Combinations

Combinations ( leetcode lintcode )

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

Example
For example,
If n = 4 and k = 2, a solution is:
[[2,4],[3,4],[2,3],[1,2],[1,3],[1,4]]

解题思路

Subsets 的变形题，找到所有长度为 k 的子集。

Java 实现

public class Solution {
    /**
     * @param n: Given the range of numbers
     * @param k: Given the numbers of combinations
     * @return: All the combinations of k numbers out of 1..n
     */
    public List<List<Integer>> combine(int n, int k) {
        List<List<Integer>> result = new ArrayList<List<Integer>>();
        if (n < 1 || k < 1 || n < k) {
            return result;
        }

        List<Integer> path = new ArrayList<Integer>();
        dfs(result, path, n, k, 1);
        return result;
    }

    private void dfs(List<List<Integer>> result, List<Integer> path,
                        int n, int k, int pos) {
        if (path.size() == k) {
            result.add(new ArrayList<Integer>(path));
            return;
        }          

        for (int i = pos; i <= n; i++) {
            path.add(i);
            dfs(result, path, n, k, i + 1);
            path.remove(path.size() - 1);
        }
    }
}