打印此序列的算术表达式是什么? [英] What is arithmetic Expression that print this Sequence?

问题描述

打印此序列的算术表达式是什么?

8,7,8,7,8,7，.......

What is arithmetic Expression that print this Sequence?

8,7,8,7,8,7,.......

x=??;
While(true){
x=[??????];            //Arithmetic Expression.
System.Out.Print(x+",");

}

推荐答案

尝试类似

? = x ₀
8 = x ₁ = c-x ₀ →x ₀ = c-8
7 = x ₂ = c-x ₁ →x ₁ = c-7 = 8→c =? →x ₀ =?
...
... = x _{n + 1} = c-x _n

那么，c是什么，x ₀ 是什么?
说的太多了吗?

玩得开心！
干杯
Andi

Try something like

? = x₀
8 = x₁ = c - x₀ → x₀ = c - 8
7 = x₂ = c - x₁ → x₁ = c - 7 = 8 → c = ? → x₀ = ?
...
... = x_n+1 = c - x_n

So, what is c and what is x₀?
Too much said?

Have fun!
Cheers
Andi

如果您要求的是位运算表达式(&, |, ~)而不是算术表达式(+, -, *, /, %)，则这些特定值有一个简单的解决方案:

x = ~x & 0x0F;

原因:7的位模式是00000111，8的位模式是00001000-> 7和8是最低4位中彼此的反位.
~00000111 & 00001111 = 00001000
~00001000 & 00001111 = 00000111

干杯
Andi

If you asked for a bit operations expression (&, |, ~) instead of an arithmetic expression (+, -, *, /, %), the particular values have a simple solution:

x = ~x & 0x0F;

Reason: the bit pattern of 7 is 00000111 and of 8 is 00001000 --> 7 and 8 are the inverse bits of each other in the lowest 4 bits.
~00000111 & 00001111 = 00001000
~00001000 & 00001111 = 00000111

Cheers
Andi

这个问题的解决方案需要一分钟左右的时间:x = 7; /* … */ x = (x % 2) + 7;就可以了.



另一种解决方案:x = x + 2 * (x & 1) - 1;在除法运算符比加法运算符慢得多的CPU上，它可能是最快的.和位掩码运算符总是非常快.



更准确地说，由于安德烈亚斯·吉列(Andreas Gieriet)的出色发言，更快的解决方案是:x = x + ((x & 1) << 1) - 1;

—SA

The solution of this problem requires a minute or so: x = 7; /* … */ x = (x % 2) + 7; that''s it.



One more solution: x = x + 2 * (x & 1) - 1; it can be the fastest on the CPUs where division operators are much slower than additive ones; and bit mask operators are always fast.



More exactly, even faster solution, thanks to the great note by Andreas Gieriet, would be this: x = x + ((x & 1) << 1) - 1;

—SA

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