F - 水之矢 URAL - 1353

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 N th VF in the point S is an amount of integers from 1 to N that have the sum of digits S. You seem to be great programmers, so Vasya gave you a task to find the milliard VF value (i.e. the VF with N = 10 9) 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.
Example
input output
1
10

題目大意：
給出各個位置上的數字之和，然後問你有多少種組成情況。
dp[i][j]代表前j位的數字之和爲i的個數。

#include <bits/stdc++.h>
using namespace std;
int dp[123][123];
int main()
{
    int n;
    cin>>n;
    memset(dp, 0, sizeof(dp));
    for(int i=1;i<=9;i++)
        dp[i][1] = 1;
    for(int j=1;j<=9;j++)
    {
        for(int i=1;i<=n;i++)
        {
            for(int k=0;k<=9;k++)
            {
                if(i>=k)
                dp[i][j] = dp[i][j] + dp[i-k][j-1];//j位的時候，
                //各個位置上的數字之和爲i的個數，等於當前的+j-1位和爲i-k;
            }
        }
    }
    long long int maxn = 0;
    for(int i=1;i<=9;i++)
    {
        maxn = maxn + dp[n][i];
    }
    if(n==1)
        cout<<10<<endl;
    else
    printf("%lld\n", maxn);
    return 0;
}