一位面试官最近问了我这样一个问题:给定三个布尔变量a、b和c,如果三个变量中至少有两个为真,则返回true。

我的解决方案如下:

boolean atLeastTwo(boolean a, boolean b, boolean c) {
    if ((a && b) || (b && c) || (a && c)) {
        return true;
    }
    else{
        return false;
    }
}

他说这还可以进一步改进,但如何改进呢?


当前回答

这个问题的非约简解是:

a'bc + abc' + abc + ab'c

减少使用k - map,可以得到:

bc + ab + ac

可以通过在a'bc和abc' minterms上使用exclusive或,并结合abc和ab'c minterms来进一步减少此值:

b(a ^ c) + ac

其他回答

当我看到这个问题时,我的第一个想法是:

int count=0;
if (a)
    ++count;
if (b)
    ++count;
if (c)
    ++count;
return count>=2;

在看了其他帖子后,我承认

return (a?1:0)+(b?1:0)+(c?1:0)>=2;

更优雅。我想知道相对运行时是什么。

不过,无论如何,我认为这种解决办法比那种解决办法要好得多

return a&b | b&c | a&c;

variety because is is more easily extensible. What if later we add a fourth variable that must be tested? What if the number of variables is determined at runtime, and we are passed an array of booleans of unknown size? A solution that depends on counting is much easier to extend than a solution that depends on listing every possible combination. Also, when listing all possible combinations, I suspect that it is much easier to make a mistake. Like try writing the code for "any 3 of 4" and make sure you neither miss any nor duplicate any. Now try it with "any 5 of 7".

字面解释适用于所有主要语言:

return (a ? 1:0) + (b ? 1:0) + (c ? 1:0) >= 2;

但是我可能会让人们更容易阅读,并且扩展到三个以上——这一点似乎被许多程序员遗忘了:

boolean testBooleans(Array bools)
{
     int minTrue = ceil(bools.length * .5);
     int trueCount = 0;

     for(int i = 0; i < bools.length; i++)
     {
          if(bools[i])
          {
               trueCount++;
          }
     }
     return trueCount >= minTrue;
}

X = OR(a+b,c)

a b c X

1, 1, 0, 1

0, 0, 1, 1

0, 1, 1, 1

通过真值表计算:

return (a & b) | (c & (a ^ b));

在Clojure中:

(defn at-least [n & bools]
  (>= (count (filter true? bools)) n)

用法:

(at-least 2 true false true)