Leetcode 15th Dec daily Problem | 2110. Number of Smooth Descent Periods of a Stock

Welcome to today's LeetCode Daily Challenge! In this video, we'll dive deep into problem 2110: "Number of Smooth Descent Periods of a Stock." This is a fantastic problem that tests your understanding of array manipulation and recognizing simple, yet powerful, linear-time solutions.
🔍 What You Will Learn:
Problem Breakdown: Clearly defining what a "smooth descent period" is and how to identify it within a given array of stock prices.
The Intuitive Approach: How to find a solution that works in O(n^2) time by checking all subarrays, and why that's too slow for the constraints.
The Optimal O(n) Solution: We will walk through the most efficient approach, which is surprisingly simple! We'll show how to use a single pass (linear time) to count all valid periods without needing complex Dynamic Programming or a full Sliding Window setup.
Mathematical Insight: Discovering the hidden mathematical pattern that allows us to calculate the total number of smooth descent periods in constant time ($O(1)$) once the length of a descent segment is known.
💡 The Core Concept:A segment of length L that is a smooth descent period (where each $prices[i] = prices[i-1] - 1$) contributes a total of $\frac{L(L+1)}{2}$ smooth descent periods. We only need to find the length of consecutive smooth segments!