Search Exercise --------------- Exercise 1: For given N, create a list of length N whose members are numbers between 1 and N (inclusive), which are all different (easy so far) and satisfy the following constraint. For each element E of the list, its successors are divided into two sets, BiggerE: the successors which are greater than E and SmallerE: the successors less than E. (Thus no successor takes the same value as E). The cardinalities of the sets BiggerE and SmallerE differ by at most 1. Exercise 2 (during the week...): A harder version of the problem is similar. For given N, create a list of length N whose members are numbers between 1 and some upper bound Max (start with, say Max = N^2), which are all different (easy so far) and satisfy the following (more complex) constraint. For each K from 1..N, call the Kth element of the list Ek. Its successors are divided into two sets, as before: BiggerEk: the successors which are greater than or equal to Ek + K and SmallerEk: the successors less than or equal to Ek - K. (Thus no successor takes a value between Ek-K+1 and Ek+K-1.) The cardinalities of the sets BiggerEk and SmallerEk differ by at most 1. What is the smallest upper bound Max for which there is a feasible solution?