1997/98 ACM International Collegiate Programming Contest
University of Ulm Local Contest
Source file: addition.(c|C|pas)
Input file: addition.in
An addition chain for n is an integer sequence <a0,
a1,a2,...,am> with the following
You are given an integer n. Your job is to construct an addition chain
for n with minimal length. If there is more than one such sequence,
any one is acceptable.
- a0 = 1
- am = n
- For each k (1<=k<=m) there exist two
(not neccessarily different)
integers i and j (0<=i, j<=k-1)
For example, <1,2,3,5> and <1,2,4,5> are both valid solutions
when you are asked for an addition chain for 5.
The input file will contain one or more test cases.
Each test case consists of one line containing one integer n
Input is terminated by a value of zero (0) for n.
For each test case, print one line containing the required integer sequence.
Separate the numbers by one blank.
Hint: The problem is a little time-critical, so use proper break
conditions where necessary to reduce the search space.
1 2 4 5
1 2 4 6 7
1 2 4 8 12
1 2 4 5 10 15
1 2 4 8 9 17 34 68 77