编程求计算24点的方法是什么？

解法用到的基本思想就是回溯，树的深度为最深为4，树的判断分支为 加减乘除，对不满足条件的解进行剪枝（即当前结果>=24）,当到达递归边界（即树的深度为四时）时，即判断当前的结果是否符合条件（=24），符合即找到解，否则继续进行。

参考代码如下：

#include<敏谨iostream>

#include<math.h>

using namespace std

const double MIN=1E-6

void Print(int *Rank,double *FourNum)

{

for(int i=0i<笑拿前4i++)

cout<<FourNum[Rank[i]]<<" "

cout<<endl

}

void Calculate_24(int *Rank,int *FourNum,char *Oper,int i,int j,int k,bool &def)

{

double res=0

switch(i)

{

case 0:

res=FourNum[Rank[0]]+FourNum[Rank[1]]

break

case 1:

res=FourNum[Rank[0]]-FourNum[Rank[1]]

break

case 2:

res=FourNum[Rank[0]]*FourNum[Rank[1]]

break

case 3:

res=FourNum[Rank[0]]/FourNum[Rank[1]]

break

}

switch(j)

{

case 0:

res=res+FourNum[Rank[2]]

break

case 1:

res=res-FourNum[Rank[2]]

break

case 2:

res=res*FourNum[Rank[2]]

break

case 3:

res=res/FourNum[Rank[2]]

break

}

switch(k)

{

case 0:

res=res+FourNum[Rank[3]]

break

case 1:

res=res-FourNum[Rank[3]]

break

case 2:

res=res*FourNum[Rank[3]]

break

case 3:

res=res/FourNum[Rank[3]]

break

}

if(fabs(res-24)>MIN)

return

else

{

def=true

for(int num=1num<=7num++)

{

switch(num)

{

case 1:

cout<<FourNum[Rank[0]]

break

case 3:

cout<<FourNum[Rank[1]]

break

case 5:

cout<<FourNum[Rank[2]]

break

case 7:

cout<<FourNum[Rank[3]]

break

case 2:

cout<<Oper[i]

break

case 4:

cout<<Oper[j]

break

case 6:

cout<<Oper[k]

break

}

}

cout<<endl

}

}

void SearchTree(int Depth,int *Rank,int *FourNum,char *Oper,bool &def)

{

int i,j,k

if(Depth==4)

{

for(i=0i<4i++)

for(j=0j<4j++)

for(k=0k<4k++)

Calculate_24(Rank,FourNum,Oper,i,j,k,def)

}

else

{

for(i=0i<4i++)

{

int Remember=0

for(j=0j<Depthj++)

{

if(Rank[j]==i)

Remember=1

}

if(Remember)

continue

Rank[Depth]=i

SearchTree(Depth+1,Rank,FourNum,Oper,def)

}

}

}

int main()

{

int a[4],b[4],time

char c[4]={'+','-','*','/'}

bool def=false

cin>>time

while(time--)

{

for(int i=0i<4i++)//输入碰清测试数据

cin>>a[i]

cout<<"所有可能的结果："<<endl

SearchTree(0,b,a,c,def)

if(def==false)

cout<<"No"<<endl

}

return 0

}

#include<stdio.h>伏液

double fun(double a1,double a2,int b)

{switch(b)

{case 0:return (a1+a2)

case 1:return (a1-a2)

case 2:return (a1*a2)

case 3:return (a1/a2)

}

}

void main()

{int i,j,k,l,n,m,r,save[4]

double num[4]={1,1,1,1},tem1,tem2,tem3,abc=1111

char sign[5]="+-*/"

printf("input 4 numbers:")

for(i=0i<4i++)

{scanf("%lf",num+i)save[i]=num[i]}

for(i=0i<4i++)

for(j=0j<4j++)

if(j!=i)

{for(k=0k<4k++)

if(k!=i&&k!=j)

{for(l=0l<4l++)

if(l!=i&&l!=j&&l!=k)

{for(n=0n<4n++)

for(m=0m<4m++)

for(r=0r<4r++)

{tem1=fun(num[i],num[j],n)

tem2=fun(tem1,num[k],m)

tem3=fun(tem2,num[l],r)

if(tem3==24.0)printf("枝厅没{(%d%c%d)%c%d}%c%d=24\n",save[i],sign[n],save[j],sign[m],save[k],sign[r],save[l])

else if(tem3==-24.0)printf("{%d%c(%d%c%d)}%c%d=24\n",save[k],sign[m],save[i],sign[n],save[j],sign[r],save[l])

else if(tem3==1.0/24.0)printf("%d%c{(%d%c%d)%c%d}=24\猛纳n",save[l],sign[r],save[i],sign[n],save[j],sign[m],save[k])

else if(tem3==-1.0/24.0)printf("%d%c{%d%c(%d%c%d)}=24\n",save[l],sign[r],save[k],sign[n],save[i],sign[m],save[j])

else

{tem1=fun(num[i],num[j],n)

tem2=fun(num[k],num[l],r)

tem3=fun(tem1,tem2,m)

if(tem3==24.0) printf("(%d%c%d)%c(%d%c%d)=24\n",save[i],sign[n],save[j],sign[m],save[k],sign[r],save[l])

}

}

}

}

}

}

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