Combinations

Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.

For example,
If n = 4 and k = 2, a solution is:

[
  [2,4],
  [3,4],
  [2,3],
  [1,2],
  [1,3],
  [1,4],
]
Solution:
采用位运算来做，但是这样时间复杂度很高O(n* 2^ n)。

public class Solution {
    public ArrayList<ArrayList<Integer>> combine(int n, int k) {
        // Start typing your Java solution below
        // DO NOT write main() function
        ArrayList<ArrayList<Integer>> result = new ArrayList<ArrayList<Integer>>();
        for(int i = 0; i < Math.pow(2,n); i ++){
            ArrayList<Integer> row = new ArrayList<Integer>();
            for(int j = 0; j < n; j ++){
                if((i >> j & 1)  == 1){
                    row.add(j + 1);
                } 
            }
            if(row.size() == k)
                result.add(row);
        }
        return result;
    }
}

 第二遍： 使用递归。过不了大循环。

public class Solution {
    ArrayList<ArrayList<Integer>> result = null;
    public ArrayList<ArrayList<Integer>> combine(int n, int k) {
        // Start typing your Java solution below
        // DO NOT write main() function
        result = new ArrayList<ArrayList<Integer>>();
        boolean[] map = new boolean[n];
        getAnswer(map, new ArrayList<Integer>(), k);
        return result;
    }
    public void getAnswer(boolean[] map, ArrayList<Integer> row, int n){
        if(n == 0) result.add(row);
        for(int i = 0; i < map.length; i ++){
            if(!map[i]){
                map[i] = true;
                row.add(i + 1);
                getAnswer(map, row, n - 1);
                map[i] = false;
            }
        }
    }
}