首页SupposewehaveT(n)≤c=O(1)foralln≤3,andforeveryn≥4,wehave ，T(n)<=T(n/4)+T(3*n/4)+c*n,Use Mathematical Induction to prove that T (n) = O(n log n) for all n ≥ 4.

SupposewehaveT(n)≤c=O(1)foralln≤3,andforeveryn≥4,wehave ，T(n)<=T(n/4)+T(3n/4)+cn,Use Mathematical Induction to prove that T (n) = O(n log n) for all n ≥ 4.

时间: 2023-03-13 10:48:28 浏览: 105

T型接头双侧激光同步焊接缺陷补焊工艺及性能

针对国产大型客机6056/6156铝合金机身壁板T型接头双侧激光同步焊接的表面成形缺陷，从焊缝成形、微观组织、接头性能等方面对焊接缺陷的补焊工艺进行系统研究。结果表明：采用双侧填丝补焊方法能够有效消除焊缝原始缺陷获得成形良好的接头；补焊焊缝中心的等轴晶粒明显细化，热影响区弥散分布的第二相粒子有所减少，接头软化现象更为明显；补焊接头平均横向和轴向拉伸强度分别为323.9 MPa和183.5 MPa，为原始接头的95.8%和89.8%；轴向拉伸断口表现为脆性与韧性混合断裂，横向拉伸断口呈现脆性断裂特征。

证明过程应该是这样的：首先，假设T (k) = O(k log k) 成立，其中 k ≥ 4。接着，T (k+1) = T (3/4(k+1)) ≤ c*3/4(k+1) = c*k + c*3/4 ≤ c*k + c ≤ c*(k+1) = O (k+1)。由于T (k) = O(k log k)，所以有T (k+1) = O (k+1 log (k+1))。因此，T (n) = O(n log n) 也成立。

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SupposewehaveT(n)≤c=O(1)foralln≤3,andforeveryn≥4,wehave ，T(n)<=T(n/4)+T(3*n/4)+c*n,Use Mathematical Induction to prove that T (n) = O(n log n) for all n ≥ 4.

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