class Solution:
def maxProfit(self, prices: List[int]) -> int:
"""
Calculate the maximum profit from a series of stock prices allowing unlimited transactions.
Parameters:
prices (List[int]): A list of stock prices where prices[i] is the price on the i-th day.
Returns:
int: The maximum profit achievable by summing all positive price differences.
"""
total_profit = 0 # Accumulates the overall profit from transactions
# Iterate from the second day onward, comparing each day's price with the previous day's price.
for i in range(1, len(prices)):
# Compute the profit by selling today and having bought yesterday.
profit = prices[i] - prices[i - 1]
# If the result is positive, it contributes to the overall profit.
if profit > 0:
total_profit += profit
return total_profit
Summary of Techniques and Approaches:
Greedy Strategy: The solution accumulates profit whenever there is a positive difference between consecutive days. This approach directly captures all profitable opportunities without complex decision-making.
Single-Pass Iteration: By iterating once through the list, we achieve O(n) time complexity, a common and efficient pattern for problems involving sequential analysis.
Problem Decomposition: Instead of attempting to identify the best buy and sell points, the problem is simplified by breaking it into daily profit calculations. This technique of breaking a problem into simpler, local decisions can be broadly applied in optimization problems.
Applicability: The greedy, single-pass method is applicable when local optimizations (like immediate profitable moves) lead to a global optimum. Identifying such opportunities can simplify various problems in array manipulation, scheduling, or resource allocation.