1167 . Enhanced Addition Chains

Submit
Status
Discussion / Solution
Ranklist
Back to Problems List

TopCoder

User's AC Ratio

NaN% (0/0)

Submission's AC Ratio

NaN% (0/0)

Tags

Description

An addition chain for n is an integer sequence a0, a1,a2,...,am with the following four properties:

  • a0 = 1

  • am = n

  • a0 < a1 < a2 < ... < am-1 < am


  • For each k (1<=k<=m) there exist two (not necessarily different) integers i and j (0<=i, j<=k-1) with ak=ai+aj


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.

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.

Input Format

The input will contain one or more test cases. Each test case consists of one line containing one integer n (1<=n<=12509). Input is terminated by a value of zero (0) for n.


There are at most 5 test cases that n > 1000.

Output Format

For each test case, print one line containing the length of the required integer sequence.

Sample Input 1

5
7
12
15
77
0

Sample Output 1

4
5
5
6
9

Hints

The problem is a little time-critical, so use proper break conditions where necessary to reduce the search space.

Problem Source

Migrated from old NTUJ.

PKU 2248

Subtasks

No. Testdata Range Score

Testdata and Limits

No. Time Limit (ms) Memory Limit (VSS, KiB) Output Limit (KiB) Subtasks
0 20000 65536 200
Submit
Back to Top