441 Arranging Coins

441. Arranging Coins​
1. Question
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.
nis a non-negative integer and fits within the range of a 32-bit signed integer.
Example 1:
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n = 5
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​
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The coins can form the following rows:
4
¤
5
¤ ¤
6
¤ ¤
7
​
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Because the 3rd row is incomplete, we return 2.
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Example 2:
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n = 8
2
​
3
The coins can form the following rows:
4
¤
5
¤ ¤
6
¤ ¤ ¤
7
¤ ¤
8
​
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Because the 4th row is incomplete, we return 3.
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2. Implementation
(1) Binary Search
思路：我们根据等差数列公式知道 coins的总数等于 row * (row + 1) / 2， 所以我们可以根据这个公式找出row的值，使得 row * (row + 1) / 2 小于等于n，即找row的右边界
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class Solution {
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    public int arrangeCoins(int n) {
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        long start = 1, end = n, mid = 0;
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        long coins = (long)n;
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​
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        while (start + 1 < end) {
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            mid = start + (end - start) / 2;
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​
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            if (isGreaterThanN(mid, coins)) {
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                end = mid - 1;
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            }
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            else {
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                start = mid;
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            }
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        }
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        return isGreaterThanN(end, coins) ? (int)start : (int)end;
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    }
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​
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    public boolean isGreaterThanN(long row, long coins) {
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        return  (row * row  + row) > 2 * coins; 
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    }
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}
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3. Time & Space Complexity
Binary Search: 时间复杂度O(logn), 空间复杂度O(1)

436 Find Right Interval

475 Heaters

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Contents

441. Arranging Coins

1. Question

2. Implementation

3. Time & Space Complexity

441. Arranging Coins​

1. Question

2. Implementation

3. Time & Space Complexity

441. Arranging Coins