【打表】数页码 count.pas/c/cpp

数页码
count.pas/c/cpp

源程序名 count.pas|c|cpp
输入文件名 count.in
输出文件名 count.out
时间限制 1s/testcase
空间限制 32MB

问题描述
一本书的页码是从 1-n 编号的连续整数：1, 2, 3, ... , n。请你求出全部页码中所有单个数字的和，例如第 123 页，它的和就是 1+2+3=6。

输入数据
一行为 n(1 <= n <= 10^9)。

输出数据
一行，代表所有单个数字的和。

样例输入
3456789

样例输出
96342015

 

 

初看这一题，打表!这是最直接的方法了，前面也说过打表，现在细说一下

打表应该不难，就是写一个朴素的程序，把数据打出来即可，顺便打上逗号（,），可以直接不加修改复制到程序

下面是打表程序

//在主程序中定义long long 为LL
typedef long long LL;

LL calc(int x)
{
    LL sum=0;
    while(x)
    {
        sum+=x%10;
        x/=10;
    }
    return sum;
}
//下面是主程序的打表部分
    LL sum=0;
    for(int i=1;i<1000000000;i++)
    {
        sum+=calc(i);
        if(i%100000==0)//每隔100000打一个数
        {
            cout<<sum<<',';
            sum=0;
            if(i%10000000==0)printf("\n");//相当于每打100数打一个回车
        }
    }

　　

为什么要每隔100000个数打一个数，不全部打完了呢？竞赛要求选手提交的源程序是不能超过100K的，所以全部打完肯定不止100K了，到时候程序根本交不上去
当然，至于到底每隔多少打一个数是你自己根据情况而定的，后面看完以后就应该知道该多少了

那么每隔100000打一个，在中间的又怎么找呢？当然是老老实实算了~就算是199999这个数，我们也只需要算99999次，所以已经大大提升了效率

不对，我们是从1开始循环打表的，那么小于100000的就没法计算，难道加上100000的？所以我们要在表的前面加一个数0

上面打表程序中在每次输出过后还把sum清零了，为什么呢？ 如果不清零，是不是一个天文数字？所以清零是为了看起来好看，不至于一个数字很长，也是为了不超过100K，那么每次找到当前位置之后，只需要把前面的累加一次就可以了

好了，放上代码

下面代码打表出来的常量数组可能由于网页排版问题不对，所以建议自己用打表程序，生成后复制进去

C++ Code

/*
C++ Code
http://oijzh.cnblogs.com
by jiangzh
*/
#include<cstdio>
#include<iostream>
using namespace std;

typedef long long LL;
const int maxn=100000;

const int a[]={0,
2250001,2350001,2450001,2550001,2650001,2750001,2850001,2950001,3050001,3149992,2350001,2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3249992,2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3349992,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3449992,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049983,
2350001,2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3249992,2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3349992,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3449992,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149983,
2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3349992,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3449992,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249983,
2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3449992,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349983,
2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449983,
2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449992,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4549983,
2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449992,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4549992,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4649983,
2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449992,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4549992,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4649992,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4749983,
3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449992,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4549992,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4649992,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4749992,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4849983,
3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449992,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4549992,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4649992,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4749992,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4849992,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4850001,4949974,
2350001,2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3249992,2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3349992,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3449992,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149983,
2450001,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3349992,2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3449992,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249983,
2550001,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3449992,2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349983,
2650001,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3549992,2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449983,
2750001,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3649992,2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449992,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4549983,
2850001,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3749992,2950001,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3849992,3050001,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3949992,3150001,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4049992,3250001,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4149992,3350001,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4249992,3450001,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4349992,3550001,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4449992,3650001,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4549992,3750001,3850001,3950001,4050001,4150001,4250001,4350001,4450001,4550001,4649983,
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3950001,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4849992,4050001,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4850001,4949992,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4850001,4950001,5049992,4250001,4350001,4450001,4550001,4650001,4750001,4850001,4950001,5050001,5149992,4350001,4450001,4550001,4650001,4750001,4850001,4950001,5050001,5150001,5249992,4450001,4550001,4650001,4750001,4850001,4950001,5050001,5150001,5250001,5349992,4550001,4650001,4750001,4850001,4950001,5050001,5150001,5250001,5350001,5449992,4650001,4750001,4850001,4950001,5050001,5150001,5250001,5350001,5450001,5549992,4750001,4850001,4950001,5050001,5150001,5250001,5350001,5450001,5550001,5649992,4850001,4950001,5050001,5150001,5250001,5350001,5450001,5550001,5650001,5749983,
4050001,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4850001,4949992,4150001,4250001,4350001,4450001,4550001,4650001,4750001,4850001,4950001,5049992,4250001,4350001,4450001,4550001,4650001,4750001,4850001,4950001,5050001,5149992,4350001,4450001,4550001,4650001,4750001,4850001,4950001,5050001,5150001,5249992,4450001,4550001,4650001,4750001,4850001,4950001,5050001,5150001,5250001,5349992,4550001,4650001,4750001,4850001,4950001,5050001,5150001,5250001,5350001,5449992,4650001,4750001,4850001,4950001,5050001,5150001,5250001,5350001,5450001,5549992,4750001,4850001,4950001,5050001,5150001,5250001,5350001,5450001,5550001,5649992,4850001,4950001,5050001,5150001,5250001,5350001,5450001,5550001,5650001,5749992,4950001,5050001,5150001,5250001,5350001,5450001,5550001,5650001,5750001
};

int n;
LL ans;

LL calc(int x)
{
    LL sum=0;
    while(x)
    {
        sum+=x%10;
        x/=10;
    }
    return sum;
}

int main()
{
    freopen("count.in","r",stdin);
    freopen("count.out","w",stdout);
    /*************打表*******************
    LL sum=0;
    for(int i=1;i<1000000000;i++)
    {
        sum+=calc(i);
        if(i%100000==0)
        {
            cout<<sum<<',';
            sum=0;
            if(i%10000000==0)printf("\n");
        }
    }
    *************打表******************/
    
    scanf("%d",&n);
    int l=(n/maxn)*maxn;
    int r=l+n%maxn;
    ans=0;
    for(int i=1;i<=n/maxn;i++) ans+=a[i];
    for(int i=l+1;i<=r;i++)
    {
        ans+=calc(i);
    }
    cout<<ans;

    
    
    return 0;
}