2221. Find Triangular Sum of an Array
Approach
Iteratively reduce array by pairwise modular sums until one element remains.
Key Techniques
Array problems involve manipulating elements stored in a contiguous block of memory. Key techniques include two-pointer traversal, prefix sums, sliding windows, and in-place partitioning. In C#, arrays are zero-indexed and fixed in size — use List<T> when you need dynamic resizing.
Math problems test number theory, combinatorics, and modular arithmetic. Common tools: GCD/LCM (Euclidean algorithm), prime sieve, modular inverse (Fermat's little theorem), digit manipulation, and bit tricks. Overflow is a key concern in C# — use long when products may exceed 2³¹.
Simulation problems require implementing the described process step by step. Focus on correctly handling edge cases and state transitions. Common in geometry, game problems, and string manipulation. Optimize only if the naive simulation exceeds the time limit.
// Approach: Iteratively reduce array by pairwise modular sums until one element remains.
// Time: O(n²) Space: O(1)
public class Solution
{
public int TriangularSum(int[] nums)
{
for (int currentLength = nums.Length - 1; currentLength > 0; currentLength--)
{
for (int index = 0; index < currentLength; index++)
nums[index] = (nums[index] + nums[index + 1]) % 10;
}
return nums[0];
}
}