Problem 42291. GJam 2015 Rd1B: Counter Culture

Created by Richard Zapor

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This Challenge is derived from <a href = "https://code.google.com/codejam/contest/8224486/dashboard#s=p0">GJam 2015 Rd 1B: Counter Culture</a>. Fastest completion - 5 minutes.Determine minimum sequence length to reach a number. Sequence starts at 1 and the next is either +1 or the number's reverse with trailing zeros removed. (eg 2300 is followed by 2301 or 32)Input: N, a value from 1 to 1,000,000Output: L, minimum length of sequence to reach NExamples: Small Case 1&lt;=N&lt;=1000000<pre class="language-matlab">N=5, L=5 [1 2 3 4 5] L=N is true thru 19
N=23, L=15 [1:12 21 22 23]
</pre>Theory: The small case can be solved with brute force or semi-brute force using storage of past calculations. All values are processed at each depth level. Duplicates from [N+1 and flip] are purged. A fast reversal function is essential. Direct summation works well. The large case N limit is 1E14 making even semi-brute force with storage unlikely.Additional GJam solutions can be found at <a href = "http://www.go-hero.net/jam/15">Example GJam Matlab solutions</a>. Select Find Solutions, change Language to Matlab. The Test Suite, at the bottom, contains a full GJam Matlab solution.

This Challenge is derived from <https://code.google.com/codejam/contest/8224486/dashboard#s=p0 GJam 2015 Rd 1B: Counter Culture>. Fastest completion - 5 minutes.

Determine minimum sequence length to reach a number. Sequence starts at 1 and the next is either +1 or the number's reverse with trailing zeros removed. (eg 2300 is followed by 2301 or 32)

Input: N, a value from 1 to 1,000,000

Output: L, minimum length of sequence to reach N

Examples: Small Case 1<=N<=1000000

N=5,  L=5  [1 2 3 4 5] L=N is true thru 19
  N=23, L=15 [1:12 21 22 23]

Theory: The small case can be solved with brute force or semi-brute force using storage of past calculations. All values are processed at each depth level. Duplicates from [N+1 and flip] are purged. A fast reversal function is essential. Direct summation works well. The large case N limit is 1E14 making even semi-brute force with storage unlikely.

Additional GJam solutions can be found at <http://www.go-hero.net/jam/15 Example GJam Matlab solutions>. Select Find Solutions, change Language to Matlab. The Test Suite, at the bottom, contains a full GJam Matlab solution.

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Problem 42291. GJam 2015 Rd1B: Counter Culture

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Problem 42291. GJam 2015 Rd1B: Counter Culture

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