A. Little Elephant and Interval

The Little Elephant very much loves sums on intervals.

This time he has a pair of integers l and r (l ≤ r). The Little Elephant has to find the number of such integers x (l ≤ x ≤ r), that the first digit of integer x equals the last one (in decimal notation). For example, such numbers as 101, 477474 or 9 will be included in the answer and 47, 253 or 1020 will not.

Help him and count the number of described numbers x for a given pair l and r.

Input

The single line contains a pair of integers l and r (1 ≤ l ≤ r ≤ 1018) — the boundaries of the interval.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64dspecifier.

Output

On a single line print a single integer — the answer to the problem.

Sample test(s)

input

2 47

output

12

input

47 1024

output

98

看了其他博客都是数位dp,我用了不同的解法。对于n,m，分别算出cal(n),cal(m)，即（0，n]符合结果的数，然后算出cal(n)-cal(m-1);

#include<stdio.h>
#include<string.h>
int b[100]={0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101};
__int64 pow(int n,int m)
{
	int i;
	__int64 sum=1;
	for(i=1;i<=m;i++){
		sum=sum*n;
	}
	return sum;
}


__int64 cal(__int64 n)
{
	int len=0,i,j,sum;
	if(n>=0 && n<=9)return n;
	/*if(n>=10 && n<=99){            //这里两位数的可以在这里特判一下，时间会减少30ms;
		for(i=1;i<=20;i++){
			if(n>=b[i]){
				sum=i;
			}
			else break;
		}
		return sum;
	}*/
	
	
	__int64 x=n,ans=0,t,num;
	int a[100];
	memset(a,0,sizeof(a));
	while(x>0){
		a[++len]=x%10;x=x/10;
	}
	ans=ans+9;
	for(i=2;i<=len-1;i++){
		ans=ans+9*pow(10,i-2);
	}
	if(len>2) ans=ans+a[len]*(pow(10,len-2))-pow(10,len-2);
	
	if(a[1]>=a[len]){
		if(len>2)
		{
		ans=ans+(n-a[len]*pow(10,len-1))/10+1;
		return ans;
		}
		else {ans=ans+a[len];return ans;}
	}
	t=n;
	while((t%10)!=a[len]){         //如果最高位和最低位不同，那么先让这个数每次减一，减到最低位等于一开始的最高位，
		t--;                   //然后看最高位的数是否改变，如果没有改变，那么总数加上除了首尾的中间一些数，如57895，取中间为789.
	}                              //如果改变，则直接返回
	if(len==2){
		ans=ans+a[len]-1;return ans;
	}
	
	if(t-a[len]*pow(10,len-1)<0){
		return ans;
	}
	else{
		ans=ans+(t-a[len]*pow(10,len-1))/10+1;
		return ans;
	}
}


int main()
{
	__int64 n,m,n1,m1;
	int i,j;
	//while(scanf("%I64d",&n)!=EOF)
	while(scanf("%I64d%I64d",&n,&m)!=EOF)
	{
		printf("%I64d
",cal(m)-cal(n-1));
		//printf("%I64d
",cal(n));
	}
	return 0;
}

今天又用数位dp的方法做了一下。

思路：先预处理出dp[i][j]表示第i位为j符合要求的数的个数，然后就和普通的数位dp一样了，算的时候算[0,r)的个数，那么最后答案就是solve(m+1)-solve(n)。这里注意pow函数精度不够，所以要自己手写一个。

#include<iostream>
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<string>
#include<algorithm>
#define inf 99999999
#define pi acos(-1.0)
#define maxn 1000050
#define MOD 1000000007
using namespace std;
typedef long long ll;
typedef long double ldb;
ll po[25];
void init1()
{
    int i,j;
    po[0]=1;
    for(i=1;i<=18;i++)po[i]=po[i-1]*10;
}

ll dp[24][12];
void init()
{
    int i,j,k;
    memset(dp,0,sizeof(dp));
    for(j=0;j<=9;j++)dp[1][j]=1;
    for(i=2;i<=19;i++){
        for(j=0;j<=9;j++){
            if(j==0){
                for(k=0;k<=9;k++){
                    dp[i][j]+=dp[i-1][k];
                }
            }
            else{
                dp[i][j]=po[i-2];
            }
        }
    }
}
ll solve(ll x)
{
    int i,j,len=0;
    ll t=x;
    int wei[20];
    while(t){
        wei[++len]=t%10;
        t/=10;
    }
    wei[len+1]=0;
    if(len==1){
        return x;
    }

    ll sum=0;
    for(i=len;i>=1;i--){
        if(i==len){
            for(j=0;j<wei[i];j++){
                sum+=dp[i][j];
            }
        }
        else{
            if(i==1){
                if(wei[1]>wei[len] ){
                    sum++;
                }
            }
            else{
                for(j=0;j<wei[i];j++){
                    sum+=po[i-2];
                }
            }

        }
    }
    return sum;
}


int main()
{
    //freopen("o.txt","w",stdout);
    ll n,m;
    int i,j;
    init1();
    init();
    while(scanf("%I64d%I64d",&n,&m)!=EOF){
            printf("%lld
",solve(m+1)-solve(n) );
    }
    return 0;
}