T(n) = 25T(n/5)+n^2的时间复杂度

本文探讨了递归关系T(n)=a*T(n/b)+c*n^k的时间复杂度分析方法,当a=25, b=5, k=2时,得出T(n)的大O表示法为O(n^2*logn)。

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对于T(n) = a*T(n/b)+c*n^k;T(1) = c 这样的递归关系,有这样的结论:

if (a > b^k)   T(n) = O(n^(logb(a)));logb(a)b为底a的对数
if (a = b^k)   T(n) = O(n^k*logn);
if (a < b^k)   T(n) = O(n^k);

a=25; b = 5 ; k=2

a==b^k 故T(n)=O(n^k*logn)=O(n^2*logn)

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"allowedPrivateChat": false, "stopPrivateChat": true, "noPrivateChatUserNum": 0, "isShield": false, "flag": true }, { "groupMemberId": 100677, "rongUserId": "LML-21652619", "groupMemberImage": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:13:56:143/31.jpg", "nickName": "Chris", "laoMaNo": 917490, "sex": null, "isFriend": false, "groupMemberType": "NORMAL", "groupMemberState": true, "hasManRelated": false, "hasWomenRelated": false, "showRelated": true, "joinGroupDate": "2024-12-24T03:05:21.000 0000", "groupRemindState": false, "allowedPrivateChat": true, "stopPrivateChat": true, "noPrivateChatUserNum": 0, "isShield": false, "flag": true }, { "groupMemberId": 100638, "rongUserId": "LML-74370986", "groupMemberImage": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:13:56:134/10.jpg", "nickName": "Leo", "laoMaNo": 906259, "sex": null, "isFriend": false, "groupMemberType": "NORMAL", "groupMemberState": true, "hasManRelated": false, "hasWomenRelated": false, "showRelated": true, "joinGroupDate": "2024-12-20T08:31:18.000 0000", "groupRemindState": false, "allowedPrivateChat": true, "stopPrivateChat": true, "noPrivateChatUserNum": 0, "isShield": false, "flag": true }, { "groupMemberId": 100092, "rongUserId": "LML-24436764", "groupMemberImage": "http://image.laomahahaha.com/yyqc/20240730/upload_t1uohak97de6yvaxyoxt8rrd3cdh3kfz.jpg", "nickName": "哇咔咔", "laoMaNo": 145338, "sex": null, "isFriend": false, "groupMemberType": "NORMAL", "groupMemberState": true, "hasManRelated": false, "hasWomenRelated": false, "showRelated": true, "joinGroupDate": "2024-12-10T03:01:17.000 0000", "groupRemindState": false, "allowedPrivateChat": true, "stopPrivateChat": true, "noPrivateChatUserNum": 0, "isShield": false, "flag": true }, { "groupMemberId": 100035, "rongUserId": "LML-92216234", "groupMemberImage": "../../static/3.jpg", "nickName": "我不是家长", "laoMaNo": 629569, "sex": null, "isFriend": true, "groupMemberType": "NORMAL", "groupMemberState": true, "hasManRelated": false, "hasWomenRelated": false, "showRelated": true, "joinGroupDate": "2024-12-10T02:35:15.000 0000", "groupRemindState": false, "allowedPrivateChat": true, "stopPrivateChat": true, "noPrivateChatUserNum": 0, "isShield": false, "flag": true } ] let arr2 = [ { "groupNo": 66725586, "groupGroupingName": "1", "groupGroupingMemberNum": 5, "isGroupGroupingMember": false, "rongGroupId": "GROUP66725586", "group": [ { "groupGroupingMemberId": 100677, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:13:56:143/31.jpg", "joinGroupGroupingDate": "2025-06-26T08:14:49.000 0000", "nickName": "Chris" }, { "groupGroupingMemberId": 100011, "headPicture": "http://image-laomale.test.upcdn.net/yyqc/20240717/upload_vdhdfg3skcosyqcwl6nc2iqt8tyd25fd.png", "joinGroupGroupingDate": "2025-06-26T08:14:49.000 0000", "nickName": "该喝喝" }, { "groupGroupingMemberId": 99998, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:23:06:432/93.jpg", "joinGroupGroupingDate": "2025-06-26T08:14:49.000 0000", "nickName": "蜡笔小新" }, { "groupGroupingMemberId": 100000, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:23:06:362/65.png", "joinGroupGroupingDate": "2025-06-26T08:14:49.000 0000", "nickName": "冷眸" }, { "groupGroupingMemberId": 100691, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:17:36:694/79.jpg", "joinGroupGroupingDate": "2025-06-26T08:14:49.000 0000", "nickName": "敏" } ] }, { "groupNo": 66725586, "groupGroupingName": "2", "groupGroupingMemberNum": 6, "isGroupGroupingMember": false, "rongGroupId": "GROUP66725586", "group": [ { "groupGroupingMemberId": 100638, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:13:56:134/10.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:09.000 0000", "nickName": "Leo" }, { "groupGroupingMemberId": 99998, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:23:06:432/93.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:09.000 0000", "nickName": "蜡笔小新" }, { "groupGroupingMemberId": 100000, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:23:06:362/65.png", "joinGroupGroupingDate": "2025-06-26T08:15:09.000 0000", "nickName": "冷眸" }, { "groupGroupingMemberId": 100691, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:17:36:694/79.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:09.000 0000", "nickName": "敏" }, { "groupGroupingMemberId": 100091, "headPicture": "http://image.laomahahaha.com/yyqc/20240828/upload_shgeloxr0zgr03a5dyep1pq1tg1xeyvi.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:09.000 0000", "nickName": "暖阳" }, { "groupGroupingMemberId": 99999, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:13:56:143/31.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:09.000 0000", "nickName": "茄子豆角" } ] }, { "groupNo": 66725586, "groupGroupingName": "3", "groupGroupingMemberNum": 5, "isGroupGroupingMember": true, "rongGroupId": "GROUP66725586", "group": [ { "groupGroupingMemberId": 100035, "headPicture": "../../static/3.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:30.000 0000", "nickName": "我不是家长" }, { "groupGroupingMemberId": 100092, "headPicture": "http://image.laomahahaha.com/yyqc/20240730/upload_t1uohak97de6yvaxyoxt8rrd3cdh3kfz.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:30.000 0000", "nickName": "哇咔咔" }, { "groupGroupingMemberId": 100009, "headPicture": "../../static/8.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:30.000 0000", "nickName": "天大地大我是老大" }, { "groupGroupingMemberId": 100008, "headPicture": "http://image.laomahahaha.com/yyqc/20240828/upload_p7wg8dzkk104qzs38vreshu1s5yiz9s2.jpg", "joinGroupGroupingDate": "2025-06-26T08:15:30.000 0000", "nickName": "瀟雨萌" }, { "groupGroupingMemberId": 100001, "headPicture": "http://images.laomahahaha.com/App/laomaleImage/2024-09-06 16:17:36:657/1.png", "joinGroupGroupingDate": "2025-06-26T08:15:30.000 0000", "nickName": "张哥哥" } ] } ] 根据arr2 中 group内 groupGroupingMemberId 和 arr1 中 groupMemberId 进行判断 如果相等的话证明arr2中有arr中的这个值 就新增一个flag值 = true 不相等就是没有的时候 flag值 = false
最新发布
07-16
<think>嗯,用户让我用Python编程计算h=25t-0.5gt&sup2;在t=2时的结果。首先,我需要理解这个公式的物理意义。看起来像是自由落体运动的位移公式,通常h = v₀t - 0.5gt&sup2;,其中v₀是初速度,g是重力加速度,t是时间。这里给出的h=25t-0.5gt&sup2;,所以v₀应该是25 m/s,g通常是9.8 m/s&sup2;。不过用户可能希望用这个公式计算t=2秒时的位移h。 接下来,我需要考虑如何用Python实现这个计算。首先,应该定义变量t和g的值,然后代入公式进行计算。用户可能希望代码简单明了,直接输出结果。可能需要处理的问题包括变量的赋值、数学运算的顺序,尤其是平方和乘法的顺序是否正确。 可能的步骤是: 1. 设定t的值为22. 设定g的值,通常取9.8。 3. 计算h = 25*t - 0.5*g*t**2。 4. 输出结果。 需要注意的是,Python中的指数运算符是**,所以t的平方应该写成t**2。同时,乘法运算符不能省略,比如0.5g要写成0.5 * g * t**2,否则会语法错误。 另外,用户可能希望得到浮点数的结果,所以需要确保所有运算都是浮点数计算。如果用户需要更精确的结果,可能需要使用更精确的数值,比如g取9.80665,但通常9.8就足够了。 测试一下,当t=2时,代入数值计算: h = 25*2 - 0.5*9.8*(2)^2 = 50 - 0.5*9.8*4 = 50 - 19.6 = 30.4米 所以正确的输出应该是30.4。在Python中,代码是否正确?比如: t = 2 g = 9.8 h = 25 * t - 0.5 * g * t ** 2 print("当t=2时,h的值为:", h) 运行这段代码应该得到正确的结果。可能还需要考虑输出格式,比如保留几位小数,但用户没有特别说明,所以默认即可。 另外,是否需要考虑单位?用户可能只是需要数值结果,所以可能不需要处理单位。但可以提醒用户注意单位的一致性,比如g的单位是m/s&sup2;,t的单位是秒,结果h的单位是米。 最后,检查是否有其他可能的错误,比如括号是否正确,运算符优先级是否正确。这里乘法优先级高于减法,所以没有问题。</think>好的,让我们通过Python计算公式 $h = 25t - 0.5gt^2$ 在 $t=2$ 时的结果(假设重力加速度 $g=9.8\ \mathrm{m/s^2}$)。 ### 步骤如下: 1. **定义变量** ```python t = 2 # 时间(秒) g = 9.8 # 重力加速度(m/s&sup2;) ``` 2. **计算公式** ```python h = 25 * t - 0.5 * g * t ** 2 ``` 3. **输出结果** ```python print(f"当 t=2 时,h 的值为: {h} 米") ``` --- ### 完整代码 ```python t = 2 g = 9.8 h = 25 * t - 0.5 * g * t ** 2 print(f"当 t=2 时,h 的值为: {h} 米") ``` --- ### 输出结果 ``` 当 t=2 时,h 的值为: 30.4 米 ``` --- ### 公式说明 - **物理意义**:该公式描述物体以初速度 $25\ \mathrm{m/s}$ 竖直上抛的位移随时间变化的规律(含重力减速)。 - **符号解释**: - $h$:位移(米) - $t$:时间(秒) - $g$:重力加速度(通常取 $9.8\ \mathrm{m/s^2}$) 如需计算其他时间点的结果,直接修改变量 `t` 的值即可。
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