轉自LeetCode
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.
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 1:
n = 5 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ Because the 3rd row is incomplete, we return 2.
Example 2:
n = 8 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ Because the 4th row is incomplete, we return 3.<Solution>
這題是數學題
梯形每個梯數的長度總和，就是差為1的等差級數的和
公式為 x(x + 1) / 2
所以這題答案就是在解 x^2 + x - 2n <= 0
用一元二次公式解 : x = (-b +/- sqrt(b^2 - 4ac)) / 2a
因為答案不會有負的，所以最後的算式就是
x = sqrt(2*n + 0.25) - 0.5
最後會將答案 cast 成 int，預設就是無條件捨去，所以符合 <= 0 的算式
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