zerojudge d063. 0 與 1

題意：若輸入０輸出１，若輸入１輸出０

解法大全：

判斷式：

三元運算子

布林代數：！

n=!n;

n= not n;

n=n^1 (n^=1)

n= n xor 1

布林代數比較：

n=(n!=1)

n=(n==0);

n=(n<1);

式子：

求經過（1,0）和（0,1）的點

ans:

1)y=-(x-1);

2)y=(x-1)*(x-1);

3)y=| x-1|;

[process and proof]

1)Let it be a linear equation(y=mx+b)

replace the points (0,1) and (1,0).

0=1*m+b;

1=0*m+b;

get m=-1,b=1;

2)Let it be a quadratic equation(y=a*x*x+b*x+c)

replace the points (0,1) and (1,0).

1=a*0+b*0+c;

0=a*1+b*1+c;

get c=1; which has infinitely many solution.(a*x*x-b*x=-1)

the euation can be simplify y=(x-1)*(x-1); if a=1,b=-2;

3)according to 1),2)

we can conclude that y=|x-1|;

#end

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