Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 119
m, and let this search proceed in the order of the man's list of stated preferences. The first version based on
these assumptions is:
PROCEDURE Try (m: man);
VAR r: rank;
BEGIN
IF m < n THEN
FOR r := 0 TO n-1 DO
pick the r-th preference of man m;
IF acceptable THEN
record the marriage;
Try(successor(m));
cancel the marriage
END
END
ELSE
record the stable set
END
END Try
The initial data are represented by two matrices that indicate the men's and women's preferences.
VAR wmr: ARRAY n, n OF woman;
mwr: ARRAY n, n OF man
Accordingly, wmr m denotes the preference list of man m, i.e., wmr m,r is the woman who occupies the r-th
rank in the list of man m. Similarly, mwr w is the preference list of woman w, and mwr w,r is her r-th choice.
A sample data set is shown in Table 3.3.
The result is represented by an array of women x, such that x m denotes the partner of man m. In order
to maintain symmetry between men and women, an additional array y, such that y w denotes the partner of
woman w:
VAR x, y: ARRAY n OF INTEGER
r = 0 1 2 3 4 5 6 7 r = 0 1 2 3 4 5 6 7
m = 0 6 1 5 4 0 2 7 3 w = 0 3 5 1 4 7 0 2 6
1 3 2 1 5 7 0 6 4 1 7 4 2 0 5 6 3 1
2 2 1 3 0 7 4 6 5 2 5 7 0 1 2 3 6 4
3 2 7 3 1 4 5 6 0 3 2 1 3 6 5 7 4 0
4 7 2 3 4 5 0 6 1 4 5 2 0 3 4 6 1 7
5 7 6 4 1 3 2 0 5 5 1 0 2 7 6 3 5 4
6 1 3 5 2 0 6 4 7 6 2 4 6 1 3 0 7 5
7 5 0 3 1 6 4 2 7 7 6 1 7 3 4 5 2 0
Table 3.3. Sample Input Data for wmr and mwr.
Actually, y is redundant, since it represents information that is already present through the existence of x. In
fact, the relations
x[y[w]] = w,
y[x[m]] = m
hold for all m and w who are married. Thus, the value y w could be determined by a simple search of x; the
array y, however, clearly improves the efficiency of the algorithm. The information represented by x and y
is needed to determine stability of a proposed set of marriages. Since this set is constructed stepwise by