Exercise 1.13 Greedy algorithms for the bin packing problem. The bin packing problem is a well-known combinatorial problem with many applications such as container or pellet loading, loading trucks with weight capacity, and creating file backup in removable media. Objects of different volumes must be packed into a finite number of bins of capacity C in a way that minimizes the number of bins used. There are many variations of this problem such as 3D or 2D packing, linear packing, pack by volume, and pack by weight. Let us solve the one-dimensional bin packing problem (Fig. 1.35). Given a finite collection of n weights wi, w2, W3, ..., W. and a collection of identical bins with capacity C (which exceeds the largest of the weights), the problem is to find the minimum number k of bins into which the weights can be placed without exceeding the bin capacity C. An example of a greedy algorithm is the first fit algorithm that places each item into the first bin in which it will fit. It requires (n logn) time. Propose some improvements of this greedy algorithm. Hint: For example, a sorting of the elements may be done before the packing