算法设计与分析-1-页码统计

一本书的页码从自然数1开始顺序编码直到自然数N。数的野马按照通常的习惯编排，每个页码都不含多余的前导数字0，
例如第6页用数字6表示，而不是06，数字计数问题要求对给定数的总页码n计算出书的全部页码中分别用到多少次数字
0,1,2...9
算法设计  给定的表示数的总页码的十进制数n（1<= n <= 10^9）计算数的全部页码中分别用到多少次数字0,1,2...9


思路：
     规律，对于页码n,当n小于10时0出现0次，1-9出现1次；
                            100时0出现9    1-9出现20；
                            1000时 0出现189次 1-9 300次；
                             。。。。
    其中有规律吗？
    对于n小于100,1出现的次数是10（个位次数1.11.21.31...91）+1*10（十位次数10.11.12...19）
    对于n小于1000呢，1出现次数是百位100（百位次数100.101.102...199）+20（1-99中1出现次数）+20（101-199不计百位）+。。。20（901-999）=100+20*10=300
    所以n小于10000呢，次数千位1000+300（1-999）+300（1001-1999）+。。。=1000+300*10=4000
                              10000+4000*10=50000；
                              。。。。。
                     对于1-9均和1类似。
    零很特殊，因为00不计（计的话类似11，22,33）01计1，故
    对于n小于100，0出现仅9次，少了十位十次和个位一次即00.01.02...09十1个数
    对于N小于1000,0在1-99（9次）和100-199（200-299/300-399/..900-999）（20次）不同，并无百位出现的，也就是无最高位出现次数。
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#include<stdio.h>
#include<math.h>
void main()
{
    int l,k,index,time,ary_inf[9][2],aim,ary_out[10],ary_in_n[10],ary_in_t[10],int1,int2,m=0,int3;
ary_inf[0][0]=0;
ary_inf[0][1]=1;
for(time=1;time<9;time++)
{
   ary_inf[time][0]=ary_inf[time-1][1]*9+ary_inf[time-1][0];
ary_inf[time][1]=(int)(ary_inf[time-1][1]*10+pow(10,time));
printf("%d %d\n",ary_inf[time][0],ary_inf[time][1]);
}
scanf("%d",&aim);
for(k=0;k<=9;k++)
{
   ary_out[k]=0;
        ary_in_n[k]=0;
}
for(index=9;index>=1;index--)
{
        if(aim>=pow(10,index)&&m==0){
   m=index;
}
   if(aim>=pow(10,index))
{
ary_in_n[index]=(aim/(int)pow(10,index));
            ary_in_t[index]=aim%(int)pow(10,index)+1;
if(m!=index)
{
   for(int3=0;int3<ary_in_n[index];int3++)
ary_out[int3]+=(int)pow(10,index);
}
else{
                for(int3=1;int3<ary_in_n[index];int3++)
ary_out[int3]+=(int)pow(10,index);
}
ary_out[ary_in_n[index]]+=ary_in_t[index];
if(ary_in_n[index]==1)
{
   ary_out[0]+=ary_inf[index-1][0];
                ary_out[1]+=ary_inf[index-1][1];
   ary_out[2]+=ary_inf[index-1][1];
ary_out[3]+=ary_inf[index-1][1];
ary_out[4]+=ary_inf[index-1][1];
ary_out[5]+=ary_inf[index-1][1];
ary_out[6]+=ary_inf[index-1][1];
ary_out[7]+=ary_inf[index-1][1];
ary_out[8]+=ary_inf[index-1][1];
ary_out[9]+=ary_inf[index-1][1];
}
if(ary_in_n[index]==2)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1];
                ary_out[1]+=ary_inf[index-1][1]*2;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*2;
ary_out[3]+=ary_inf[index-1][1]*2;
ary_out[4]+=ary_inf[index-1][1]*2;
ary_out[5]+=ary_inf[index-1][1]*2;
ary_out[6]+=ary_inf[index-1][1]*2;
ary_out[7]+=ary_inf[index-1][1]*2;
ary_out[8]+=ary_inf[index-1][1]*2;
ary_out[9]+=ary_inf[index-1][1]*2;
}
if(ary_in_n[index]==3)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1]*2;
                ary_out[1]+=ary_inf[index-1][1]*3;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*3;//+(int)pow(10,index);
ary_out[3]+=ary_inf[index-1][1]*3;
ary_out[4]+=ary_inf[index-1][1]*3;
ary_out[5]+=ary_inf[index-1][1]*3;
ary_out[6]+=ary_inf[index-1][1]*3;
ary_out[7]+=ary_inf[index-1][1]*3;
ary_out[8]+=ary_inf[index-1][1]*3;
ary_out[9]+=ary_inf[index-1][1]*3;
}
if(ary_in_n[index]==4)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1]*3;
                ary_out[1]+=ary_inf[index-1][1]*4;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*4;//+(int)pow(10,index);
ary_out[3]+=ary_inf[index-1][1]*4;//+(int)pow(10,index);
ary_out[4]+=ary_inf[index-1][1]*4;
ary_out[5]+=ary_inf[index-1][1]*4;
ary_out[6]+=ary_inf[index-1][1]*4;
ary_out[7]+=ary_inf[index-1][1]*4;
ary_out[8]+=ary_inf[index-1][1]*4;
ary_out[9]+=ary_inf[index-1][1]*4;
}
if(ary_in_n[index]==5)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1]*4;
                ary_out[1]+=ary_inf[index-1][1]*5;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*5;//+(int)pow(10,index);
ary_out[3]+=ary_inf[index-1][1]*5;//+(int)pow(10,index);
ary_out[4]+=ary_inf[index-1][1]*5;//+(int)pow(10,index);
ary_out[5]+=ary_inf[index-1][1]*5;
ary_out[6]+=ary_inf[index-1][1]*5;
ary_out[7]+=ary_inf[index-1][1]*5;
ary_out[8]+=ary_inf[index-1][1]*5;
ary_out[9]+=ary_inf[index-1][1]*5;
}
if(ary_in_n[index]==6)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1]*5;
                ary_out[1]+=ary_inf[index-1][1]*6;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*6;//+(int)pow(10,index);
ary_out[3]+=ary_inf[index-1][1]*6;//+(int)pow(10,index);
ary_out[4]+=ary_inf[index-1][1]*6;//+(int)pow(10,index);
ary_out[5]+=ary_inf[index-1][1]*6;//+(int)pow(10,index);
ary_out[6]+=ary_inf[index-1][1]*6;
ary_out[7]+=ary_inf[index-1][1]*6;
ary_out[8]+=ary_inf[index-1][1]*6;
ary_out[9]+=ary_inf[index-1][1]*6;
}
if(ary_in_n[index]==7)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1]*6;
                ary_out[1]+=ary_inf[index-1][1]*7;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*7;//+(int)pow(10,index);
ary_out[3]+=ary_inf[index-1][1]*7;//+(int)pow(10,index);
ary_out[4]+=ary_inf[index-1][1]*7;//+(int)pow(10,index);
ary_out[5]+=ary_inf[index-1][1]*7;//+(int)pow(10,index);
ary_out[6]+=ary_inf[index-1][1]*7;//+(int)pow(10,index);
ary_out[7]+=ary_inf[index-1][1]*7;
ary_out[8]+=ary_inf[index-1][1]*7;
ary_out[9]+=ary_inf[index-1][1]*7;
}
if(ary_in_n[index]==8)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1]*7;
                ary_out[1]+=ary_inf[index-1][1]*8;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*8;//+(int)pow(10,index);
ary_out[3]+=ary_inf[index-1][1]*8;//+(int)pow(10,index);
ary_out[4]+=ary_inf[index-1][1]*8;//+(int)pow(10,index);
ary_out[5]+=ary_inf[index-1][1]*8;//+(int)pow(10,index);
ary_out[6]+=ary_inf[index-1][1]*8;//+(int)pow(10,index);
ary_out[7]+=ary_inf[index-1][1]*8;//+(int)pow(10,index);
ary_out[8]+=ary_inf[index-1][1]*8;
ary_out[9]+=ary_inf[index-1][1]*8;
}
if(ary_in_n[index]==9)
{
ary_out[0]+=ary_inf[index-1][0]+ary_inf[index-1][1]*8;
                ary_out[1]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
   ary_out[2]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
ary_out[3]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
ary_out[4]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
ary_out[5]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
ary_out[6]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
ary_out[7]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
ary_out[8]+=ary_inf[index-1][1]*9;//+(int)pow(10,index);
ary_out[9]+=ary_inf[index-1][1]*9;
}
if(m!=index)
{
   ary_out[0]=ary_out[0]-ary_inf[index-1][0]+ary_inf[index-1][1];
}
}
else if(m>0)
{
ary_in_n[index]=(aim/(int)pow(10,index));
            ary_in_t[index]=aim%(int)pow(10,index)+1;
ary_out[ary_in_n[index]]+=ary_in_t[index];
}
aim=aim%(int)pow(10,index);
}
for(int2=0;int2<10;int2++)
{
   if(int2<=aim&&(m!=0||int2>0))
ary_out[int2]++;
printf("%d\n",ary_out[int2]);
}
}