Addition Chains

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 < ... < a_m-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

The input will contain one or more test cases. Each test case consists of one line containing one integer n (1<=n<=100). Input is terminated by a value of zero (0) for n.

Output

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.

Sample Input

5
7
12
15
77
0

Sample Output

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

Source

Ulm Local 1997

提交地址 ： poj

依次搜索一位k， 枚举之前的i， j， 把a[i] + a[j] 加到a[k]的位置上， 然后接着搜索；

剪枝：尽量从达到小枚举i，j让序列的数尽快逼近n；

为了不重复搜索，用一个bool数组存a[i] + a[j] 是否已经被搜过；

然后因为答案的深度很小， 所以一发迭代加深；

这样差不多A了；

这个代码在poj上通过但在UVa上Re, 看到的大佬可以帮我找错！

代码奉上：

//By zZhBr
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;

int n;
int ans;

int a[1100];

bool use[1005];
bool DFS(int stp)
{
    memset(use, 0, sizeof use);

    if(stp > ans)
    {
        if(a[ans] == n) return 1;
        else return 0;
    }

    for(register int i = stp - 1 ; i >= 1 ; i --)
    {
        for(register int j = i ; j >= 1 ; j --)
        {
            if(a[i] + a[j] > n) continue;
            if(!use[a[i] + a[j]])
            {
                if(a[i] + a[j] <= a[stp - 1]) return 0;
                use[a[i] + a[j]] = 1;
                a[stp] = a[i] + a[j];
                if(DFS(stp + 1)) return 1;
                a[stp] = 0;
                use[a[i] + a[j]] = 0;
            }
        }
    }
}

int main()
{
    while(scanf("%d", &n) != EOF)
    {
        if(n == 0) return 0;
        if(n == 1)
        {
            printf("1\n");
            continue;
        }
        if(n == 2)
        {
            printf("1 2\n");
            continue;
        }
        a[1] = 1;a[2] = 2;
        for(ans = 3 ; !DFS(3) ; ans ++);
        for(register int i = 1 ; i <= ans ; i ++)
        {
            printf("%d ", a[i]);
        }
        printf("\n");
        memset(a, 0, sizeof a);
    }
    return 0;
}

zZhBr

原文地址：https://www.cnblogs.com/zZh-Brim/p/8977282.html