You are given as input an array a[1..n], with n entries. also, you know that, the array consists of a series of 0’s followed by a series of 1’s, but you don’t know how many of each there are. your goal is to find the first 1 in the array. there is a cost associated with checking the value of an entry in the array. each time you check a value and it turns out to be 0, you must pay 1 dollar. if value turns out to be 1, you have to pay 1 "famous algorithmist trading card (fatc)". in each of the parts of this question, you will have some number of dollars and some number of fatcs. you must give an algorithm which will return the index of the first (lowest indexed) 1 which works given your resources. for each part write pseudocode and explain why your algorithm works, given your resources.
(a) you have n dollars and n fatc
(b) you have 1 dollars and n fatc
(c) you have 10 log n dollars and 10 log n fatc
(d) you have 2 dollars and 10n.5 fatc
(e) you have k dollars and 10kn+/k fatc, for some constant k.