Milliard Vasya's Function

1353. Milliard Vasya's Function

Time limit: 1.0 second
Memory limit: 64 MB

Vasya is the beginning mathematician. He decided to make an important contribution to the science and to become famous all over the world. But how can he do that if the most interesting facts such as Pythagor’s theorem are already proved? Correct! He is to think out something his own, original. So he thought out the Theory of Vasya’s Functions. Vasya’s Functions (VF) are rather simple: the value of the Nth VF in the point S is an amount of integers from 1 to N that have the sum of digitsS. You seem to be great programmers, so Vasya gave you a task to find the milliard VF value (i.e. the VF with N = 109) because Vasya himself won’t cope with the task. Can you solve the problem?

Input

Integer S (1 ≤ S ≤ 81).

Output

The milliard VF value in the point S.

Sample

inputoutput

1

10

/**题意：每位数字和为s的数字个数是多少**/#include <map>#include <set>#include <list>#include <queue>#include <stack>#include <cmath>#include <ctime>#include <vector>#include <bitset>#include <cstdio>#include <string>#include <numeric>#include <cstring>#include <cstdlib>#include <iostream>#include <algorithm>#include <functional>using namespace std;typedef long long  ll;typedef unsigned long long ull;int dx[4]= {-1,1,0,0};int dy[4]= {0,0,-1,1}; //up down left rightbool inmap(int x,int y,int n,int m){    if(x<1||x>n||y<1||y>m)return false;    return true;}int hashmap(int x,int y,int m){    return (x-1)*m+y;}#define eps 1e-8#define inf 0x7fffffff#define debug puts("BUG")#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1#define read freopen("in.txt","r",stdin)#define write freopen("out.txt","w",stdout)//dp[i][j] = (i - 1位数最低位全部补0) + (i - 1位数最高位补j - k {k| 1 <= k <= 9} )。int dp[20][88]={0};//dp[i][j] (i = 1 to 9, j = 1 to 81)，表示位数为i的数各位数之和为j的数的个int main()//dp[i][j] = dp[i-1][j] + sum(dp[i-1][j - 1] , dp[i-1][j-2] ,  ...  , dp[i-1][j-9]){    int i, j, k;    memset(dp, 0, sizeof(dp));    for(i=1; i<=9; i++)        dp[1][i]=1;    for(i=2; i<10; i++)    {        for(j=1; j<=81; j++)        {            dp[i][j]=dp[i-1][j];            for(k=1; k<=9&&j-k>=0; k++)                dp[i][j]+=dp[i-1][j-k];        }    }    int s, ans;    while(cin >> s)    {        if(s == 1)        {            cout << "10\n";            continue;        }        for(ans=0,i=1;i<10;i++)            ans+=dp[i][s];        cout <<ans<<endl;    }    return 0;}