Coins in a Line

There are n coins in a line. (Assume n is even). Two players take turns to take a coin from one of the ends of the line until there are no more coins left. The player with the larger amount of money wins.

 

Solution:

 

typedef pair<int, int> i_pair;
int path[100];
//define pair here 

int max(int m, int n, int p, int q)
{
	vector<int> i_v;
	i_v.push_back(m);
	i_v.push_back(n);
	i_v.push_back(p);
	i_v.push_back(q);
	sort(i_v.begin(), i_v.end());
	int max_path = *(i_v.end()-1);
	
	return max_path;
}
int MaxPath(int depth, int a[], int s_z, int i, int j, int max_path)
{
	if(s_z%2 != 0) return 0;
	else
	{
		if(depth == s_z/2)
		{
			return max_path;
		}
		else
		{
			int m = a[i] + MaxPath(depth+1, a, s_z, i+2, j, max_path); 
			int n = a[i] + MaxPath(depth+1, a, s_z, i+1, j-1, max_path);
			int p = a[j] + MaxPath(depth+1, a, s_z, i, j-2, max_path);
			int q = a[j] + MaxPath(depth+1, a, s_z, i+1, j-1, max_path);
			max_path = max(m,n,p,q);
			int pos = depth * 2;
			if(max_path== m)
			{
				path[pos] = i;
				path[pos+1] = j;
			}
			else if(max_path == n)
			{
				path[pos] = i;
				path[pos+1] = i+1;
			}
			else if(max_path == p)
			{
				path[pos] = j;
				path[pos+1] = j-1;
			}
			else
			{
				path[pos] = j;
				path[pos+1] = i;
			}
			
		}
	}
}