/// <summary>
/// Given a histogram, find the area of largest rectangle that can be formed
///
/// -----
/// ----| |
/// | | |
/// | | |----
/// | | | |
/// | | | |
///
/// Using a stack, push any histogram of greater height. Once we encounter a short
/// histogram, we will pop off any greater height ones and calculate the area
/// If this area is greater than the max area, then replace max
/// </summary>
/// <param name="heights"></param>
/// <returns></returns>
public static long GetLargestRectangle(int[] heights)
{
long maxArea = 0;
Stack<LargestStorage> storage = new Stack<LargestStorage>();
int index = 0;
foreach (int height in heights)
{
while ((storage.Count > 0) && (storage.Peek().Height > height))
{
LargestStorage last = storage.Pop();
long area = (index - last.Index) * last.Height;
if (area > maxArea)
{
maxArea = area;
}
}
//need to put the current one for the future
storage.Push(new LargestStorage { Index = index, Height = height });
index++;
}
//need to pop stuff off the stack
while (storage.Count > 0)
{
LargestStorage last = storage.Pop();
long area = (index - last.Index) * last.Height;
if (area > maxArea)
{
maxArea = area;
}
}
return maxArea;
}
/// <summary>
/// Use a variable s to denote the start of the valid pattern
///
/// when we encounter ) at index i, there are 3 cases:
/// 1. stack is empty - no valid pattern, s = i + 1
/// 2. stack has 1 element - we found the end of a pattern...calculate length as i - s + 1...and compare to max
/// 3. stack has multiple elements - since all patterns from the top of the stack (only invalid is many ')'), meaning stack would be empty,
/// length is i - s.top...only if we push index into s
/// </summary>
/// <param name="parantheses"></param>
/// <returns></returns>
public static int LengthOfLongestBalancedParanthese(string parantheses)
{
int max = 0;
int start = 0;
Stack<int> tracker = new Stack<int>();
for (int index = 0; index < parantheses.Length; index++)
{
char chr = parantheses[index];
if (chr == '(')
{
tracker.Push(index);
}
else
{
if (tracker.Count == 0)
{
//invalid pattern...case 1
start = index + 1;
}
else
{
tracker.Pop();
if (tracker.Count == 0)
{
//case 2
max = System.Math.Max(max, index - start + 1);
}
else
{
//sub pattern...if everything afterward is invalid or we run out of closing brackets, this could be longest
//case 3
//(((()())
// _)
// ___)
// _____)
max = System.Math.Max(max, index - tracker.Peek());
}
}
}
}
return max;
}