Solve stock-pattern trading and substring elimination

Part A — Stock trading by pattern signals:

• Input: an integer array prices (length n) of daily stock prices; an array buyPattern and an array sellPattern, each containing only -1 or 1, where 1 means the price went up from the previous day and -1 means it went down.
• Define sign(prices[i] - prices[i-1]) as 1 if positive, -1 if negative, and 0 if zero. A pattern of length k matches on day t (t >=

1. if the last k day-to-day signs [sign(prices[t-k+1]-prices[t-k]), ..., sign(prices[t]-prices[t-1])] equals the pattern exactly (zeros break a match since patterns contain only -1 or 1).

• Start with 0 shares. On each day t, if a sellPattern match occurs, sell 1 share (only if holdings > 0); if a buyPattern match occurs, buy 1 share. Both actions can occur on the same day; process the sell before the buy. Shorting is not allowed; holdings never go below 0.
• Output: an array holdings of length n where holdings[t] is the number of shares held after processing day t. Example output format: [0,0,1,2,1,0].
• Target: O(n) time and O(

1. extra space beyond the output.

Part B — Remove fixed substrings repeatedly:

• Input: a string s and a set P of disallowed 2-character substrings (e.g., {"ab", "bc", "cd"}).
• Task: Repeatedly remove any occurrence of any substring in P until none remain. Return the final string length (and discuss how to return the final string as well).
• Constraints: n up to 2e5; |P| up to 26*26. Design an O(n) time solution with O(

1. or O(min(n, alphabet)) extra space, and explain correctness.