Baidu Ball(y) = x

[JohnsonElizeee]

Baidu:
用天平（只能比较，不能称重）从一堆小球中找出其中唯一一个较轻的，
使用x次天平 最多可以从y个小球中找出较轻的那个，求y与x的关系式。

set Ball(y) = x, we could get the following relation:
Ball(1) = 0;
Ball(2) = 1;
Ball(3) = 1;
Ball(4) = 2;
Ball(5) = 2;
Ball(6) = 2;
Ball(7) = 2;
Ball(8) = 2;
Ball(9) = 2;
Ball(10) = 3;
....
Ball(14) = 3;

set j is the second-max factor of y, as for number 28,
all the factors are 1, 2, 4, 7, 14, 28. so, j = 14.
set i is times number for i*j = y,
I get a relation between y and x: Ball(y) = (i/2) + Ball(j);

if y is a prime number, as 17, and its factors are 1 and itself, 17.
Ball(y) = Ball(y-1);

conclusion:

set j is the second-max factor of y and i*j = y;
if(j == 1) j = y-1; /* y is a prime number */
Ball(y) = (i/2) + Ball(j)

This opinion is out of full validation and test.
is it right?

[JohnsonElizeee]

Yeah, this is a wrong deduce.
set j is the second-max factor of y and i*j = y;
if(j == 1) j = y-1; /* y is a prime number */
Ball(y) = (i/2) + Ball(j)

in fact, this one may be better.

set j is the second-max factor of y and i*j = y;
if(j == 1) j = y-1; /* y is a prime number */
Ball(y) = (i/2) + Ball(j)  

Ball(  2)=1     Ball(  3)=1     Ball(  4)=2     Ball(  5)=2
Ball(  6)=2     Ball(  7)=2     Ball(  8)=2     Ball(  9)=2     Ball( 10)=3
Ball( 11)=3     Ball( 12)=3     Ball( 13)=3     Ball( 14)=3     Ball( 15)=3
Ball( 16)=3     Ball( 17)=3     Ball( 18)=3     Ball( 19)=3     Ball( 20)=3
Ball( 21)=3     Ball( 22)=3     Ball( 23)=3     Ball( 24)=3     Ball( 25)=3
Ball( 26)=3     Ball( 27)=3     Ball( 28)=4     Ball( 29)=4     Ball( 30)=4
Ball( 31)=4     Ball( 32)=4     Ball( 33)=4     Ball( 34)=4     Ball( 35)=4
Ball( 36)=4     Ball( 37)=4     Ball( 38)=4     Ball( 39)=4     Ball( 40)=4
Ball( 41)=4     Ball( 42)=4     Ball( 43)=4     Ball( 44)=4     Ball( 45)=4
Ball( 46)=4     Ball( 47)=4     Ball( 48)=4     Ball( 49)=4     Ball( 50)=4
Ball( 51)=4     Ball( 52)=4     Ball( 53)=4     Ball( 54)=4     Ball( 55)=4
Ball( 56)=4     Ball( 57)=4     Ball( 58)=4     Ball( 59)=4     Ball( 60)=4
Ball( 61)=4     Ball( 62)=4     Ball( 63)=4     Ball( 64)=4     Ball( 65)=4
Ball( 66)=4     Ball( 67)=4     Ball( 68)=4     Ball( 69)=4     Ball( 70)=4
Ball( 71)=4     Ball( 72)=4     Ball( 73)=4     Ball( 74)=4     Ball( 75)=4
Ball( 76)=4     Ball( 77)=4     Ball( 78)=4     Ball( 79)=4     Ball( 80)=4
Ball( 81)=4     Ball( 82)=5     Ball( 83)=5     Ball( 84)=5     Ball( 85)=5
Ball( 86)=5     Ball( 87)=5     Ball( 88)=5     Ball( 89)=5     Ball( 90)=5
Ball( 91)=5     Ball( 92)=5     Ball( 93)=5     Ball( 94)=5     Ball( 95)=5
Ball( 96)=5     Ball( 97)=5     Ball( 98)=5     Ball( 99)=5     Ball(100)=5
Ball(101)=5     Ball(102)=5     Ball(103)=5     Ball(104)=5     Ball(105)=5
Ball(106)=5     Ball(107)=5     Ball(108)=5     Ball(109)=5     Ball(110)=5
Ball(111)=5     Ball(112)=5     Ball(113)=5     Ball(114)=5     Ball(115)=5
Ball(116)=5     Ball(117)=5     Ball(118)=5     Ball(119)=5     Ball(120)=5
Ball(121)=5     Ball(122)=5     Ball(123)=5     Ball(124)=5     Ball(125)=5
Ball(126)=5     Ball(127)=5     Ball(128)=5     Ball(129)=5     Ball(130)=5
Ball(131)=5     Ball(132)=5     Ball(133)=5     Ball(134)=5     Ball(135)=5
Ball(136)=5     Ball(137)=5     Ball(138)=5     Ball(139)=5     Ball(140)=5
Ball(141)=5     Ball(142)=5     Ball(143)=5     Ball(144)=5     Ball(145)=5
Ball(146)=5     Ball(147)=5     Ball(148)=5     Ball(149)=5     Ball(150)=5
Ball(151)=5     Ball(152)=5     Ball(153)=5     Ball(154)=5     Ball(155)=5
Ball(156)=5     Ball(157)=5     Ball(158)=5     Ball(159)=5     Ball(160)=5
Ball(161)=5     Ball(162)=5     Ball(163)=5     Ball(164)=5     Ball(165)=5
Ball(166)=5     Ball(167)=5     Ball(168)=5     Ball(169)=5     Ball(170)=5
Ball(171)=5     Ball(172)=5     Ball(173)=5     Ball(174)=5     Ball(175)=5
Ball(176)=5     Ball(177)=5     Ball(178)=5     Ball(179)=5     Ball(180)=5
Ball(181)=5     Ball(182)=5     Ball(183)=5     Ball(184)=5     Ball(185)=5
Ball(186)=5     Ball(187)=5     Ball(188)=5     Ball(189)=5     Ball(190)=5
Ball(191)=5     Ball(192)=5     Ball(193)=5     Ball(194)=5     Ball(195)=5
Ball(196)=5     Ball(197)=5     Ball(198)=5     Ball(199)=5

[JohnsonElizeee]

  1 #include <stdio.h>
  2 #include <math.h>
  3
  4 int Ball(int y)
  5 {
  6     if(y <= 3) return 1;
  7     return 1+Ball( y/3 * 3 == y ? y/3 : y/3 +1 );
  8 }
  9 int main()
 10 {
 11     int i = 0;
 12     for(i = 2; i < 200; i++) {
 13         printf("Ball(%3d)=%d \t", i, Ball(i));
 14         if(i%5 == 0) puts("");
 15     }
 16     puts("");
 17     return 0;
 18 }

[JohnsonElizeee]

#include <stdio.h>

int Ball(int y)
{
	if(y <= 3) return 1;
	return 1+Ball( y/3 * 3 == y ? y/3 : y/3 +1 );
}

int F(int x)
{
	//assert(x > 0);
	int y = 2;
	while(1) if(Ball(y++) > x) break;
	return y-2;
}

int main()
{
	int i = 0;
	for(i = 1; i < 16; i++) {
		printf("F(%2d)=%9d \t", i, F(i));
		if(i%3 == 0) puts("");
	}
	puts("");
	return getchar();
}

[michael122]

不就是3^n的关系么

[zbo]

5楼说的很有道理，值得我学习。
我只是举了个反例，没有考虑过真正的结论应该是什么。
还有，昨天看了另一篇帖子才知道楼主也是中国人，我还以为是老外，回帖时一个中文没敢打。

[zbo]

Ball(23)=Ball(22),
Ball(22)=(2/2)+ball(11).
Ball(11)=3,

Ball(22)=3->

if ([1,2,3,4,5,6,7]>[8,9,10,11,12,13,14])
{ if ([1,2]>[3、4]) then [3]vs[4]->find out.
else if [1,2]==[3,4] then [5]vs[6] find out
}
else if ([1,2,3,4,5,6,7]==[8,9,10,11,12,13,14])
{ if [15、16、17]>[18、19、20] then [18]vs[19],find out
else if [15、16、17]=[18、19、20]，then [21]vs[22] find out}
}