1 package day20170206;
2 //LeetCode:441. Arranging Coins
3 /*
4 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.
5 Given n, find the total number of full staircase rows that can be formed.
6
7 n is a non-negative integer and fits within the range of a 32-bit signed integer.
8
9 Example 1:
10
11 n = 5
12
13 The coins can form the following rows:
14 ¤
15 ¤ ¤
16 ¤ ¤
17
18 Because the 3rd row is incomplete, we return 2.
19 Example 2:
20
21 n = 8
22
23 The coins can form the following rows:
24 ¤
25 ¤ ¤
26 ¤ ¤ ¤
27 ¤ ¤
28
29 Because the 4th row is incomplete, we return 3.
30 Subscribe to see which companies asked this question.
31 */
32 public class arrangeCoins441 {
33 public static int arrangeCoins(int n) {
34 int i=1;
35 for(;n>=i;i++){
36 n=n-i;
37 }
38 return i-1;
39 }
40 //study (k+1)k<=2n--> 4k^2+4k+1<=8n+1--> (2k+1)^2<=8n+1
41 public static int arrangeCoins2(int n){
42 return (int)((Math.sqrt(8.0*n+1)-1)/2);
43 }
44 //study left right mid*mid是一个很大的数，0.5要放在前面 left=0和left=1无差
45 public static int arrangeCoins3(int n){
46 int left=1,right=n;
47 int mid=0;
48 while(left<=right){
49 mid=(left+right)/2;
50 if(0.5*mid*(mid+1)>n)
51 right=mid-1;
52 else
53 left=mid+1;
54 }
55 return left-1;
56 }
57 public static void main(String[] args) {
58 // TODO Auto-generated method stub
59
60 System.out.println(arrangeCoins(1));
61 System.out.println(arrangeCoins(3));
62 System.out.println(arrangeCoins(4));
63 System.out.println(arrangeCoins(5));
64 System.out.println(arrangeCoins(6));
65 System.out.println(arrangeCoins(7));
66 System.out.println(arrangeCoins(8));
67 System.out.println(arrangeCoins(1804289383));
68
69 System.out.println(arrangeCoins2(1));
70 System.out.println(arrangeCoins2(3));
71 System.out.println(arrangeCoins2(4));
72 System.out.println(arrangeCoins2(5));
73 System.out.println(arrangeCoins2(6));
74 System.out.println(arrangeCoins2(7));
75 System.out.println(arrangeCoins2(8));
76 System.out.println(arrangeCoins2(1804289383));
77
78 System.out.println(arrangeCoins3(1));
79 System.out.println(arrangeCoins3(3));
80 System.out.println(arrangeCoins3(4));
81 System.out.println(arrangeCoins3(5));
82 System.out.println(arrangeCoins3(6));
83 System.out.println(arrangeCoins3(7));
84 System.out.println(arrangeCoins3(8));
85
86 System.out.println(arrangeCoins3(1804289383));
87 }
88
89 }
