Solve the recurrence relation using a recursion tree AND substitution method: T(n) = T(n-1) + 10n
Solve the recurrence relation using a recursion tree AND substitution method:
T(n) = T(n-1) + 10n
Homework Answers
Recursion tree: -------------------Time complexity = T(0) + 10(1) + .... + 10(n-2) + 10(n-1) + 10n = 1+ 10(1+2+3+....+n) = 1+ 10(n(n+1)/2) = 1 + 5(n(n+1)) = O(n^2) ================================= Substitution method: ------------------------ T(n) = T(n-1) + 10n = T(n-2) + 10(n-1) + 10n = T(n-3) + 10(n-2) + 10(n-1) + 10n ...... ...... ...... = T(n-n) + 10(1) + .... + 10(n-2) + 10(n-1) + 10n = 1+ 10(1+2+3+....+n) = 1+ 10(n(n+1)/2) = 1 + 5(n(n+1)) = O(n^2)
Time complexity
= T(0) + 10(1) + .... + 10(n-2) + 10(n-1) + 10n
= 1+ 10(1+2+3+....+n) = 1+ 10(n(n+1)/2) = 1 + 5(n(n+1)) = O(n^2)
=================================
Substitution method:
------------------------
T(n) = T(n-1) + 10n
= T(n-2) + 10(n-1) + 10n
= T(n-3) + 10(n-2) + 10(n-1) + 10n
......
......
......
= T(n-n) + 10(1) + .... + 10(n-2) + 10(n-1) + 10n
= 1+ 10(1+2+3+....+n)
= 1+ 10(n(n+1)/2)
= 1 + 5(n(n+1))
= O(n^2)Add Answer to:
Solve the recurrence relation using a recursion tree AND
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void insert(int data) {
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