Integer sharding problem _ C ++, integer sharding _ c

Integer sharding problem _ C ++, integer sharding _ c

I. Problem background

Integer splitting refers to dividing an integer into the sum of several integers.

For example, 3 = 2 + 1 = 1 + 1 + 1.

We think that 2 + 1 and 1 + 2 are the same split.

Ii. Definition

In the integer n split, the maximum number of splits is m. Let's note that the number of splits is f (n, m)

That is, n = x1 + x2 +... + XK-1 + xk, arbitrary x ≤ m

Here we use the recursive Progressive Method

Iii. Recursive relationship

1. When n = 1 or m = 1

The splitting scheme is only n = 1 or n = 1 + 1 + 1 + ······

F (n, m) = 1

2. n = m

When S1 selects m, f (n, m) = 1, that is, n = m

F (n, m) = f (n, m) = f (n, s-1) = f (n, n-1) when m is not selected for S2. In this case, we will discuss the situation where the maximum number of splits is expressed as S-1.

F (n, m) = f (n, n-1) + 1

3. n <m hours

Because m cannot be selected, m can be considered as n. When n is m, f (n, m) = f (n, n)

4. n> m

When m is selected in S1, f (n, m) = f (n-m, m), the split score is changed to n-m because m is selected, in addition, the maximum number of m values may be selected in n-m.

When m is not selected for S2, f (n, m) = f (m-1). In this case, we will discuss the situation where the maximum number of splits is S-1.

F (n, m) = f (m-1) + f (n-m, m)

The total recurrence formula is

 

 

The Code is as follows:

 1 #include <algorithm> 2 #include <iostream> 3 #include <cstdlib> 4 #include <cstring> 5 #include <cstdio> 6 #include <cmath> 7 using namespace std; 8  9 int f(int n,int m)10 {11     if ((n!=1)&&(m!=1))12         {13             if (n>m) return f(n-m,m)+f(n,m-1);14             else return 1+f(n,n-1);15         }16     else return 1;17 }18 void work()19 {20     int n,m;21     cin>>n>>m;22     cout<<f(n,m);23 }24 int main()25 {26     freopen("cut.in","r",stdin);27     freopen("cut.out","w",stdout);28     work();29     return 0;30 }

In addition, the master function method is provided. For more information, see

Http://blog.chinaunix.net/uid-26548237-id-3503956.html

 

 

 

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