This paper presents new algorithms for generating all n-node t-ary trees in linked representation which take constant average time per tree. They use fewer memory references and are considerably faster than previous such algorithms.

This paper presents a new algorithm for generating all n node t-ary trees in linked representation by providing a context and generalizing Skarbek's algorithm for generating binary trees. It initially appeared that Skarbek's algorithm could not be generalized to even 3-ary trees, which motivated the author to previously develop an algorithm for generating all n node t-ary trees in linked representation based on a particular listing of integer sequences representing the trees. The context for the generalization of Skarbek's algorithm turns out to also be a particular listing of integer sequences representing the trees. The paper also gives two constant average time implementations. The first generates the next tree from its predecessor given in linked representation while the second retains additional information about the predecessor beyond just its linked representation.

Beyer and Hedetniemi [1980] gave the first constant average-time algorithm for the generation of all rooted trees with n nodes. This article presents the first combinatorial Gray code for these trees and a loopless algorithm for its generation.

This paper presents a new algorithm for the generation of all n node t-ary trees in linked representation. It also gives two constant average time implementations of the algorithm. The first directly generates the next tree from its predecessor while the second retains additional information about the predecessor and is faster for t > 4.

This paper presents a loopless algorithm to generate all permutations of a multiset. Each is obtained from its predecessor by making one transposition. It differs from previous such algorithms by using an array for the permutations but requiring storage only linear in its length.

The well-known Schröder numbers have appeared in different combinatorial contexts, including Schröder trees and well-weighted binary trees. The only loopless algorithm for generating Schröder trees actually generated representations for their well-weighted binary tree counterparts. This paper presents the first loopless algorithms for directly generating Schröder tree representations. They use a new loopless algorithm for generating $k$-compositions of $n$ in inverse lexicographic order.

An ordered tree with specified degrees and $n$ nodes has $a_{i}$ nodes of degree $i$ where $a_{0} = 1+\sum _{i = 1,h}(i-1)a_{i}$ and $n = \sum_{i = 0,h}a_{i}$. This paper presents a new and simpler loopless algorithm for generating all ordered trees with specified degrees. When $a_{k} = N$, $a_{0} = (k-1)N+1$ and all other $a_{i}$'s are 0, then all $N$ node $k$-ary trees are generated.

This paper describes the use of a system which will allow effortless visualization and animation of standard C/C++ piogrhms.tie system brings alive programs so.that students in CS 1 and CS 2 classes can more easily see each instruction and its effects.They can also see the effects of larger entities such as functions.The system serves as an excellent instructional tool and debugger.introduction " Conventional programming environments provide some support 'for program 'understanding, development, and debugging.Once .aprogram is syntactically correct, a student can use a debugger to monitor the Values of variables and step through a program's instructions.Although very useful, this-,process can be quite,involved A-. and laborious.1 The feedback a programmer receives does not provide an over+1 v&w of the program's behavior.It is more instructive to display the dynamics of a program rather than static snapshots of data structure values that are constantly Updated as program instructions are executed.Software visualization systems ,allow custom animations that attempt $0 capture these dynamics [l].Such systems generally require the writing of animation code ' and understanding of the, program one is trying to animate.The aim of our system is to provide automatic animations that are useful and require no additional coding and may lead to understanding of the underlying algorithm.One area, for instance, which has been identified as particularly troublesome for students is parameter passing [2].

A natural, and readily computable, first guess at a solution to the coin changing problem is the canonical solution. This solution is a special case of the greedy solution which is a reasonable heuristic guess for the knapsack problem. In this paper, efficient tests are given to determine whether all greedy solutions are optimal with respect to a given set of knapsack objects or coin types. These results improve or extend previous tests given in the literature. Both the incomplete and complete cases are considered.

A cost is defined for demand paging algorithms with respect to a formal stochastic model of program behavior. This cost is shown to exist under rather general assumptions, and a computational procedure is given which makes it possible to determine the optimal cost and optimal policy for moderate size programs, when the formal model is known and not time dependent. In this latter case it is shown that these computational procedures may be extended to larger programs to obtain arbitrarily close approximations to their optimal policies. In previous models either unwarranted information is assumed beyond the formal model, or the complete stochastic nature of the model is not taken into account.