Blue glass Interpretations endo - Minato formula (full permutation variant)

topic

This is a result of the Blue Bridge Cup 2016 Seventh Provincial Group C match B combination has a fill in the blank:

凑算式

     B      DEF
A + --- + ------- = 10
     C      GHI

（如果显示有问题，可以参见【图1.jpg】）


这个算式中A~I代表1~9的数字，不同的字母代表不同的数字。

比如：
6+8/3+952/714 就是一种解法，
5+3/1+972/486 是另一种解法。

这个算式一共有多少种解法？

注意：你提交应该是个整数，不要填写任何多余的内容或说明性文字。

analysis

Because this is a result of fill in the blank, so do not consider performance too, can be directly used violence recursive perfection arrangement and then to complete the verification, full permutation nine digits is 9! = 362,880, is certainly completed within seconds.

So just in the algorithm thinking (recursively) Training: full array output string of characters based on a slightly modified on the line.

Code

/**
 * 凑算式
 * A+B/C+DEF/GHI=10，A~I可以是1~9的任意不同数字
 *
 * 暴力求解实际就是1~9的全排列，然后验证某一种排列是否能凑成算式
 * */
public class 凑算式 {

  static int res;

  public static void main(String[] args) {
    String s = "123456789";
    // 全排列
    permutation(s.toCharArray(), 0);
    System.out.println(res);
  }

  //每一段全排列，都是将每个字符换到前面，求后面段的全排列
  //index代表0~index-1都已确认排列，[index,n-1]待排列
  private static void permutation(char[] arr, int index) {
    //至于什么时候输出，要考虑清楚
    if (index == arr.length) {
      // 算式凑成功了，打印并计数
      if (Double.parseDouble(arr[0] + "") +
          Double.parseDouble(arr[1] + "") / Double.parseDouble(arr[2] + "") +
          (Double.parseDouble(arr[3] + "") * 100 + Double.parseDouble(arr[4] + "") * 10 + Double.parseDouble(arr[5] + "")) /
              (Double.parseDouble(arr[6] + "") * 100 + Double.parseDouble(arr[7] + "") * 10 + Double.parseDouble((arr[8] + ""))) == 10.0) {
        // System.out.println(String.valueOf(arr));
        res++;
      }
    }
    //现在index之前的字符都已就位，把之后的每个字符都交换到index这个位置
    for (int k = index; k < arr.length; k++) {
      //尝试交换
      swap(arr, index, k);
      //交换之后index这个位置就定好了，接下来的事就是递归去解决index+1位置开始的全排列就好了
      permutation(arr, index + 1);
      // 前面我们尝试交换，把全排列求出来了，交换时只尝试了一个字符，因此for循环继续之前要换回来，继续尝试交换下一个字符
      swap(arr, index, k);
    }
  }

  private static void swap(char[] arr, int index, int k) {
    char tmp = arr[k];
    arr[k] = arr[index];
    arr[index] = tmp;
  }
}

trap

Note that this problem checking formula, you must use double, as the title says 6+8/3+952/714is the right formula, but the direct System.out.println(6+8/3+952/714);output is 9, which shows all doing integer arithmetic is wrong.

Again verification System.out.println(6+8.0/3+952.0/714);result 10.0, which shows that we need to use floating-point numbers in division.

Eschewing this pit to get the correct answer.