寻找和为定值的n个数

寻找和为定值的N个数

题目：

输入两个整数n和sum，要求从数列1, 2, 3, ...,n中随意取出几个数，使得它们的和等于sum，请将其中所有可能的组合列出来。

思路：

上述问题是典型的背包问题的应用，即先找出n个数的所有组合，再在这些组合中寻找组合数相加之和等于sum的组合，并依次输出这些组合中的数。

实现：

public class ManySumN {

       public static void main(String[] args) {

              new ManySumN().printManySumN(5, 4);

       }    

       public String[] getAllGroup(int n) {

              intlen = (int) Math.pow(2, n);

              String[] result = new String[len];

              if(n == 1) {

                     result[0]= "0";

                     result[1]= "1";

                     return result;

              }

              String[] temp = getAllGroup(n - 1);

              for(int i = 0; i < temp.length; i++) {

                     result[i]= "0" + temp[i];

                     result[len- 1 - i] = "1" + temp[i];

              }

              return result;

       }  

       public void printManySumN(int n, int sum){

              String[] allGroup = getAllGroup(n);

              for(int i = 0; i < allGroup.length; i++) {

                     char[]temp = allGroup[i].toCharArray();

                     inttempSum = 0;

                     for(int j = 0; j < temp.length; j++) {

                            if(temp[j]=='1'){

                                   tempSum+=(j+1);

                            }

                     }

                     if(tempSum== sum){

                            for(int j=0;j<temp.length;j++){

                                   if(temp[j]=='1'){

                                          System.out.print((j+1)+"");

                                   }

                            }

                            System.out.println();

                     }

              }

       }

}