如何使它的空间复杂度为O（1）而不是O（n）？

Question

I'm trying to convert a decimal into binary number using iterative process. How can I make this have a space complexity of O(1) instead of O(n)?

int i = 0;
int j;
int bin[] = new int[n]; //n here is my paramater int n
while(n > 0) {
   bin[i] = n % 2;
   n /= 2;
   i++;
}

//I'm reversing the order of index i with variable j to get right order (e.g. 26 has 11010, instead of 01011)
for(j = i -1; j >= 0; j--) {
   System.out.print(bin[j]);
}   

Answer 1

First, you don't need place for n bits if the value itself is n . You just need log2(n)+1 . It won't give you wrong results to use n bits, but for big values of n , the memory available to your Java process might be not enough.

And, about O(1) ... maybe not really what you were thinking, but:
Javas int has a specific fixed value range, which leads to the guarantee that a (positive) int value needs max 31 bit (if you have negative numbers too, storing the sign somewhere is necessary, that's bit 32).

With that information, strictly speaking, you can get O(1) just by rewriting your loops so that they loop exactly 31 times. Then, for each value of n , your code has exactly the same amount of steps, and that is O(1) per definition.

Going the bit fiddling route won't help here. There are some useful shortcuts if your values fulfil certain conditions, but if you want your code to work with any int value, the normal loop as you have here is likely the best you can get.

(Of yourse, CPU intrinsics may help, but not for Java...)