poj 3252 Round Numbers (数位DP）

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

6

题意：求出区间内二进制表示是0的个数不小于1的个数的数的个数 ；

思路：用记忆化搜索dfs(len,num0,num1,x,flag)len表示二进制的位置，num0表示0的个数,x表示到当前位表示的十进制数，flag标记是不是访问到上限,这题有趣的是由于要记录0和1的数并且要记忆化搜索，我们用数组记录位的时候就需要记录二进制位，才能记忆化，刚开始用的十进制出错了，原来是记忆化的时候出错了；

代码：

#include<cstdio>#include<algorithm>#include<cstring>using namespace std;int dp[50][50][50];int b[15];int find(int n,int flag){    int ans=0,end;    for(int i=0;i<32;i++)        if((1<<i)&n)        {            ans++;            end=i;        }    if(flag)        return ans;    else        return end-ans+1;}int dfs(int len,int num0,int num1,int x,int flag){    if(len==0)        return num0>=num1;    if(!flag&&dp[len][num0][num1]!=-1)    {        return dp[len][num0][num1];    }    int ans=0;    int end=flag?b[len]:1;    for(int i=0;i<=end;i++)    {        ans+=dfs(len-1,x*2+i?find(x*2+i,0):0,x*2+i?find(x*2+i,1):0,x*2+i,flag&&i==end);    }    if(!flag)        dp[len][num0][num1]=ans;    return ans;}int solve(int n){    int len=0;    while(n)    {        b[++len]=n%2;        n=n/2;    }    return dfs(len,0,0,0,1);}int main(){    int n,m;    memset(dp,-1,sizeof(dp));    while(~scanf("%d%d",&n,&m))    {        printf("%d\n",solve(m)-solve(n-1));    }}