Combinations

Given two integers n and k, return all possible combinations ofk 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],
]

public class Solution {
    ArrayList<ArrayList<Integer>> res;
	public ArrayList<ArrayList<Integer>> combine(int n, int k) {
		// Start typing your Java solution below
		// DO NOT write main() function
		res = new ArrayList<ArrayList<Integer>>();
		if(k > n || k == 0)
			return res;
		ArrayList<Integer> com = new ArrayList<Integer>();
		DFS(com, 0, k, n);
		return res;
	}
	public void DFS(ArrayList<Integer> com, int level, int k, int n){
		if(com.size() == k){
			res.add(new ArrayList<Integer>(com));
			return;
		}
		if(level == n)
			return;
		else{
			level++;
			DFS(com, level, k, n);// com does not contain current level
			com.add(level);
			DFS(com, level, k, n);// com contains current level
			com.remove(com.size() - 1);
		}
	}
}

public class Solution {
    ArrayList<ArrayList<Integer>> res;
    public ArrayList<ArrayList<Integer>> combine(int n, int k) {
		// Start typing your Java solution below
		// DO NOT write main() function
		res = new ArrayList<ArrayList<Integer>>();
		ArrayList<Integer> temp = new ArrayList<Integer>();
		subsets(temp, n, k, 1);
		return res;
	}

	private void subsets(
			ArrayList<Integer> temp, int n, int k, int level) {
		if (temp.size() == k) {
			res.add(new ArrayList<Integer>(temp));
			return;
		}
		for (int i = level; i <= n; i++) {
			temp.add(i);// from level to n pick one.
			subsets(temp, n, k, i + 1);
			temp.remove(temp.size() - 1);
		}
	}
}

public class Solution {
    ArrayList<ArrayList<Integer>> res;
    public ArrayList<ArrayList<Integer>> combine(int n, int k) {
		// Start typing your Java solution below
		// DO NOT write main() function
		res = new ArrayList<ArrayList<Integer>>();
		ArrayList<Integer> temp = new ArrayList<Integer>();
		com_rec(temp, n, k, 1);
		return res;
	}

	private void com_rec(
			ArrayList<Integer> temp, int n, int k, int index) {
		if (k == 0) {
			res.add(new ArrayList<Integer>(temp));
		}
		else if(k > 0 && index <= n){
			temp.add(index);
			com_rec(temp, n, k - 1, index + 1);
			
			temp.remove(temp.size() - 1);
			com_rec(temp, n, k, index + 1);
		}
	}
}

第三种方法适用于C(n,k) = C(n-1,k-1） + C(n-1,k)结论。