🔷 Find Triangular Sum of an Array — Clear, Detailed Explanation

Overview
You are given a 0-indexed integer array nums where each element is a single digit between 0 and 9 (inclusive). The goal is to compute the triangular sum — the single digit that remains after repeatedly transforming the array until only one element remains.

---

🔁 What the transformation does (step-by-step)

1. Check length. Look at the current array (call its length n). If n = 1, the process stops — that single element is the triangular sum.
2. Build the next row. Otherwise, create a new array of length n − 1. Each entry in the new array is the sum of two adjacent entries from the current array, reduced modulo 10 (i.e., keep only the last decimal digit). Concretely, for every index i with 0 <= i < n-1, use the expression newNums[i] = (nums[i] + nums[i+1]) % 10.
3. Replace and repeat. Replace the current array with the new array and repeat from step 1. Each iteration reduces the length by 1, so the process always terminates.

---

🧾 Why % 10 at every step?

• % 10 keeps only the units (last) digit of each sum.
  Example: (7 + 8) % 10 = 15 % 10 = 5.
• Applying modulo at each step ensures every intermediate element remains a single digit (0–9), matching the input domain.

---

✏️ Detailed walkthrough of the example

Input: nums = [1, 2, 3, 4, 5]

Step-by-step:

• Start (length 5):
  [1, 2, 3, 4, 5]
• First reduction → length 4:
  • (1 + 2) % 10 = 3 → first element
  • (2 + 3) % 10 = 5 → second element
  • (3 + 4) % 10 = 7 → third element
  • (4 + 5) % 10 = 9 → fourth element
    New array: [3, 5, 7, 9]
• Second reduction → length 3:
  • (3 + 5) % 10 = 8
  • (5 + 7) % 10 = 2 (12 % 10 = 2)
  • (7 + 9) % 10 = 6 (16 % 10 = 6)
    New array: [8, 2, 6]
• Third reduction → length 2:
  • (8 + 2) % 10 = 0 (10 % 10 = 0)
  • (2 + 6) % 10 = 8 (8 % 10 = 8)
    New array: [0, 8]
• Fourth reduction → length 1:
  • (0 + 8) % 10 = 8
    New array: [8]

✅ Result: The triangular sum for [1, 2, 3, 4, 5] is 8.

---

🔎 Important details & clarifications

• Input domain: Every value in nums is an integer digit from 0 through 9. The modulo step preserves that range for all intermediate values.
• Termination guarantee: Each pass reduces the array length by exactly one. After n − 1 passes you reach a single element.
• Singleton input: If nums already has one element (e.g., nums = [5]), that element is the triangular sum.
• Carries are discarded at each step: When two digits sum to a two-digit number (e.g., 7 + 8 = 15), the tens place is dropped — only 5 remains because 15 % 10 = 5.

---

🎯 Output

Return the single remaining digit (an integer 0–9) after performing the repeated reductions. That value is the triangular sum of the input array.

— Written by Saurabh Patil • B.Tech CSE • Software Developer