Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 118
END
ELSE
write;
m := m+1 (*solutions count*)
END
END Try;
PROCEDURE AllQueens*;
VAR i, j: INTEGER;
BEGIN
FOR i := 0 TO 7 DO a[i] := TRUE; x[i] := -1 END;
FOR i := 0 TO 14 DO b[i] := TRUE; c[i] := TRUE END;
m := 0;
Try(0);
Log.String('no. of solutions: '); Log.Int(m); Log.Ln
END AllQueens.
x0 x1 x2 x3 x4 x5 x6 x7 n
0 4 7 5 2 6 1 3 876
0 5 7 2 6 3 1 4 264
0 6 3 5 7 1 4 2 200
0 6 4 7 1 3 5 2 136
1 3 5 7 2 0 6 4 504
1 4 6 0 2 7 5 3 400
1 4 6 3 0 7 5 2 072
1 5 0 6 3 7 2 4 280
1 5 7 2 0 3 6 4 240
1 6 2 5 7 4 0 3 264
1 6 4 7 0 3 5 2 160
1 7 5 0 2 4 6 3 336
Table 3.2. Twelve Solutions to the Eight Queens Problem.
3.6 The Stable Marriage Problem
Assume that two disjoint sets A and B of equal size n are given. Find a set of n pairs such that a
in A and b in B satisfy some constrains. Many different criteria for such pairs exist; one of them is the rule
called the stable marriage rule.
Assume that A is a set of men and B is a set of women. Each man and each women has stated distinct
preferences for their possible partners. If the n couples are chosen such that there exists a man and a
woman who are not married, but who would both prefer each other to their actual marriage partners, then
the assignment is unstable. If no such pair exists, it is called stable. This situation characterizes many related
problems in which assignments have to be made according to preferences such as, for example, the choice
of a school by students, the choice of recruits by different branches of the armed services, etc. The
example of marriages is particularly intuitive; note, however, that the stated list of preferences is invariant
and does not change after a particular assignment has been made. This assumption simplifies the problem,
but it also represents a grave distortion of reality (called abstraction).
One way to search for a solution is to try pairing off members of the two sets one after the other until the
two sets are exhausted. Setting out to find all stable assignments, we can readily sketch a solution by using
the program schema of AllQueens as a template. Let Try(m) denote the algorithm to find a partner for man