section-1.1.md

TEMP <- a
a <- b
b <- c
c <- d
d <- TEMP

2. 因为 r 是 remainer 不能被 n 整出，所以 r < n, 所以 n < m

3. Algo F:

F1. Divide m by n and let m be the remainer F2. if m = 0 the algorithm terminates n is answer. F3. swap m and n, then jump to F1.

57

j	theta	phi	a	b
0	"ab"	"c"	1	0
1	"ac"	"cb"	2	1
2	"b"	"b"	4	3
3	"c"	"a"	0	3
4	"c"	"b"	5	4

• j0: r <- |m - n|, c represents TEMP <- min(m, n), the remain a or b represents reminder r;
• j1: set n <- r;
• j2: notice r is set to n in j1, jump to final step if r is zero, otherwise jump to next step;
• j3: set m <- TEMP(min(m, n)), then go back to j0;
• j4: final step, r is zero, the result n is represents in inner letter "c", this step convert "c" to "b", to according the output format.