[LeetCode] 441. Arranging Coins

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.

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

	class Solution {
	public:
	int arrangeCoins(int n) {
	unsigned int num = 2 * n;
	int ans = static_cast<int>(sqrt(num + 0.25) - 0.5);
	return ans;
	}
	};

view raw coins.cpp hosted with ❤ by GitHub