You are given two independent interview questions. ## 1) Triangle minimum path sum (DP) Given a triangular array `triangle` with `n` rows, find the minimum path sum from the top to the bottom. - You start at `triangle[0][0]`. - From row `i`, column `j`, you may move to row `i+1` at column `j` or `j+1`. - Return the minimum possible sum along any valid top-to-bottom path. **Input:** A list of lists, where row `i` has length `i+1`. **Output:** An integer (or numeric) minimum path sum. **Constraints (typical):** `1 <= n <= 2000`, values may be negative/positive. --- ## 2) Two dice stopping problem + Monte Carlo There are two fair dice: - Die A has faces `{1,2,3,4,5}` (a 5-sided die). - Die B has faces `{1,2,3,4,5,6}` (a 6-sided die). The experiment proceeds in **rounds**. In each round, you roll **both** dice once. - The process **stops** at the first round where **at least one** die shows `1`. - In the stopping round: - Die A **wins** if `A=1` and `B≠1`. - Die B **wins** if `B=1` and `A≠1`. - It is a **tie** if `A=1` and `B=1`. Answer the following: 1. What is the probability that the **5-sided die (Die A) wins**? 2. What is the **expected number of rounds** until the process stops? 3. Implement a **Monte Carlo simulation** to estimate (1) and (2), and discuss how many trials you would run to get a stable estimate.