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 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 computer vision system that can assemble canonical jigsaw puzzles is described. The most novel aspect of this system is that the methodology derives a new set of critical points that define a feature that can be used in matching partial boundaries (or contours) of planar regions. This global feature, called an isthmus, can be efficiently and reliably computed from the Euclidean skeleton or medial axis transformation of an object. A heuristic matching technique using isthmus critical points is applied to the partial boundary matching problem of jigsaw puzzle fitting. The isthmus may also be a useful feature in any application in which the point of narrowest necking of a planar region needs to be located.>