LeetCode--Combinations（动态规划与深度优先搜索）

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],]

及从1到n中选出k个数，得到所有的结果。题目中没有刻意强调升序。

开始想到的是动态规划，后一个数依赖前面的数字。具体实现如下。

public class Solution {    public List<List<Integer>> combine(int n, int k) {        if (k > n)            return null;        else {            List<List<Integer>> result = new ArrayList<List<Integer>>();            List<List<Integer>> resultSwitch = new ArrayList<List<Integer>>();            for (int i1 = 0; i1 < k; i1++) {                if (i1 == 0) {                    for (int i2 = 1; i2 <= n - k + 1; i2++) {                        List<Integer> temp = new ArrayList<Integer>();                        temp.add(i2);                        result.add(temp);                    }                } else {                    while (result.size() != 0) {                        List<Integer> temp = result.get(0);                        for (int i = temp.get(temp.size() - 1) + 1; i <= n - k + temp.size() + 1; i++) {                            List<Integer> tempClone = this.clone(temp);                            tempClone.add(i);                            resultSwitch.add(tempClone);                        }                        result.remove(0);                    }                    List<List<Integer>> temp = result;                    result = resultSwitch;                    resultSwitch = temp;                }            }            return result;        }    }    private List<Integer> clone(List<Integer> source) {        List<Integer> result = new ArrayList<Integer>();        for (int i = 0; i < source.size(); i++) {            result.add(source.get(i));        }        return result;    }}

后来在网上看到dfs深度优先搜寻，代码更简洁。

public class Solution {    public List<List<Integer>> combine(int n, int k) {        if (k > n)            return null;        else {            List<List<Integer>> result = new ArrayList<List<Integer>>();            List<Integer> rs = new ArrayList<Integer>();            this.dfs(n, k, rs, result);            return result;        }    }    private void dfs(int n, int k, List<Integer> rs, List<List<Integer>> result) {        if (k == 0) {            result.add(rs);            return;        } else {            for (int i = rs.size() == 0 ? 1 : rs.get(rs.size() - 1) + 1; i <= n - k + 1; i++) {                List<Integer> tempList = this.clone(rs);                tempList.add(i);                this.dfs(n, k - 1, tempList, result);            }        }    }    private List<Integer> clone(List<Integer> source) {        List<Integer> result = new ArrayList<Integer>();        for (int i = 0; i < source.size(); i++) {            result.add(source.get(i));        }        return result;    }}