Iterated Difference - c++

Question

This is an spoj problem. It works, but It's too slow.
Here is the question:
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.
Input
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.
Output
For each case, there will be one line of output, specifying the case
number and the number of iterations, in the format shown in the sample
output. If the list does not attain the desired form after 1000
iterations, print 'not attained'.
Sample Input
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
Sample Output
Case 1: 8 iterations
Case 2: not attained
Case 3: 3 iterations
Case 4: 50 iterations
Case 5: 0 iterations
Case 6: 1 iterations
I'm not sure of what to do to make it faster. I tried using arrays, but I get all sorts of problems trying to allocate the memory and set one array to another.
How can I make it faster? Here's my code:
#include <iostream>
#include <vector>
#include <cmath>
#include <sstream>
#include <string>
using namespace std;
bool checker(vector<int>& nums2) {
int n = nums2[0];
for (int i = 1; i < nums2.size(); i++)
{
if (n != nums2[i])
return false;
}
return true;
}
vector<int> iterate(vector<int>& nums, int& iter, bool& attained) {
if (iter == 1000) {
attained = false;
return nums;
}
vector<int> nums2;
for (int i = 0; i < nums.size(); i++) {
if (i == nums.size() - 1)
nums2.push_back((int)abs((double)nums[i] - (double)nums[0]));
else
nums2.push_back((int)abs((double)nums[i] - (double)nums[i + 1]));
}
iter++;
return nums2;
}
int main()
{
int N = -1, count = 1;
while (1) {
int num = 0;
vector<int> nums;
string List = "";
stringstream ss;
cin >> N;
if (N == 0)
break;
cin.ignore();
cin.clear();
getline(cin, List);
ss << List;
while (ss >> num) {
nums.push_back(num);
}
int iterations = 0;
bool attained = true;
while (!checker(nums)) {
nums = iterate(nums, iterations, attained);
}
if (!attained)
cout << "case " << count << ": not attained";
else
cout << "case " << count << ": " << iterations << " iterations" << endl;
count++;
}
}

Answer 1

I fixed it. It was a problem with the while loop in the main function. The condition was:
while (!checker(nums)) { ... }
It would stay in the loop and repeatedly call the iterate function because if it is not attainable, then the checker will always be false. So changing the condition to:
while (!checker(nums) && attained) { ... }
would break the loop if it was not attainable.
Basically, it was just getting stuck on doing the same thing over and over; it wasn't actually slow.
Thanks, xan, for your answer.

Answer 2

If you want it to be a little faster you should work on debugging your array variation to avoid the vector allocations. If you want it to be a lot faster you need to do some analysis of the problem to find a better algorithm. For instance, if you see the same list twice you're in a loop and will exceed 1000 iterations. And the result will be the same if you rotate the list, which you can consider when checking for a repeated list.

Answer 3

Your implementation executes 1000 iterations in 25ms on my mainstream lapton. Fixed one, because there's a bug and case 2 will execute forever.
To do faster you can reuse the same vector and modify it in place, your iterator() function signature would look like:
void iterate(vector<int>& nums);
This version takes 7ms on my machine, because it doesn't allocate memory in loop.