ural 1353. Milliard Vasya's Function（背包/递归深搜）

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 N^th 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

input	output
1	10

题意：求1到 $109$ 中各位数字之和为s的数有多少个；

思路1：背包思路；

 1 #include<iostream>
 2 #include<cstdio>
 3 
 4 
 5 using namespace std;
 6 
 7 int dp[2][82]={0};
 8 
 9 
10 int main()
11 {
12 //    freopen("1.txt","r",stdin);
13     int s;
14     cin>>s;
15     int i,j,k;
16     dp[0][0]=1;
17     dp[1][0]=1;
18     for(i=1;i<10;i++)
19     {
20         for(j=1;j<=(i*9)&&j<=s;j++)
21         {
22             dp[i%2][j]=dp[1-i%2][j];
23             for(k=1;k<10&&k<=j;k++)
24                 dp[i%2][j]+=dp[1-i%2][j-k];
25         }
26     }
27     dp[1][1]++;
28     cout<<dp[1][s]<<endl;
29     return 0;
30 }

View Code

思路2：递归的深搜；

 1 #include<iostream>
 2 #include<cstdio>
 3 
 4 using namespace std;
 5 
 6 
 7 int ks(int s,int k)
 8 {
 9     if(k==1)
10     {
11         if(s>9)
12             return 0;
13         return 1;
14     }
15     if(s==0)return 1;
16     int sum=0;
17     int i;
18     for(i=0;i<10&&i<=s;i++)
19     {
20         sum+=ks(s-i,k-1);
21     }
22     return sum;
23 }
24 
25 
26 int main()
27 {
28 //    freopen("1.txt","r",stdin);
29     int s;
30     cin>>s;
31     if(s==1)
32     {
33         cout<<ks(s,10)<<endl;
34         return 0;
35     }
36     cout<<ks(s,9)<<endl;
37     return 0;
38 }

View Code