InterviewStreet,

Problem:

2's complement (10 Points)
One of the basics of Computer Science is knowing how numbers are represented in 2's complement. Imagine that you write down all numbers between A and B inclusive in 2's complement representation using 32 bits. How many 1's will you write down in all ?
Input:
The first line contains the number of test cases T (<1000). Each of the next T lines contains two integers A and B.
Output:
Output T lines, one corresponding to each test case.
Constraints:
-2^31 <= A <= B <= 2^31 - 1

Sample Input:
3
-2 0
-3 4
-1 4
Sample Output:
63
99
37

Explanation:
For the first case, -2 contains 31 1's followed by a 0, -1 contains 32 1's and 0 contains 0 1's. Thus the total is 63.
For the second case, the answer is 31 + 31 + 32 + 0 + 1 + 1 + 2 + 1 = 99

The big part of this problem is to deal with the big number, the programmer needs to convert the integer to long very first, then do the other operations.

Source Code:

/**
* Problem: 2's complement, from interviewStreet.
*
* The solution is from the link, which reached a log(n) time complexity on this
* one.
*/

/**
* @author antonio081014
* @since Jan 5, 2012, 1:41:35 PM
*/
public class Solution {

public static void main(String[] args) throws Exception {
// new DataInputStream(new FileInputStream(args[0]))));
// BufferedWriter bw = new BufferedWriter(new FileWriter(args[1]));
for (int t = 1; t <= T; t++) {
int a = Integer.parseInt(str[0]);
int b = Integer.parseInt(str[1]);
System.out.println(solve(a, b));
// bw.write(Long.toString(solve(a, b)) + "\n");
}
br.close();
// bw.close();
}

/**
* http://stackoverflow.com/questions/7942732/number-of-1s-in-the-twos-
* complement-binary-representations-of-integers-in-a-ran
*
* The explanation greatly explans everything.
*
* */
public static long solve(int a, int b) {
if (a >= 0) {
long ret = counter(b);
if (a > 0)
ret -= counter(a - 1);
return ret;
}
long ret = ((long32 * (-(long) a)) - counter(-a - 1);
if (b > 0)
ret += counter(b);
else if (b < -1) {
b++;
ret -= ((long32 * (-(long) b)) - counter(-b - 1);
}
return ret;
}

/**
* Calculate the number of 1s from number 0 to number num;
*
* */
public static long counter(int num) {
if (num == 0)
return 0L;
if (num % 2 == 0)
return counter(num - 1) + ones(num);
return (((long) num + 1) / 2) + 2 * counter(num / 2);
}

/**
* Calculate the number of 1s in the number
*/
public static long ones(int num) {
String str = Integer.toBinaryString(num);
long sum = 0L;
for (int i = 0; i < str.length(); i++)
if (str.charAt(i) == '1')
sum++;
return sum;
}
}