ural 1150. Page Numbers

1150. Page Numbers

Time limit: 1.0 second
Memory limit: 64 MB

John Smith has decided to number the pages in his notebook from 1 to N. Please, figure out the number of zeros, ones, twos, …, nines he might need.

Input

One number N (1 ≤ N < 109).

Output

Output 10 lines. The first line should contain the number of zeros needed, the second line should contain the number of ones needed, …, the tenth line should contain the number of nines needed.

Sample

input	output
12	1 5 2 1 1 1 1 1 1 1

Problem Author: Eugene Bryzgalov 
Problem Source: Ural Collegiate Programming Contest, April 2001, Perm, English Round 

Tags: none  (hide tags for unsolved problems)

Difficulty: 236

 

题意：1-n中各个数字 0-9各出现多少次

分析：简单的逐位计算+数学统计

 #include <cstdio>
 #include <cstring>
 #include <cstdlib>
 #include <cmath>
 #include <deque>
 #include <vector>
 #include <queue>
 #include <iostream>
 #include <algorithm>
 #include <map>
 #include <set>
 #include <ctime>
 using namespace std;
 typedef long long LL;
 typedef double DB;
 #define For(i, s, t) for(int i = (s); i <= (t); i++)
 #define Ford(i, s, t) for(int i = (s); i >= (t); i--)
 #define Rep(i, t) for(int i = (0); i < (t); i++)
 #define Repn(i, t) for(int i = ((t)-1); i >= (0); i--)
 #define rep(i, x, t) for(int i = (x); i < (t); i++)
 #define MIT (2147483647)
 #define INF (1000000001)
 #define MLL (1000000000000000001LL)
 #define sz(x) ((int) (x).size())
 #define clr(x, y) memset(x, y, sizeof(x))
 #define puf push_front
 #define pub push_back
 #define pof pop_front
 #define pob pop_back
 #define ft first
 #define sd second
 #define mk make_pair
 inline void SetIO(string Name) {
     string Input = Name+".in",
     Output = Name+".out";
     freopen(Input.c_str(), "r", stdin),
     freopen(Output.c_str(), "w", stdout);
 }

 inline int Getint() {
     int Ret = ;
     char Ch = ' ';
     while(!(Ch >= '' && Ch <= '')) Ch = getchar();
     while(Ch >= '' && Ch <= '') {
         Ret = Ret*+Ch-'';
         Ch = getchar();
     }
     return Ret;
 }

 const int N = ;
 int n;
 LL Ans[N];

 inline void Input() {
     scanf("%d", &n);
 }

 inline void Solve() {
     LL x, y;
     int Now = ;
     while(n/Now) {
         x = n/(Now*), y = n%Now;
         int p = (n/Now)%;
         if(!p) Ans[] += (x-)*Now+y+;
         else Ans[] += x*Now;
         For(i, , p-) Ans[i] += (x+)*Now;
         if(p) Ans[p] += x*Now+y+;
         For(i, p+, ) Ans[i] += x*Now;
         Now *= ;
         //cout<<Ans[0]<<endl;
     }

     Rep(i, N) cout<<Ans[i]<<endl;
 }

 int main() {
     #ifndef ONLINE_JUDGE
     SetIO("A");
     #endif
     Input();
     Solve();
     return ;
 }