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Re:谁能给个清晰的思路

Posted by 20053565 at 2009-07-21 09:05:29 on Problem 3252 and last updated at 2009-07-21 09:05:58
In Reply To:谁能给个清晰的思路 Posted by:smallport at 2009-04-27 11:14:48
> 小女子哭求~~~
> ps:ACM的女生太少了
我就是在搞ACM的时候认识我女朋友的,呵呵
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First note that you only need to count the number of round numbers not exceeding Start-1 and subtract that from the number of round numbers not exceeding Finish. So we are only concerned with counting the number of round numbers not exceeding some number X. Since X can be up to a two billion, we cannot count round numbers one by one. 

Consider X in binary. Let N be the number of digits in X. 

Let A(x,y) be the number of binary strings with x '0's and y '1's that begin with 0. Let B(x,y) be the number of binary strings with x '0's and y '1's that begin with 1. Let C(x,y) be the number of binary strings with x '0's and y '1's that begin with 0 where each string represents a number not exceeding the number represented by the last x+y digits of X. Let D(x,y) be the number of binary strings with x '0's and y '1's that begin with 1 where each string represents a number not exceeding the number represented by the last x+y digits of X. 

We update A, B, C, D using dynamic programming bottom up for each x+y=k, incrementing k until k = N. 

The desired result is the sum of all D(x,y) where x+y = N and x>=y, plus the sum of all B(x,y) with x+y=y. 

Do this procedure for both Finish and Start-1 and subtract to get answer. 

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