internal void CopyTo(cell cell)
{
cell.states.AddRange(this.states);
}
static void Main(string[] args)
{
//Electoral College Votes for each state (the actual state to index is ilrelevant for this problem). Obtained from http://www.iweblists.com/us/government/2012ElectoralVotesPerState.html
votes = new int[] { 9, 3, 11, 6, 55, 9, 7, 3, 3, 29, 16, 4, 4, 20, 11, 6, 6, 8, 8, 4, 10, 11, 16, 10, 6, 10, 3, 5, 6, 4, 14, 5, 29, 15, 3, 18, 7, 7, 20, 4, 9, 3, 11, 38, 6, 3, 13, 12, 5, 10, 3 };
//votes = new int[] { 3, 1, 1, 2, 2, 1 };
//votes = new int[] { 3, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 1 };
partition = votes.Sum() / 2;
matrix = new cell[partition + 1, votes.Length + 1];
// For the zero-sum, we can always include no votes, so this is our base case of 1.
for (int i = 0; i <= votes.Length; i++)
{
matrix[0, i] = new cell(1,votes.Length);
}
// Zero out the rest of the matrix
for (int i = 1; i <= partition; i++)
{
for (int j = 0; j <= votes.Length; j++)
{
matrix[i, j] = new cell(0, votes.Length);
}
}
Dictionary<int,int> startingVoteOccurances = DistinctCounts(votes);
//O(Votes.Length * Sum/2)
for (int targetSum = 1; targetSum <= partition; targetSum++)
{
Dictionary<int, int> voteOccurrances = new Dictionary<int, int>();
for (int j = 1; j <= votes.Length; j++)
{
int vote = votes[j - 1];
//Keep track of the vote occurances we've seen so far.
if (voteOccurrances.ContainsKey(vote))
voteOccurrances[vote]++;
else
voteOccurrances[vote] = 1;
if (targetSum < vote) //We can't fit any more votes into this target sum. Use the last Optimal solution
{
matrix[targetSum, j].count = matrix[targetSum, j - 1].count;
matrix[targetSum, j - 1].CopyTo(matrix[targetSum, j]);
}
else //Else, include this vote to get to the target sum.
{
//If the backtrack cells contain a vote occurrance too many times, then we've exhausted all our votes.
cell Left = matrix[(targetSum - vote), j];
cell Up = matrix[targetSum, j - 1];
if (Left.SelectCount(vote) + Up.SelectCount(vote) >= voteOccurrances[vote])
{
matrix[targetSum, j].count = Left.count;
}
else
{
matrix[targetSum, j].count = Left.count + Up.count;
Left.CopyTo(matrix[targetSum, j]);
Up.CopyTo(matrix[targetSum, j]);
matrix[targetSum, j].Add(vote);
}
}
//Or call recursively
//matrix[i, c] = count(i, c);
}
}
printMatrix();
Console.ReadLine();
}
