1. (a) Precisely specify the conditions under which the following algorithm returns True, and then discuss, in detail, the running time of the algorithm. If you think it has different best- and worst-case running times then these should be considered separately, and you should explain the conditions under which best and worst-cases arise. You must fully explain your answer and use 0, N and O appropriately to receive full marks. Algorithm Ex1 ((an, ... an),(61, ...,bm)) kan xm for it + 1 to n do for j 0 [10 marks] (b) Precisely specify the conditions under which the following algorithm returns True, and then discuss, in detail, the running time of the algorithm. If you think it has different best- and worst-case running times then these should be considered separately, and you should explain the conditions under which best and worst-cases arise. You must fully explain your answer and use 0, 12 and 0 appropriately to receive full marks. En Algorithm Ex2 ((an, ... an), (b1, ..., bn)) qe true for i+ 1 to n do j while j > 0 and q == true do If ai! = b; q+ false juj-1 return a 2 (c) Precisely specify the conditions under which the following algorithm returns True, and then discuss, in detail, the running time of the algorithm. If you think it has different best- and worst-case running times then these should be considered separately, and you should explain the conditions under which best and worst-cases arise. You must fully explain your answer and use 0, 12 and 0 appropriately to receive full marks. Algorithm Ex3 (T,c) T is a balanced binary search tree containing integer number values and c is an integer. Each node in T has two child nodes, either a numeric value or the value null to indicate the lack of a child value. node -root(T) found + false == == while (node! = null) and (found false) if node, value found + true else if c