HDU 5308 I Wanna Become A 24-Point Master（2015多校第二场）

 

 

Problem Description

 

Recently Rikka falls in love with an old but interesting game -- 24 points. She wants to become

a master of this game, so she asks Yuta to give her some problems to practice.

Quickly, Rikka solved almost all of the problems but the remained one is really difficult:

In this problem,  you need to write a program which can get 24 points with n numbers,  which are all equal to n.

 

Input

 

There are no more then 100 testcases and there are no more then 5 testcases with n≥100. Each testcase contains only one integer n (1≤n≤10⁵)

 

Output

 

For each testcase:

If there is not any way to get 24 points, print a single line with -1.

Otherwise, let A be an array with 2n−1 numbers and at firsrt A_i=n (1≤i≤n). You need to print 

n−1 lines and the ith line contains one integer a,  one char b and then one integer c,  where 

1≤a, c<n+i and b is "+","-","*" or "/". This line means that you let A_a and A_c do the operation 

b and store the answer into A_n+i.

If your answer satisfies the following rule, we think your answer is right:

1. A_2n−1=24

2. Each position of the array A is used at most one tine.

3. The absolute value of the numerator and denominator of each element in array A is no more

    than 10⁹

 

Sample Input

 

4

 

Sample Output

 

1 * 2

5 + 3

6 + 4

 

题意：有一个长度为2n-1的数组，数组中前n个数字都为n，对数组进行n-1次+-*/操作，将第i次的操作结果存入A_n+i中， 使得A_2n-1等于24，数组中每个数只能使用一次， 中间运算可以有浮点数。

 

题解：对于1-13直接打表，14以上的数可以通过前12个相同数字得到24（转换成4*6），对于多余的n，我们可以用2个相减得0把多余的n乘掉。

 

注：对于5而言，可以表示为5 * （5 - （5 / 5）/ 5）

 

#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
int main()
{
    int n;
    while (scanf("%d", &n) != EOF){
        if (n <= 3)
            printf("-1
");
        else if (n == 4){
            printf("1 * 2
");
            printf("5 + 3
");
            printf("6 + 4
");
        }
        else if (n == 5){
            printf("1 / 2
");
            printf("6 / 3
");
            printf("4 - 7
");
            printf("5 * 8
");
        }
        else if (n == 6){
            printf("1 + 2
");
            printf("3 + 4
");
            printf("5 - 6
");
            printf("7 + 8
");
            printf("9 + 10
");
        }
        else if (n == 7){
            printf("1 + 2
");
            printf("3 + 8
");
            printf("9 / 4
");
            printf("5 / 6
");
            printf("11 + 7
");
            printf("10 * 12
");
        }
        else if (n == 8){
            printf("1 + 2
");
            printf("3 + 9
");
            printf("4 - 5
");
            printf("11 * 6
");
            printf("12 * 7
");
            printf("13 * 8
");
            printf("10 + 14
");
        }
        else if (n == 9){
            printf("1 + 2
");
            printf("3 + 4
");
            printf("11 + 5
");
            printf("12 + 6
");
            printf("13 + 7
");
            printf("14 + 8
");
            printf("15 / 9
");
            printf("10 + 16
");
        }
        else if (n == 10){
            printf("1 + 2
");
            printf("11 / 3
");
            printf("4 + 12
");
            printf("6 + 5
");
            printf("14 + 7
");
            printf("8 + 15
");
            printf("9 + 10
");
            printf("16 / 17
");
            printf("13 * 18
");
        }
        else if (n == 11){
            printf("1 + 2
");
            printf("12 / 3
");
            printf("4 / 5
");
            printf("6 + 14
");
            printf("7 - 8
");
            printf("16 * 9
");
            printf("17 * 10
");
            printf("18 * 11
");
            printf("13 * 15
");
            printf("20 + 19
");
        }
        else if (n == 12){
            printf("1 + 2
");
            printf("3 - 4
");
            printf("14 * 5
");
            printf("6 * 15
");
            printf("7 * 16
");
            printf("8 * 17
");
            printf("9 * 18
");
            printf("10 * 19
");
            printf("11 * 20
");
            printf("12 * 21
");
            printf("13 + 22
");
        }
        else if (n == 13){
            printf("1 + 2
");
            printf("3 + 14
");
            printf("15 / 4
");
            printf("5 + 6
");
            for (int i=7; i<=12; i++)
                printf("%d + %d
", i, i+10);
            printf("23 / 13
");
            printf("16 * 24
");
        }
        else{
            printf("1 + 2
");
            for (int i=3; i<=4; i++)
                printf("%d + %d
", i, n+i-2);
            printf("%d / 5
", n+3);
            printf("6 + 7
");
            for (int i=8; i<=11; i++)
                printf("%d + %d
", i, n+i-3);
            printf("%d / 12
", n+9);
            printf("13 - 14
");
            for (int i=15; i<=n; i++)
                printf("%d * %d
", i, n+i-4);
            printf("%d * %d
", n+4, n+10);
            printf("%d + %d
", 2*n-2, 2*n-3);
        }
    }
    return 0;
}