Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 121
2. There might be a man pm, preferred to m by w, who himself prefers w over his wife.
Pursuing trouble source 1, we compare ranks rwm pw,m and rwm pw,y[pw] for all women preferred to m
by w, i.e. for all pw = wmr m,i such that i < r. We happen to know that all these candidate women are
already married because, were anyone of them still single, m would have picked her beforehand. The
described process can be formulated by a simple linear search; S denotes stability.
i := -1; S := TRUE;
REPEAT
INC(i);
IF i < r THEN
pw := wmr[m,i];
IF ~single[pw] THEN S := rwm[pw,m] > rwm[pw, y[pw]] END
END
UNTIL (i = r) OR ~S
Hunting for trouble source 2, we must investigate all candidates pm who are preferred by w to their
current assignation m, i.e., all preferred men pm = mwr w,i such that i < rwm w,m . In analogy to tracing
trouble source 1, comparison between ranks rmwp m,w and rmw pm,x[pm] is necessary. We must be
careful, however, to omit comparisons involving x pm where pm is still single. The necessary safeguard is a
test pm < m, since we know that all men preceding mare already married.
The complete algorithm is shown below. Table 3.4 specifies the nine computed stable solutions from
input data wmr and mwr given in Table 3.3.
PROCEDURE write; (* ADenS36_Marriages *)
(*global writer W*)
VAR m: man; rm, rw: INTEGER;
BEGIN
rm := 0; rw := 0;
FOR m := 0 TO n-1 DO
Texts.WriteInt(W, x[m], 4);
rm := rmw[m, x[m]] + rm; rw := rwm[x[m], m] + rw
END;
Texts.WriteInt(W, rm, 8); Texts.WriteInt(W, rw, 4); Texts.WriteLn(W)
END write;
PROCEDURE stable (m, w, r: INTEGER): BOOLEAN;
VAR pm, pw, rank, i, lim: INTEGER;
S: BOOLEAN;
BEGIN
i := -1; S := TRUE;
REPEAT
INC(i);
IF i < r THEN
pw := wmr[m,i];
IF ~single[pw] THEN S := rwm[pw,m] > rwm[pw, y[pw]] END
END
UNTIL (i = r) OR ~S;
i := -1; lim := rwm[w,m];
REPEAT
INC(i);
IF i < lim THEN