5730\u8ba1\u7b97\u548c\u5e94\u7528\u7ec4\u5408\u6570\u3002\u65e0\u8bba\u662f\u4f7f\u7528\u5185\u7f6e\u51fd\u6570\u8fd8\u662f\u624b\u52a8\u5b9e\u73b0\uff0c\u4e86\u89e3\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\u539f\u7406\u548c\u5e94\u7528\u573a\u666f\u90fd\u80fd\u5e2e\u52a9\u4f60\u5728\u5b9e\u9645\u9879\u76ee\u4e2d\u66f4\u597d\u5730\u89e3\u51b3\u95ee\u9898\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5982\u4f55\u5728Python\u4e2d\u8ba1\u7b97\u7ec4\u5408\u6570\uff1f<\/strong>
\u8981\u8ba1\u7b97\u7ec4\u5408\u6570\uff0c\u53ef\u4ee5\u4f7f\u7528Python\u4e2d\u7684\u6570\u5b66\u5e93\u3002math<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u4e00\u4e2a\u540d\u4e3acomb<\/code>\u7684\u51fd\u6570\uff0c\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\u7ec4\u5408\u6570\u3002\u7ec4\u5408\u6570\u516c\u5f0f\u4e3aC(n, k) = n! \/ (k!(n-k)!)\uff0c\u60a8\u53ea\u9700\u4f20\u5165n\u548ck\u7684\u503c\u5373\u53ef\u83b7\u53d6\u7ed3\u679c\u3002\u4f8b\u5982\uff1a<\/p>\n
import math\n\nn = 5\nk = 2\nresult = math.comb(n, k)\nprint(result)  # \u8f93\u51fa10\n<\/code><\/pre>\n
Python\u662f\u5426\u6709\u5185\u7f6e\u51fd\u6570\u6765\u5904\u7406\u7ec4\u5408\u6570\uff1f<\/strong>
\u662f\u7684\uff0cPython\u7684math<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86comb<\/code>\u51fd\u6570\uff0c\u53ef\u4ee5\u65b9\u4fbf\u5730\u8ba1\u7b97\u7ec4\u5408\u6570\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u53ef\u4ee5\u4f7f\u7528\u81ea\u5b9a\u4e49\u51fd\u6570\u5b9e\u73b0\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\uff0c\u8fd9\u6837\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u5176\u80cc\u540e\u7684\u903b\u8f91\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u81ea\u5b9a\u4e49\u7ec4\u5408\u6570\u8ba1\u7b97\u7684\u793a\u4f8b\uff1a<\/p>\n
def combination(n, k):\n    if k > n:\n        return 0\n    if k == 0 or k == n:\n        return 1\n    return factorial(n) \/\/ (factorial(k) * factorial(n - k))\n\nprint(combination(5, 2))  # \u8f93\u51fa10\n<\/code><\/pre>\n
\u5728\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\u4e2d\uff0c\u5982\u4f55\u5904\u7406\u5927\u6570\u95ee\u9898\uff1f<\/strong>
\u5728\u8ba1\u7b97\u8f83\u5927\u7684\u7ec4\u5408\u6570\u65f6\uff0c\u53ef\u80fd\u4f1a\u9047\u5230\u6574\u6570\u6ea2\u51fa\u7684\u95ee\u9898\u3002Python\u7684\u6574\u6570\u7c7b\u578b\u662f\u52a8\u6001\u7684\uff0c\u53ef\u4ee5\u81ea\u52a8\u6269\u5c55\uff0c\u56e0\u6b64\u60a8\u53ef\u4ee5\u653e\u5fc3\u4f7f\u7528\u3002\u4e0d\u8fc7\uff0c\u4e3a\u4e86\u63d0\u9ad8\u6027\u80fd\uff0c\u53ef\u4ee5\u8003\u8651\u4f7f\u7528math.comb<\/code>\u51fd\u6570\uff0c\u5b83\u5728\u5185\u90e8\u8fdb\u884c\u4e86\u4f18\u5316\u5904\u7406\uff0c\u80fd\u591f\u6709\u6548\u8ba1\u7b97\u5927\u6570\u7684\u7ec4\u5408\u6570\u3002<\/p>\n
\u5982\u4f55\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u4f7f\u7528\u7ec4\u5408\u6570\uff1f<\/strong>
\u7ec4\u5408\u6570\u5728\u8bb8\u591a\u9886\u57df\u90fd\u6709\u5e7f\u6cdb\u5e94\u7528\uff0c\u4f8b\u5982\u5728\u6982\u7387\u8bba\u3001\u7edf\u8ba1\u5b66\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u3002\u60a8\u53ef\u4ee5\u7528\u7ec4\u5408\u6570\u6765\u89e3\u51b3\u9009\u62e9\u95ee\u9898\uff0c\u6bd4\u5982\u4ece\u4e00\u7ec4\u7269\u54c1\u4e2d\u9009\u62e9\u7279\u5b9a\u6570\u91cf\u7684\u7269\u54c1\u3002\u5728\u6570\u636e\u5206\u6790\u548c\u673a\u5668\u5b66\u4e60<\/a>\u4e2d\uff0c\u7ec4\u5408\u6570\u4e5f\u5e38\u7528\u4e8e\u7279\u5f81\u9009\u62e9\u548c\u6a21\u578b\u8bc4\u4f30\u3002\u901a\u8fc7\u7406\u89e3\u7ec4\u5408\u6570\u7684\u8ba1\u7b97\uff0c\u60a8\u53ef\u4ee5\u66f4\u597d\u5730\u5e94\u7528\u8fd9\u4e9b\u6982\u5ff5\u4e8e\u5b9e\u9645\u95ee\u9898\u4e2d\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\u7f16\u5199\u7ec4\u5408\u6570\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u6807\u51c6\u5e93\u4e2d\u7684math\u6a21\u5757\u6765\u5b9e\u73b0\uff0c\u5176\u4e2dmath.comb\u51fd\u6570\u662f\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\u3002 […]","protected":false},"author":3,"featured_media":974987,"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\/974979"}],"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=974979"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/974979\/revisions"}],"predecessor-version":[{"id":974989,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/974979\/revisions\/974989"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/974987"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=974979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=974979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=974979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}