{"id":1187941,"date":"2025-01-15T20:11:20","date_gmt":"2025-01-15T12:11:20","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1187941.html"},"modified":"2025-01-15T20:11:23","modified_gmt":"2025-01-15T12:11:23","slug":"%e5%a6%82%e4%bd%95%e7%94%a8python%e7%ae%97%e5%87%ba24%e7%82%b9","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1187941.html","title":{"rendered":"\u5982\u4f55\u7528python\u7b97\u51fa24\u70b9"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25140401\/b35aa463-b15e-4079-b386-7b17c8576916.webp\" alt=\"\u5982\u4f55\u7528python\u7b97\u51fa24\u70b9\" \/><\/p>\n<p><p> <strong>\u8981\u7528Python\u7b97\u51fa24\u70b9\uff0c\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u3001\u5229\u7528\u56db\u5219\u8fd0\u7b97\u7b26\u3001\u6392\u5217\u7ec4\u5408\u7b49\u65b9\u6cd5\u3002<\/strong>\u3001<strong>\u5176\u4e2d\u4e00\u4e2a\u6709\u6548\u7684\u65b9\u6cd5\u662f\u4f7f\u7528\u9012\u5f52\u6765\u679a\u4e3e\u6240\u6709\u53ef\u80fd\u7684\u8fd0\u7b97\u65b9\u5f0f<\/strong>\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u8be6\u7ec6\u63cf\u8ff0\u5982\u4f55\u7528Python\u5b9e\u73b024\u70b9\u6e38\u620f\u7684\u6c42\u89e3\u3002<\/p>\n<\/p>\n<hr>\n<p><h3>\u4e00\u300124\u70b9\u6e38\u620f\u7684\u57fa\u672c\u89c4\u5219\u4e0e\u601d\u8def<\/h3>\n<\/p>\n<p><p>24\u70b9\u6e38\u620f\u662f\u4e00\u79cd\u6570\u5b66\u76ca\u667a\u6e38\u620f\uff0c\u4f7f\u75284\u4e2a1\u523010\u4e4b\u95f4\u7684\u724c\uff0c\u901a\u8fc7\u52a0(+)\u3001\u51cf(-)\u3001\u4e58(*)\u3001\u9664(\/)\u56db\u79cd\u8fd0\u7b97\u4f7f\u5176\u7ed3\u679c\u7b49\u4e8e24\u3002\u73a9\u5bb6\u53ef\u4ee5\u6539\u53d8\u6570\u5b57\u7684\u987a\u5e8f\u548c\u8fd0\u7b97\u7684\u987a\u5e8f\uff0c\u4f46\u6bcf\u5f20\u724c\u5fc5\u987b\u4e14\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21\u3002<\/p>\n<\/p>\n<p><h3>\u4e8c\u3001\u9012\u5f52\u6c42\u89e3\u6cd5<\/h3>\n<\/p>\n<p><p>\u9012\u5f52\u6c42\u89e3\u6cd5\u662f\u89e3\u51b324\u70b9\u95ee\u9898\u7684\u5e38\u7528\u65b9\u6cd5\u3002\u5176\u57fa\u672c\u601d\u8def\u662f\uff1a<\/p>\n<\/p>\n<ol>\n<li>\u4ece4\u4e2a\u6570\u4e2d\u9009\u62e9\u4e24\u4e2a\u6570\u8fdb\u884c\u4e00\u6b21\u8fd0\u7b97\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u6570\uff0c\u5269\u4e0b\u76843\u4e2a\u6570\u7ee7\u7eed\u8fdb\u884c\u76f8\u540c\u7684\u64cd\u4f5c\uff0c\u76f4\u5230\u53ea\u6709\u4e00\u4e2a\u6570\uff0c\u8fd9\u4e2a\u6570\u662f\u5426\u7b49\u4e8e24\u3002<\/li>\n<li>\u8981\u8003\u8651\u6240\u6709\u7684\u8fd0\u7b97\u987a\u5e8f\u4ee5\u53ca\u6570\u5b57\u987a\u5e8f\u3002<\/li>\n<\/ol>\n<p><h4>1. \u679a\u4e3e\u6240\u6709\u53ef\u80fd\u7684\u8fd0\u7b97<\/h4>\n<\/p>\n<p><p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u51fd\u6570\u6765\u679a\u4e3e\u4e24\u4e2a\u6570\u5b57\u7684\u6240\u6709\u53ef\u80fd\u8fd0\u7b97\u7ed3\u679c\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def possible_results(a, b):<\/p>\n<p>    return [a + b, a - b, b - a, a * b] + ([a \/ b] if b != 0 else []) + ([b \/ a] if a != 0 else [])<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u8fd9\u91cc\uff0c<code>possible_results<\/code>\u51fd\u6570\u8fd4\u56de\u4e24\u4e2a\u6570\u7684\u6240\u6709\u53ef\u80fd\u8fd0\u7b97\u7ed3\u679c\u3002<\/p>\n<\/p>\n<p><h4>2. \u5b9e\u73b0\u9012\u5f52\u6c42\u89e3\u51fd\u6570<\/h4>\n<\/p>\n<p><p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5b9e\u73b0\u4e00\u4e2a\u9012\u5f52\u51fd\u6570\u6765\u89e3\u51b324\u70b9\u95ee\u9898\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def can_reach_24(nums):<\/p>\n<p>    if len(nums) == 1:<\/p>\n<p>        return abs(nums[0] - 24) &lt; 1e-6  # \u8bef\u5dee\u8303\u56f4\u5185\u5224\u65ad\u662f\u5426\u7b49\u4e8e24<\/p>\n<p>    for i in range(len(nums)):<\/p>\n<p>        for j in range(len(nums)):<\/p>\n<p>            if i != j:<\/p>\n<p>                # \u9009\u62e9nums[i]\u548cnums[j]\u8fdb\u884c\u8fd0\u7b97<\/p>\n<p>                rem<a href=\"https:\/\/docs.pingcode.com\/blog\/59162.html\" target=\"_blank\">AI<\/a>ning = [nums[k] for k in range(len(nums)) if k != i and k != j]<\/p>\n<p>                for result in possible_results(nums[i], nums[j]):<\/p>\n<p>                    if can_reach_24(remaining + [result]):<\/p>\n<p>                        return True<\/p>\n<p>    return False<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>3. \u6d4b\u8bd5\u51fd\u6570<\/h4>\n<\/p>\n<p><p>\u6211\u4eec\u53ef\u4ee5\u7f16\u5199\u4e00\u4e2a\u7b80\u5355\u7684\u6d4b\u8bd5\u51fd\u6570\u6765\u9a8c\u8bc1\u6211\u4eec\u768424\u70b9\u6c42\u89e3\u5668\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def test_24_point_game():<\/p>\n<p>    test_cases = [<\/p>\n<p>        [3, 3, 8, 8],<\/p>\n<p>        [1, 2, 3, 4],<\/p>\n<p>        [5, 5, 5, 1],<\/p>\n<p>        [6, 6, 6, 6]<\/p>\n<p>    ]<\/p>\n<p>    for case in test_cases:<\/p>\n<p>        result = can_reach_24(case)<\/p>\n<p>        print(f&quot;Numbers: {case} -&gt; Can reach 24: {result}&quot;)<\/p>\n<p>test_24_point_game()<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e09\u3001\u4f18\u5316\u4e0e\u6269\u5c55<\/h3>\n<\/p>\n<p><p>\u867d\u7136\u4e0a\u8ff0\u65b9\u6cd5\u53ef\u4ee5\u89e3\u51b324\u70b9\u95ee\u9898\uff0c\u4f46\u5176\u6548\u7387\u5e76\u4e0d\u662f\u6700\u4f18\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u8fdb\u884c\u4f18\u5316\uff1a<\/p>\n<\/p>\n<p><h4>1. \u526a\u679d\u4f18\u5316<\/h4>\n<\/p>\n<p><p>\u5728\u9012\u5f52\u8fc7\u7a0b\u4e2d\uff0c\u5982\u679c\u67d0\u4e9b\u64cd\u4f5c\u660e\u663e\u65e0\u6548\uff08\u5982\u4e24\u4e2a\u6570\u76f8\u51cf\u7ed3\u679c\u4e3a\u8d1f\u6570\u4e14\u540e\u7eed\u8fd0\u7b97\u65e0\u610f\u4e49\uff09\uff0c\u53ef\u4ee5\u63d0\u524d\u526a\u679d\uff0c\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u8fd0\u7b97\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def can_reach_24_optimized(nums):<\/p>\n<p>    if len(nums) == 1:<\/p>\n<p>        return abs(nums[0] - 24) &lt; 1e-6<\/p>\n<p>    for i in range(len(nums)):<\/p>\n<p>        for j in range(len(nums)):<\/p>\n<p>            if i != j:<\/p>\n<p>                remaining = [nums[k] for k in range(len(nums)) if k != i and k != j]<\/p>\n<p>                for result in possible_results(nums[i], nums[j]):<\/p>\n<p>                    if result &lt; 0:<\/p>\n<p>                        continue  # \u526a\u679d<\/p>\n<p>                    if can_reach_24_optimized(remaining + [result]):<\/p>\n<p>                        return True<\/p>\n<p>    return False<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2. \u8bb0\u5f55\u8fd0\u7b97\u8fc7\u7a0b<\/h4>\n<\/p>\n<p><p>\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u548c\u8c03\u8bd5\uff0c\u6211\u4eec\u53ef\u4ee5\u8bb0\u5f55\u8fd0\u7b97\u8fc7\u7a0b\u5e76\u8f93\u51fa\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def can_reach_24_with_trace(nums, trace=[]):<\/p>\n<p>    if len(nums) == 1:<\/p>\n<p>        if abs(nums[0] - 24) &lt; 1e-6:<\/p>\n<p>            print(&quot; -&gt; &quot;.join(trace + [str(nums[0])]))<\/p>\n<p>            return True<\/p>\n<p>        return False<\/p>\n<p>    for i in range(len(nums)):<\/p>\n<p>        for j in range(len(nums)):<\/p>\n<p>            if i != j:<\/p>\n<p>                remaining = [nums[k] for k in range(len(nums)) if k != i and k != j]<\/p>\n<p>                for result in possible_results(nums[i], nums[j]):<\/p>\n<p>                    new_trace = trace + [f&quot;({nums[i]} op {nums[j]}) = {result}&quot;]<\/p>\n<p>                    if can_reach_24_with_trace(remaining + [result], new_trace):<\/p>\n<p>                        return True<\/p>\n<p>    return False<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u56db\u3001\u66f4\u591a\u7684\u8fd0\u7b97\u7b26\u4e0e\u89c4\u5219\u6269\u5c55<\/h3>\n<\/p>\n<p><p>\u572824\u70b9\u6e38\u620f\u7684\u57fa\u672c\u89c4\u5219\u57fa\u7840\u4e0a\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u6269\u5c55\u66f4\u591a\u7684\u8fd0\u7b97\u7b26\uff0c\u5982\u5e42\u8fd0\u7b97\u3001\u53d6\u4f59\u8fd0\u7b97\u7b49\uff0c\u6216\u8005\u6539\u53d8\u76ee\u6807\u6570\u503c\uff0c\u589e\u52a0\u6e38\u620f\u7684\u591a\u6837\u6027\u548c\u96be\u5ea6\u3002<\/p>\n<\/p>\n<p><h4>1. \u589e\u52a0\u5e42\u8fd0\u7b97<\/h4>\n<\/p>\n<p><pre><code class=\"language-python\">def possible_results_extended(a, b):<\/p>\n<p>    return [a + b, a - b, b - a, a * b, a &lt;strong&gt; b, b &lt;\/strong&gt; a] + ([a \/ b] if b != 0 else []) + ([b \/ a] if a != 0 else [])<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h4>2. \u6539\u53d8\u76ee\u6807\u6570\u503c<\/h4>\n<\/p>\n<p><p>\u6211\u4eec\u53ef\u4ee5\u5c06\u76ee\u6807\u6570\u503c\u4ece24\u6539\u4e3a\u4efb\u610f\u6574\u6570\u6216\u6d6e\u70b9\u6570\uff0c\u589e\u52a0\u6e38\u620f\u7684\u6311\u6218\u6027\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def can_reach_target(nums, target):<\/p>\n<p>    if len(nums) == 1:<\/p>\n<p>        return abs(nums[0] - target) &lt; 1e-6<\/p>\n<p>    for i in range(len(nums)):<\/p>\n<p>        for j in range(len(nums)):<\/p>\n<p>            if i != j:<\/p>\n<p>                remaining = [nums[k] for k in range(len(nums)) if k != i and k != j]<\/p>\n<p>                for result in possible_results(nums[i], nums[j]):<\/p>\n<p>                    if can_reach_target(remaining + [result], target):<\/p>\n<p>                        return True<\/p>\n<p>    return False<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h3>\u4e94\u3001\u603b\u7ed3<\/h3>\n<\/p>\n<p><p>\u901a\u8fc7\u9012\u5f52\u4e0e\u679a\u4e3e\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u6709\u6548\u5730\u89e3\u51b324\u70b9\u6e38\u620f\u95ee\u9898\u3002\u867d\u7136\u57fa\u672c\u7b97\u6cd5\u5df2\u7ecf\u80fd\u591f\u89e3\u51b3\u5927\u591a\u6570\u60c5\u51b5\uff0c\u4f46\u901a\u8fc7\u526a\u679d\u4f18\u5316\u3001\u8bb0\u5f55\u8fd0\u7b97\u8fc7\u7a0b\u548c\u6269\u5c55\u8fd0\u7b97\u7b26\u7b49\u65b9\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u8fdb\u4e00\u6b65\u63d0\u9ad8\u7b97\u6cd5\u7684\u6548\u7387\u548c\u8da3\u5473\u6027\u3002\u603b\u7684\u6765\u8bf4\uff0c24\u70b9\u6e38\u620f\u4e0d\u4ec5\u662f\u4e00\u4e2a\u6709\u8da3\u7684\u6570\u5b66\u76ca\u667a\u6e38\u620f\uff0c\u4e5f\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u7f16\u7a0b\u7ec3\u4e60\u9898\u3002\u5e0c\u671b\u901a\u8fc7\u672c\u6587\u7684\u8be6\u7ec6\u4ecb\u7ecd\uff0c\u80fd\u5e2e\u52a9\u8bfb\u8005\u66f4\u597d\u5730\u7406\u89e3\u548c\u5b9e\u73b024\u70b9\u6e38\u620f\u7684\u6c42\u89e3\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5982\u4f55\u4f7f\u7528Python\u5b9e\u73b024\u70b9\u6e38\u620f\u7684\u7b97\u6cd5\uff1f<\/strong><br \/>\u8981\u5b9e\u73b024\u70b9\u6e38\u620f\u7684\u7b97\u6cd5\uff0c\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u7684\u65b9\u6cd5\u6765\u5c1d\u8bd5\u6240\u6709\u53ef\u80fd\u7684\u8fd0\u7b97\u7b26\u548c\u6570\u5b57\u7ec4\u5408\u3002\u901a\u8fc7\u904d\u5386\u6240\u6709\u6570\u5b57\u7684\u6392\u5217\u548c\u8fd0\u7b97\u7b26\u7684\u7ec4\u5408\uff0c\u53ef\u4ee5\u68c0\u67e5\u662f\u5426\u80fd\u591f\u5f97\u5230\u7ed3\u679c24\u3002\u901a\u5e38\u53ef\u4ee5\u7528\u5230\u7684\u8fd0\u7b97\u7b26\u5305\u62ec\u52a0\u3001\u51cf\u3001\u4e58\u3001\u9664\u3002\u8fd8\u9700\u6ce8\u610f\u9664\u6cd5\u8fd0\u7b97\u4e2d\u7684\u9664\u6570\u4e0d\u80fd\u4e3a\u96f6\u3002<\/p>\n<p><strong>\u54ea\u4e9bPython\u5e93\u53ef\u4ee5\u5e2e\u52a9\u6211\u89e3\u51b324\u70b9\u95ee\u9898\uff1f<\/strong><br 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