balanced ternary notation

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"Perhaps the prettiest number system of all... is the balanced ternary notation."——Donald Knuth

平衡三进制(balanced ternary notation)，是一种以3为基数，-1（以下用T表示）、0、1为基本数码的进制。

例题：砝码问题

解法1：

枚举

#include <iostream>using namespace std;int main(){        /*     *-1,0,1 represent 3 status     */        int testNum=7;        int w1=1;    int w2=3;    int w3=9;    int w4=27;    int w5=81;        for (int i=-1; i<=1; i++) {        for (int j=-1; j<=1; j++) {            for (int k=-1; k<=1; k++) {                for (int m=-1; m<=1; m++) {                    for (int n=-1; n<=1; n++) {                        int tmp=w1*i+w2*j+w3*k+w4*m+w5*n;                        if (tmp==testNum) {                            cout<<w5<<" "<<n<<endl;                            cout<<w4<<" "<<m<<endl;                            cout<<w3<<" "<<k<<endl;                            cout<<w2<<" "<<j<<endl;                            cout<<w1<<" "<<i<<endl;                        }                    }                }            }        }    }        return 0;}

解法2：

使用平衡三进制

#include <iostream>using namespace std;int main(){    cout<<"pls input one number between 1 and 121"<<endl;    int input_Number;    cin>>input_Number;        if (input_Number<0||input_Number>121) {        cout<<"pls input the right number between 1 and 121"<<endl;        return 0;    }        char sign[10];    int temp[10]={0};    int tem=1;    int len=0;        int remainder=0;    int quotient=1;        while (quotient!=0) {        quotient=input_Number/3;        remainder=input_Number%3;        if (remainder==2) {            input_Number=quotient+1;            temp[len]=tem;            sign[len++]='-';        }                if(remainder==1){            input_Number=quotient;            temp[len]=tem;            sign[len++]='+';        }                if (remainder==0) {            input_Number=quotient;        }               tem=tem*3;            }    cout<<temp[len-1];    for (int i=len-2; i>=0; i--) {        cout<<sign[i]<<temp[i];    }    cout<<endl;        return 0;}

输出所有情况

#include <iostream>using namespace std;int main(){    int len=0,a[10]={0},j;char op[10];int t,k,m,input,i;for(j=1;j<=122;j++){        input=j;        m=j;        len=0;        t=1;        while(input)        {            k=input%3;            input/=3;//关键是这里的两步            switch(k)            {                case 0:break;                case 1:a[len]=t;op[len++]='+';break;                case 2:a[len]=t;op[len++]='-';input++;break;            }            t*=3;        }        printf("%d=%d",m,a[len-1]);        for(i=len-2;i>=0;i--)            printf("%c%d",op[i],a[i]);        printf("\n");}    return 0;}

参考：

平衡三进制

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