动态规划之复杂的整数划分问题

注意初始值的给定

#include <iostream>
#include <memory.h>

#define MaxLen 55
using namespace std;
int result1[MaxLen][MaxLen];//result1[i][j]表示将整数i划分为j个数字
int result2[MaxLen][MaxLen];//result2[i][j]表示将整数i划分为不超过j的整数
int result3[MaxLen][MaxLen];//result2[i][j]表示将整数i划分为不超过j的整数
int n,k;
void dp()
{
    memset( result1, 0, sizeof(result1) );
    for( int i = 1; i <= n; i++)
        result1[i][1] = 1;
    for( int i = 1; i <= n; i++)
        for( int j = 2; j <= i; j++)
            result1[i][j] = result1[i-j][j] + result1[i-1][j-1];
    cout << result1[n][k] <<endl;
}
void dp2()//最大数不超过k
{
    memset( result2, 0, sizeof(result2) );
    result2[0][0] = 1;
    for( int i = 0; i <= n; i++)
        for( int j = 1; j <= n; j++)
        {
            if( i >= j)
            {
                result2[i][j] = result2[i-j][j-1] + result2[i][j-1];
            }
            else
            {
                result2[i][j] = result2[i][i];
            }
        }
    cout << result2[n][n] <<endl;

}
void dp3()
{
    memset( result3, 0, sizeof(result3) );
    for( int i = 0; i <= n; i++ )
    {
        result3[i][1] = 1;
        if( i%2 )
        {
            result3[0][i] = 1;
        }
    }
    for( int i = 1; i <= n; i++)
        for( int j = 1; j <= n; j++)
    {
        if( j%2 )
        {
            if( i >= j)
            {
                result3[i][j] = result3[i-j][j] + result3[i][j-1];
            }
            else
                result3[i][j] = result3[i][i];
        }
        else
            result3[i][j] = result3[i][j-1];
    }
    cout << result3[n][n] <<endl;
}
int main()
{
    while( cin >> n >> k)
    {
        dp();
        dp2();
        dp3();
    }
    return 0;
}