Number of Smooth Descent Periods of a Stock

Problem Description

You are given an integer array prices representing the daily price history of a stock, where prices[i] is the stock price on the ith day. A smooth descent period of a stock consists of one or more contiguous days such that the price on each day is lower than the price on the preceding day by exactly 1. The first day of the period is exempted from this rule. Return the number of smooth descent periods.

Key Insights

• A single day price is always a smooth descent period.
• A contiguous sequence of days forming a smooth descent period must decrease by exactly 1 each day.
• We can count the number of smooth descent periods by iterating through the array and checking the conditions for descent.
• The total count of smooth descent periods can be derived from the lengths of valid segments.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use a linear scan through the prices array. We maintain a count of smooth descent periods. For each day, we check if the current price is exactly 1 less than the previous day's price. If it is, we can extend the currently counted descent period. If not, we reset the count. We also add the count of individual days as valid smooth descent periods.

1. Initialize a total count of smooth descent periods.
2. Iterate through the prices array:
   • For each price, check the difference with the previous price.
   • If the difference is 1, increment the current period's count.
   • If not, reset the count to 1 (for the current day).
   • Add the current period's count to the total count.
3. Return the total count.

Code Solutions