Let T(n) be the running time of an algorithm with the input size n. If we have: T(n) ? { O(1) if n < 140 T(?n/5?) + T(7n/10 + 6) + O(n) if n ? 140, show that T(n) = O(n).

          Let T(n) be the running time of an algorithm with the input size n. If we have:
T(n) ? {
O(1) if n < 140
T(?n/5?) + T(7n/10 + 6) + O(n) if n ? 140,
show that T(n) = O(n).

Added by Nicole H.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Akash M

10/19/2023

Step 1

This is already less than O(n), so we don't need to worry about this case. For n ≥ 140, the running time is T(n/5) + T(7n/10+6) + O(n). We can see that the function T is called recursively with smaller inputs, n/5 and 7n/10+6. The O(n) term represents the time Show more…

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Let T(n) be the running time of an algorithm with the input size n. If we have: T(n) ≤ { O(1) if n < 140; T(⌈n/5⌉) + T(7n/10 + 6) + O(n) if n ≥ 140, show that T(n) = O(n).