How do you solve Find Triangular Sum of an Array on LeetCode?

Find Triangular Sum of an Array (LeetCode #2221) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The process of reducing the array can be viewed as a series of combinations that can be computed directly.

What is the brute force solution for Find Triangular Sum of an Array?

The brute force approach for Find Triangular Sum of an Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach simulates the entire process of reducing the array until only one element remains. It repeatedly creates a new array by summing adjacent elements and taking the modulo 10 until the array is reduced to a single element. The optimal Optimal Solution approach improves this to O(n).

What are the interview tips for Find Triangular Sum of an Array?

Always consider edge cases, such as arrays with a single element. Think about how you can reduce space complexity by modifying the input array directly. Practice simulating the process on paper to better understand how the values change.

What are common mistakes when solving Find Triangular Sum of an Array?

Not recognizing that the array can be modified in place, leading to unnecessary space usage. Failing to realize that the process can be optimized by directly calculating the final result.

#2221

Find Triangular Sum of an Array

Medium

ArrayMathSimulationCombinatoricsNumber TheoryArraySimulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution recognizes that the triangular sum can be computed directly without simulating the entire process. By observing the patterns in how elements combine, we can derive the final result using a mathematical approach.

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Algorithm

3 steps

1Step 1: Initialize a variable to store the current array.
2Step 2: For each index from 0 to n-1, compute the triangular sum using a formula that combines the contributions of each digit based on its position.
3Step 3: Return the final computed value.

solution.py7 lines

1def triangularSum(nums):
2    n = len(nums)
3    while n > 1:
4        for i in range(n - 1):
5            nums[i] = (nums[i] + nums[i + 1]) % 10
6        n -= 1
7    return nums[0]

ℹ

Complexity note: The time complexity is O(n) because we only need to iterate through the array once per level of reduction, and the space complexity is O(1) since we are modifying the array in place.

1The process of reducing the array can be viewed as a series of combinations that can be computed directly.
2Understanding the modulo operation helps in recognizing patterns in the sums.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.