acm题目及我的程序（4）——正整数n的加法组合的最大乘积

题目：

给定一个正整数n，则在n所有的分解式中，求因子乘积最大的一个分解及此乘积。
n=5时，有如下分解式：
5=5
5=4+1
5=3+2
5=3+1+1
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1
在这些分解式中，3*2=6最大，这就是所要求的结果。
若n = 12，最大为3*3*3*3 = 81。

算法思想：

可以参考“acm题目及我的程序（3）——正整数n的加法组合”，不再赘述

代码如下：

/**//************************************************************************


* 给定一个正整数n, 则在n所有的分解式中, 求因子乘积最大的一个分解及此乘积


* n=5时, 则8有如下分解式:


* 5=5


* 5=4+1


* 5=3+2


* 5=3+1+1


* 5=2+2+1


* 5=2+1+1+1


* 5=1+1+1+1+1


* 在这些分解式中，3*2=6最大，这就是所要求的结果。


* 若n = 12，最大为3*3*3*3 = 81。


************************************************************************/




#include <stdio.h>


#include <string.h>


#include <CONIO.H>


#include <vector>


using namespace std;




#define MAXCOL 80


#define FILENAMELENGTH 100




class AdditionCombination




...{


public:


int a[MAXCOL];


int m_number; //条用GetCombinations函数时count的值


long m_lproduct;//最大乘积




public:


AdditionCombination(int number)




...{


m_lproduct=0;


m_number=number;


for(int j=0;j<MAXCOL;j++)


a[j]=1;


}






~AdditionCombination()...{}




void Initialize()




...{


for(int j=0;j<m_number;j++)


a[j]=1;


}




void Initialize(int jcol)




...{


for(int j=jcol;j<m_number;j++)


a[j]=1;


}




int GetCombinations(int n,int jcol,int col);


void display(int n);


};




//在数组中从irow行,jcol列开始对n阶子矩阵进行


//col记录调用该函数前jcol的值


int AdditionCombination::GetCombinations(int n,int jcol,int col)




...{


int nTotalCount=0;


int j=0,newn=0;


int count=n;





while(count>1)




...{


if(jcol==0)


Initialize();


else


Initialize(jcol);


a[jcol]=count;





//算法优化,删除不满足的序列


if(a[jcol]>a[col])




...{


count--;


continue;


}




for(j=jcol+1;j<jcol+count;j++)


a[j]=0;




newn=n-count;


if(newn>1)




...{


int newj=jcol+count;


int newcount=GetCombinations(newn,newj,jcol);


nTotalCount+=newcount;


}





count--;


display(m_number);


nTotalCount++;


}




if(jcol==0)




...{


Initialize();


display(m_number);


nTotalCount++;


}


else


Initialize(jcol);




return nTotalCount;


}




void AdditionCombination::display(int n)




...{


long product=a[0];


//printf(" %d=%d",n,a[0]);


for(int j=1;j<n;j++)




...{


if(a[j])




...{


//printf("+%d",a[j]);


product*=a[j];


}


}


if(m_lproduct<product)


m_lproduct=product;


}




//将结果写入文件


void WriteToFile(vector<vector<int> > info)




...{


char filename[FILENAMELENGTH];




int size=info.size();


//构造文件名


sprintf(filename,"%d-%d result.txt",info[0][0],info[size-1][0]);


FILE *fp=fopen(filename,"w");


if(fp==NULL)




...{


printf("can not wirte file!");


exit(0);


}




//写入个数


for(int i=0;i<size;i++)


fprintf(fp,"n=%d count=%d maxproduct=%ld ",info[i][0],info[i][1],info[i][2]);




fclose(fp);


}




//显示菜单


void show_menu()




...{


printf("--------------------------------------------- ");


printf("input command to test the program ");


printf(" i or I : input n to test ");


printf(" t or T : get count from n1 to n2 ");


printf(" q or Q : quit ");


printf("--------------------------------------------- ");


printf("$ input command >");


}




void main()




...{


char sinput[10];


int n;




show_menu();




scanf("%s",sinput);


while(stricmp(sinput,"q")!=0)




...{


if(stricmp(sinput,"i")==0)




...{


printf(" please input an integer:");


scanf("%d",&n);




AdditionCombination obj(n);


int count=obj.GetCombinations(n,0,0);


printf(" count = %d maxproduct=%ld ",count,obj.m_lproduct);


}


else if(stricmp(sinput,"t")==0)




...{


int n1,n2;


printf(" please input the begin number:");


scanf("%d",&n1);


printf(" please input the end number:");


scanf("%d",&n2);




printf(" press any key to start ... ");


getch();




vector<vector<int> > info;


vector<int> line;




AdditionCombination obj(n1);


for(int i=n1;i<=n2;i++)




...{


obj.Initialize();


obj.m_number=i;


int count=obj.GetCombinations(i,0,0);


printf(" n=%d count=%d maxproduct=%ld ",i,count,obj.m_lproduct);


line.clear();


line.push_back(i);


line.push_back(count);


line.push_back(obj.m_lproduct);


info.push_back(line);


}


printf(" ");




//写入文件


printf("$ write the numbers to file(Y,N)? >");


scanf("%s",sinput);


if(stricmp(sinput,"y")==0) //写入文件




...{


WriteToFile(info);


printf(" write successfully! ");


}


printf(" ");


}




//输入命令


printf("$ input command >");


scanf("%s",sinput);


}


}

运行结果如下（1<=n<=80的结果）：

n=1 count=1 maxproduct=1
n=2 count=2 maxproduct=2
n=3 count=3 maxproduct=3
n=4 count=5 maxproduct=4
n=5 count=7 maxproduct=6
n=6 count=11 maxproduct=9
n=7 count=15 maxproduct=12
n=8 count=22 maxproduct=18
n=9 count=30 maxproduct=27
n=10 count=42 maxproduct=36
n=11 count=56 maxproduct=54
n=12 count=77 maxproduct=81
n=13 count=101 maxproduct=108
n=14 count=135 maxproduct=162
n=15 count=176 maxproduct=243
n=16 count=231 maxproduct=324
n=17 count=297 maxproduct=486
n=18 count=385 maxproduct=729
n=19 count=490 maxproduct=972
n=20 count=627 maxproduct=1458
n=21 count=792 maxproduct=2187
n=22 count=1002 maxproduct=2916
n=23 count=1255 maxproduct=4374
n=24 count=1575 maxproduct=6561
n=25 count=1958 maxproduct=8748
n=26 count=2436 maxproduct=13122
n=27 count=3010 maxproduct=19683
n=28 count=3718 maxproduct=26244
n=29 count=4565 maxproduct=39366
n=30 count=5604 maxproduct=59049
n=31 count=6842 maxproduct=78732
n=32 count=8349 maxproduct=118098
n=33 count=10143 maxproduct=177147
n=34 count=12310 maxproduct=236196
n=35 count=14883 maxproduct=354294
n=36 count=17977 maxproduct=531441
n=37 count=21637 maxproduct=708588
n=38 count=26015 maxproduct=1062882
n=39 count=31185 maxproduct=1594323
n=40 count=37338 maxproduct=2125764
n=41 count=44583 maxproduct=3188646
n=42 count=53174 maxproduct=4782969
n=43 count=63261 maxproduct=6377292
n=44 count=75175 maxproduct=9565938
n=45 count=89134 maxproduct=14348907
n=46 count=105558 maxproduct=19131876
n=47 count=124754 maxproduct=28697814
n=48 count=147273 maxproduct=43046721
n=49 count=173525 maxproduct=57395628
n=50 count=204226 maxproduct=86093442
n=51 count=239943 maxproduct=129140163
n=52 count=281589 maxproduct=172186884
n=53 count=329931 maxproduct=258280326
n=54 count=386155 maxproduct=387420489
n=55 count=451276 maxproduct=516560652
n=56 count=526823 maxproduct=774840978
n=57 count=614154 maxproduct=1162261467
n=58 count=715220 maxproduct=1549681956
n=59 count=831820 maxproduct=2066242608
n=60 count=966467 maxproduct=2066242608
n=61 count=1121505 maxproduct=2142770112
n=62 count=1300156 maxproduct=2142770112
n=63 count=1505499 maxproduct=2142770112
n=64 count=1741630 maxproduct=2142770112
n=65 count=2012558 maxproduct=2143260000
n=66 count=2323520 maxproduct=2143260000
n=67 count=2679689 maxproduct=2143260000
n=68 count=3087735 maxproduct=2145927168
n=69 count=3554345 maxproduct=2146959360
n=70 count=4087968 maxproduct=2146959360
n=71 count=4697205 maxproduct=2146959360
n=72 count=5392783 maxproduct=2146959360
n=73 count=6185689 maxproduct=2146959360
n=74 count=7089500 maxproduct=2146959360
n=75 count=8118264 maxproduct=2146959360
n=76 count=9289091 maxproduct=2147087250
n=77 count=10619863 maxproduct=2147359744
n=78 count=12132164 maxproduct=2147359744
n=79 count=13848650 maxproduct=2147359744
n=80 count=15796476 maxproduct=2147359744