POJ 3252 Round Numbers 组合数

最新推荐文章于 2019-04-10 19:03:00 发布

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本文介绍了一种算法，用于计算给定范围内二进制形式中零的数量大于等于一的数量的正整数（即“圆数”）的数量。通过寻找规律并使用组合数学的方法，实现了高效的计算。

Round Numbers

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 12765		Accepted: 4913

Description

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).

Input

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

Output

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

Sample Input

2 12

Sample Output

Source

USACO 2006 November Silver

题意是求两个数之间 "round number"数的个数

"round number"是指二进制0个数大于等于1的个数的数

细心找规律。。。

坑点：看讨论区说的longlong不能过，int才能过。。。。没试

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<string>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
#include<set>
#define ll long long
using namespace std;
int myc(int n,int r)
{
	int sum=1;
	for(int i=1;i<=r;i++)
	sum=sum*(n+1-i)/i;
	return sum;
}
int numm(int x)
{
	int a[60],i=0,j,ans=0,len;
	while(x)
	{
		a[i++]=x&1;
		x>>=1;
	}
	len=i;
//	for(i=len-1;i>=0;i--)
//	printf("%d",a[i]);
	for(i=2;i<len;i++)
	{
		for(j=i-1;j>=(i+1)/2;j--)
		{
			ans+=myc(i-1,j);
		}	
	}
//	printf("%d\n",ans);
	int zero=0,one=1;
	for(i=len-2;i>=0;i--)
	{
		if(a[i]&1)
		{
			for(j=i;(j+zero+1>=i-j+one)&&j>=0;j--)
			{
				ans+=myc(i,j);
			}
			one++;
		}
		else
		zero++;
	}
	return ans;
	
}

int main()
{
 int a,b,c,ans,one=0,zero=0;
	scanf("%d %d",&a,&b);
 
 	ans=one=zero=0;
 	c=b;
 	while(c)
 	{
 		if(c&1)
 			one++;
 		else
 			zero++; 
 		c>>=1;
 	}
	ans=numm(b)-numm(a);
	if(zero>=one)
 		ans++;
 	printf("%d\n",ans);
 
return 0;
}