1310: Addition Chains

1310: Addition Chains

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Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	205	90	Standard

An addition chain for n is an integer sequence with the following four properties:

 

• a₀ = 1
• a_m = n
• a₀<a₁<a₂<...<a_m-1<a_m
• For each k ( ) there exist two (not neccessarily different) integers i and j ( ) with a_k =a_i +a_j

You are given an integer n. Your job is to construct an addition chain for n with minimal length.

 

Input Specification

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.

Output Specification

For each test case, print one line containing the minimal length.

 

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

Sample Input

5
7
12
15
77
0

Sample Output

4
5
5
6
9

#include<iostream>
#include<cstring>
using namespace std;
int a[1005],n,minlen;
void dfs(int step)
{
    if(step>minlen) return ;
    for(int i=step-1;i>=0;i--)
    {
        a[step]=a[step-1]+a[i];
        if(a[step]>n) continue;
        if(a[step]==n)
        {
            if(step+1<minlen) minlen=step+1;
            return ;
        }
        dfs(step+1);
    }
}                  
int main()
{
    while(cin>>n&&n)
    {
        if(n==1) {cout<<1<<endl;continue;}
        a[0]=1;
        minlen=(1<<31)-1;
        dfs(1);
        cout<<minlen<<endl;
    }
    return 0;
}