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:
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| n = 5
The coins can form the following rows:
¤
¤ ¤
¤ ¤
|
Because the 3rd row is incomplete, we return 2.
Example 2:
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| n = 8
The coins can form the following rows:
¤
¤ ¤
¤ ¤ ¤
¤ ¤
|
Because the 4th row is incomplete, we return 3.
Solution:
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| class Solution {
public int arrangeCoins(int n) {
return (int) (Math.sqrt(2 * (long)n + 0.25) - 0.5);
}
public int arrangeCoins3(int n) {
long left = 0;
long right = n;
long k = 0;
long curr = 0;
while (left <= right) {
k = left + (right - left) / 2;
curr = k * (k + 1) / 2;
if (curr == n) return (int) k;
if (curr > n) {
right = k - 1;
} else {
left = k + 1;
}
}
return (int) right;
}
public int arrangeCoins2(int n) {
int i = 1;
int count = 0;
while (n > 0) {
n = n - i;
i++;
if (n >= 0)
count++;
}
return count;
}
}
|