1, Problem description

1. Set n variables x1,x2 xn. By using these variables as the base and the powers of each layer in order, we can get the N-power as follows
2. In this paper, the above N-power is regarded as indeterminate, and it can become a definite N-power only after proper parentheses are added. Different bracketed ways lead to different n-powers. For example, when n=4, all four powers have five.
3. How many different powers of N are calculated for n variables.
4. Output n power in each case

2, Problem analysis and algorithm analysis

1. Using the idea of divide and conquer, the original problem is regarded as a sequence problem, the sequence order is invariable, adding proper brackets to the sequence to determine an n-power.
2. According to the idea of divide and conquer, the original problem is decomposed into atomic problem, that is, to find a power first.
3. Find the nth power i n the form of a[i] = "(" + a[j]+a[i-j] + ")". a[j] and a[i-j] are n cases in which the nth or I-j power exists in a set.
Traversing all cases of a[n] output N-power, a[n].size() is the number of cases of N-power.

Code

import java.util.ArrayList;

/**
 * Describe multiple powers
 * @author THTF
 * @date 2018 July 9th 2013
 */

public class MultiplePower {

    private static StrList[] l; //The subscript represents the nth power. str is all forms of ArrayList array used to store the nth power

    public MultiplePower(int n) {
        l = new StrList[n + 1];     //Initialization
        for (int i = 0; i < n + 1; i++) {
            l[i] = new StrList();   //Initialization
        }
        l[0].str.add(null); //Subscript 0 is not used
        l[1].str.add("*");      //No parentheses when 1 power
        for (int i = 2; i <= n; i++) {
            for (int j = 1; j < i; j++) {
                for (String str2 : l[j].str) {
                    for (String str3 : l[i - j].str) {
                        l[i].str.add("(" + str2 + str3 + ")");
                    }
                }
            }
        }
        show(n);
    }


    /**
     * Describe all n powers of output
     * @param n
     */
    public static void show(int n) {
        for (String i : l[n].str) {
            StringBuilder sb = new StringBuilder(i);
            int counter = 0;
            for (int k = 0; k < i.length(); k++) {
                if (sb.charAt(k) == '*') {
                    sb.setCharAt(k, (char) ('A' + counter++));
                }
            }
            System.out.println(sb);
            System.out.println("common"+l[n].str.size()+"species");
        }
    }
}


/**
 * 
 * @author THTF
 * @date 2018 July 9th 2013
 */
class StrList {

    public ArrayList<String> str;

    public StrList() {
        str = new ArrayList<String>(10000);

    }
}