Knuth Art Of Computer Programming V1 p9:
[1] The values of variables m and n, can be interchanged using t = m, then m = n, then n = t. Show how the values of four variables (a,b,c,d) can be rearranged to (b,c,d,a) by a sequence of replacements. In other words, the new value of a is to be the original value of b, etc. Try to use the minimum number of replacements.
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We want to transform (a, b, c, d) → (b, c, d, a) Using a temporary variable t, here is the sequence:
t = a a = b b = c c = d d = t
Trace through to verify:
Step.: a b c d t Start: a b c d — t = a: a b c d a a = b: b b c d a b = c: b c c d a c = d: b c d d a d = t: b c d a a
Result: (a, b, c, d) → (b, c, d, a)
This uses 5 replacements, which is the minimum needed — one to save the displaced value of a into t, three to shift b→a, c→b, d→c, and one final step to place the saved value into d.
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