Problem:
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:
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¤ ¤
¤ ¤ Because the 3rd row is incomplete, we return 2.
Example 2:
n = 8 The coins can form the following rows:
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¤ ¤
¤ ¤ ¤
¤ ¤ Because the 4th row is incomplete, we return 3.
Summary:
用n枚硬币摆成塔形，求可以摆成的完整的行数。
Analysis:
1.最简单的思路，依次减去递增的每行硬币数，直到n为非整数。
class Solution {
public:
int arrangeCoins(int n) {
int i = ;
while (n > ) {
i++;
n -= i;
}
return n == ? i : i - ;
}
};
2. 解一元二次方程：x^2 + x = 2 * n 解得：x = sqrt(2 * n + 1 / 4) - 1 /2
但要注意在此处n为32位有符号整型数，2 * n后有可能溢出，故在代码中应做相应处理。
class Solution {
public:
int arrangeCoins(int n) {
return sqrt((long long) * n + 0.25) - 0.5;
}
};