简单:通过迭代法求解 T(n)=T(n-1)+n [英] Easy: Solve T(n)=T(n-1)+n by Iteration Method

问题描述

有人可以帮我解决这个问题吗?

Can someone please help me with this ?

用迭代法求解. T(n) = T(n-1) +n

Use iteration method to solve it. T(n) = T(n-1) +n

非常感谢您解释步骤.

推荐答案

T(n) = T(n-1) + n

T(n-1) = T(n-2) + n-1

T(n-2) = T(n-3) + n-2

以此类推，您可以将 T(n-1) 和 T(n-2) 的值代入 T(n) 中以大致了解该模式.

and so on you can substitute the value of T(n-1) and T(n-2) in T(n) to get a general idea of the pattern.

T(n) = T(n-2) + n-1 + n

T(n) = T(n-3) + n-2 + n-1 + n
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.
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T(n) = T(n-k) + kn - k(k-1)/2    ...(1)

对于基本情况:

n - k = 1 so we can get T(1)

=> k = n - 1
代入(1)

=> k = n - 1
substitute in (1)

  T(n) = T(1) + (n-1)n - (n-1)(n-2)/2

你可以看到的顺序是 n² => O(n²).

Which you can see is of Order n² => O(n²).

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