2015
05-23

# Iterated Difference

You are given a list of N non-negative integers a(1), a(2), … , a(N). You replace the given list by a new list: the k-th entry of the new list is the absolute value of a(k) – a(k+1), wrapping around at the end of the list (the k-th entry of the new list is the absolute value of a(N) – a(1)). How many iterations of this replacement are needed to arrive at a list in which every entry is the same integer?

For example, let N = 4 and start with the list (0 2 5 11). The successive iterations are:

2 3 6 11
1 3 5 9
2 2 4 8
0 2 4 6
2 2 2 6
0 0 4 4
0 4 0 4
4 4 4 4
Thus, 8 iterations are needed in this example.

The input will contain data for a number of test cases. For each case, there will be two lines of input. The first line will contain the integer N (2 <= N <= 20), the number of entries in the list. The second line will contain the list of integers, separated by one blank space. End of input will be indicated by N = 0.

The input will contain data for a number of test cases. For each case, there will be two lines of input. The first line will contain the integer N (2 <= N <= 20), the number of entries in the list. The second line will contain the list of integers, separated by one blank space. End of input will be indicated by N = 0.

4
0 2 5 11
5
0 2 5 11 3
4
300 8600 9000 4000
16
12 20 3 7 8 10 44 50 12 200 300 7 8 10 44 50
3
1 1 1
4
0 4 0 4
0

Case 1: 8 iterations
Case 2: not attained
Case 3: 3 iterations
Case 4: 50 iterations
Case 5: 0 iterations
Case 6: 1 iterations

//Time : 203MS
//Memory : 224K
#include <stdio.h>
int sum=-1;
int dif(int a[],int n)
{
int i,s=0;
bool zero=true;
sum++;
for(i=0;i<n-1;i++)
{	if(a[i]<0)
a[i]=0-a[i];
if(a[i+1]<0)
a[i+1]=0-a[i+1];
a[i]=a[i+1]-a[i];
if(a[i]!=0)
zero=false;
s+=a[i];
}
a[n-1]=s;
if(s==0 && zero)
return sum;
if(sum>1000)
return -1;
dif(a,n);
}
int main()
{
int a[21];
int n,temp=1;
while(scanf("%d",&n)!=EOF && n)
{
sum=-1;
for(int i=0;i<n;i++)
scanf("%d",&a[i]);
int num=dif(a,n);
printf("Case %d: ",temp);
if(num==-1)
printf("not attained\n");
else
printf("%d iterations\n",num);
temp++;
}
return 0;
}

1. 民选的美国哈佛生领导人与几个人暗箱操作定下的小学肄业生根本没有可比性民主至少有一点好处，那就是政权或领导人更换时不会杀的天昏地暗，腥风血雨。

2. 民选的美国哈佛生领导人与几个人暗箱操作定下的小学肄业生根本没有可比性民主至少有一点好处，那就是政权或领导人更换时不会杀的天昏地暗，腥风血雨。

3. 民选的美国哈佛生领导人与几个人暗箱操作定下的小学肄业生根本没有可比性民主至少有一点好处，那就是政权或领导人更换时不会杀的天昏地暗，腥风血雨。

4. 民选的美国哈佛生领导人与几个人暗箱操作定下的小学肄业生根本没有可比性民主至少有一点好处，那就是政权或领导人更换时不会杀的天昏地暗，腥风血雨。

5. 民选的美国哈佛生领导人与几个人暗箱操作定下的小学肄业生根本没有可比性民主至少有一点好处，那就是政权或领导人更换时不会杀的天昏地暗，腥风血雨。

6. 民选的美国哈佛生领导人与几个人暗箱操作定下的小学肄业生根本没有可比性民主至少有一点好处，那就是政权或领导人更换时不会杀的天昏地暗，腥风血雨。