How is the stock span calculated in the stock span problem?

The Stock Span problem is a financial problem where we have a series of n daily price quotes for a stock and we need to calculate the span of stock’s price for all n days. The span Si of the stock’s price on a given day i is defined as the maximum number of consecutive days just before the given day, for which the price of the stock on the current day is less than or equal to its price on the given day.

Here are the steps to calculate the stock span:

1. Create an empty stack and push the index of the first element to it.

2. Initialize a span array with the size of the input, and set the first element to 1 (since the span of the first day is always 1).

3. For the rest of the elements, do the following:

   a. While the stack is not empty and the top of the stack points to an element smaller than the current element, pop elements from the stack.

   b. If the stack becomes empty after the above step, then the current element is greater than all elements to its left. Therefore, its span is its index plus one.

   c. Else, the current element is greater than elements after the top of the stack. Therefore, its span is the difference of the current index and the index at the top of the stack.

4. Push the current index to the stack.

5. Repeat steps 3 and 4 for all elements in the array.

The span array calculated by the above method is the output.