Arranging Coins
You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins.
Given n, find the total number of full staircase rows that can be formed.
n is a non-negative integer and fits within the range of a 32-bit signed integer.
Example:
n = 5
The coins can form the following rows:
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¤ ¤
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Because the 3rd row is incomplete, we return 2.
Solution
Actually, this is the math problem.
The sum of length of each row of staircase shape is n(n + 1) / 2. So this question is to solve the inequality x² + x - 2n <= 0.
Use the formula : x = (-b +/- sqrt(b² - 4ac)) / 2a
The final answer will be x = sqrt(2*n + 0.25) - 0.5
import kotlin.math.sqrt
fun arrangeCoins(n: Int): Int {
return (sqrt(2 * n.toLong() +0.25) - 0.5).toInt()
}