public static int GetMinPathSum3Ways(int[,] a, int rows, int cols)
{
var memo = new PathVal[rows, cols];
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
memo[i, j] = new PathVal();
}
}
for (int i = 0; i < rows; i++)
{
memo[i, cols - 1].leftsum = a[i, cols - 1];
}
int min = Int32.MaxValue;
for (int i = 0; i < rows; i++)
{
int temp = GetMinPathSum3Ways(a, ref memo, i, 0, rows, cols,constraint.left);
min = (min < temp) ? min : temp;
}
return min;
}
public static int GetMinPathSum3Ways(int[,] a, ref PathVal[,] memo, int rpos, int cpos, int rows, int cols, constraint prevdir)
{
if (rpos >= rows || cpos >= cols) return 0;
if (cpos == cols - 1) return memo[rpos, cpos].leftsum;
List<int> sums = new List<int>();
if(prevdir==constraint.left)
{
if (memo[rpos, cpos].leftsum != 0 && memo[rpos, cpos].upsum != 0 && memo[rpos, cpos].downsum != 0)
{
sums.Add(memo[rpos, cpos].leftsum);
sums.Add(memo[rpos, cpos].upsum);
sums.Add(memo[rpos, cpos].downsum);
return sums.Min();
}
}
if (prevdir == constraint.up)
{
if (memo[rpos, cpos].upsum != 0 && memo[rpos, cpos].leftsum != 0)
{
sums.Add(memo[rpos, cpos].leftsum);
sums.Add(memo[rpos, cpos].upsum);
return sums.Min();
}
}
if (prevdir == constraint.down)
{
if (memo[rpos, cpos].downsum != 0 && memo[rpos, cpos].leftsum != 0)
{
sums.Add(memo[rpos, cpos].leftsum);
sums.Add(memo[rpos, cpos].downsum);
return sums.Min();
}
}
bool right = true, down = true, up = true;
if (prevdir == constraint.up) up = false;
if (prevdir == constraint.down) down = false;
if (cpos + 1 >= cols) right = false;
if (rpos + 1 >= rows) down = false;
if (rpos - 1 < 0) up = false;
if (!right && !down && !up) return 0;
int temp1 = Int32.MaxValue, temp2 = Int32.MaxValue, temp3 = Int32.MaxValue;
if (right)
{
temp1 = GetMinPathSum3Ways(a, ref memo, rpos, cpos + 1, rows, cols,constraint.left);
memo[rpos, cpos + 1].leftsum = temp1;
}
if (down)
{
temp2 = GetMinPathSum3Ways(a, ref memo, rpos + 1, cpos, rows, cols,constraint.up);
memo[rpos+1, cpos].upsum = temp2;
}
if (up)
{
temp3 = GetMinPathSum3Ways(a, ref memo, rpos - 1, cpos, rows, cols,constraint.down);
memo[rpos-1, cpos].downsum = temp3;
}
memo[rpos, cpos].leftsum = a[rpos,cpos] + Math.Min(Math.Min(temp1, temp2), temp3);
return memo[rpos, cpos].leftsum;
}