Problem 8: Round Numbers [ICPSC, 1981]

The cows, as you know, have no fingers or thumbs and thus are unable
to play 'Scissors, Paper, Stone' (also known as 'Rock, Paper,
Scissors', 'Ro, Sham, Bo', and a host of other names) in order to
make arbitrary decisions such as who gets to be milked first. They
can't even flip a coin because it's so hard to toss using hooves.

They have thus resorted to "round number" matching. The first cow
picks an integer less than two billion. The second cow does the
same.  If the numbers are both "round numbers", the first cow wins,
otherwise the second cow wins.

A positive integer N is said to be a "round number" if the binary
representation of N has as many or more zeroes than it has ones.
For example, the integer 9, when written in binary form, is 1001.
1001 has two zeroes and two ones; thus, 9 is a round number. The
integer 26 is 11010 in binary; since it has two zeroes and three
ones, it is not a round number.

Obviously, it takes cows a while to convert numbers to binary, so
the winner takes a while to determine.  Bessie wants to cheat and
thinks she can do that if she knows how many "round numbers" are
in a given range.

Help her by writing a program that tells how many round numbers
appear in the inclusive range given by the input (1 <= Start <
Finish <= 2,000,000,000).

PROBLEM NAME: rndnum

INPUT FORMAT:

* Line 1: Two space-separated integers, respectively Start and Finish.

SAMPLE INPUT (file rndnum.in):

2 12


OUTPUT FORMAT:

* Line 1: A single integer that is the count of round numbers in the
        inclusive range Start..Finish

SAMPLE OUTPUT (file rndnum.out):

6

OUTPUT DETAILS:

 2    10  1x0 + 1x1  ROUND
 3    11  0x0 + 2x1  NOT round
 4   100  2x0 + 1x1  ROUND
 5   101  1x0 + 2x1  NOT round
 6   110  1x0 + 2x1  NOT round
 7   111  0x0 + 3x1  NOT round
 8  1000  3x0 + 1x1  ROUND
 9  1001  2x0 + 2x1  ROUND
10  1010  2x0 + 2x1  ROUND
11  1011  1x0 + 3x1  NOT round
12  1100  2x0 + 2x1  ROUND

• 这样理解啊，thanks (0) qiqilrq 2007-10-22 15:24:09