整数中1出现的次数 分段算法

算法：

把1-100000000,分成10000段。每段100000，统计这一段的和。

这题还可以用按位DP，组合数学做

代码：

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<iostream>
#include<vector>
#include<string>
#include<math.h>
#include<map>
#include<set>
#include<algorithm>
using namespace std;

long long sum[100101] ={0,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,150001,250001,349999,250000,250000,250000,250000,250000,250000,250000,249999,150001,249999,150000,150000,150000,150000,150000,150000,150000,150000,150001,249999,150000,150000,150000,150000,150000,150000,150000,150000,150001,249999,150000,150000,150000,150000,150000,150000,150000,150000,150001,249999,150000,150000,150000,150000,150000,150000,150000,150000,150001,249999,150000,150000,150000,150000,150000,150000,150000,150000,150001,249999,150000,150000,150000,150000,150000,150000,150000,150000,150001,249999,150000,150000,150000,150000,150000,150000,150000,150000,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50001,150001,249999,150000,150000,150000,150000,150000,150000,150000,149999,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000,50000,50000,50000,50000,50000,50000,50001,149999,50000,50000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long long AC( int x )
{
  long long cnt = 0;
  while( x )
  {
     if( x % 10 == 1 )
         ++cnt;
     x /= 10;       
  }
  return cnt;     
}

int main( )
{
   int a, b;
   for( int i = 1; i <= 10000; i++)
        sum[i] += sum[i-1];
   while( scanf("%d%d",&a,&b) != EOF )
   {
      if( a > b )
          swap(a,b);
      if( a != 0 )
          a -= 1;
      int x = a, y = b;
      int t1 = a / 100000, t2 = b / 100000;
      long long ret = 0;
      ret +=  sum[t2] - sum[t1];
      a -= a % 100000, b -= b % 100000;
      for (int i = a + 1; i <= x; ++i) {
            ret -= AC(i);
      }
      for (int i = b + 1; i <= y; ++i) {
            ret += AC(i);
      }
      cout<<ret<<endl;
   }    
   return 0;
}