Given a collection of distinct numbers, return all possible permutations.
For example, [1,2,3] have the following permutations:
[
[1,2,3],
[1,3,2],
[2,1,3],
[2,3,1],
[3,1,2],
[3,2,1]
]
对于nums数组中的每一个数,都依次放入结果集中,如果结果集中已经包含这个数,就继续下一次循环。
以数组[1,2,3]为例,每次循环的结果是:
[1,2,3]
[1,3,2]
[2,1,3]
[2,3,1]
[3,1,2]
[3,2,1]
public List<List<Integer>> permute(int[] nums) {
List<List<Integer>> list = new ArrayList<>();
backtrack(list, new ArrayList<>(), nums);
return list;
}
private void backtrack(List<List<Integer>> list, List<Integer> tempList, int [] nums){
if(tempList.size() == nums.length){
list.add(new ArrayList<>(tempList));
} else{
for(int i = 0; i < nums.length; i++){
if(tempList.contains(nums[i])) continue; // element already exists, skip
tempList.add(nums[i]);
backtrack(list, tempList, nums);
tempList.remove(tempList.size() - 1);
}
}
}
Given a collection of numbers that might contain duplicates, return all possible unique permutations.
For example, [1,1,2] have the following unique permutations:
[
[1,1,2],
[1,2,1],
[2,1,1]
]
这道题比上一道题多了一个条件,即数组中有重复的数。有两种思路:
必须按照从前到后的顺序使用数字
,即数组[1,1],在组合时,必须先使用第一个1,才能再使用第二个1,这样就避免了结果集重复的情况。public List<List<Integer>> permuteUnique(int[] nums) {
List<List<Integer>> list = new ArrayList<>();
Arrays.sort(nums);
backtrack(list, new ArrayList<>(), nums, new boolean[nums.length]);
return list;
}
private void backtrack(List<List<Integer>> list, List<Integer> tempList, int [] nums, boolean [] used){
if(tempList.size() == nums.length){
list.add(new ArrayList<>(tempList));
} else{
for(int i = 0; i < nums.length; i++){
if(used[i] || i > 0 && nums[i] == nums[i-1] && !used[i - 1]) continue;
used[i] = true;
tempList.add(nums[i]);
backtrack(list, tempList, nums, used);
used[i] = false;
tempList.remove(tempList.size() - 1);
}
}
}
Given a set of distinct integers, nums, return all possible subsets.
Note: The solution set must not contain duplicate subsets.
For example, If nums = [1,2,3], a solution is:
[
[3],
[1],
[2],
[1,2,3],
[1,3],
[2,3],
[1,2],
[]
]
与题目Permutations
类似,但是Permutations
是达到数组长度才将结果保存,而本题目是求子集,任何集合都需要保存。其中for循环的条件也稍微有些变化。
public List<List<Integer>> subsets(int[] nums) {
List<List<Integer>> list = new ArrayList<>();
Arrays.sort(nums);
backtrack(list, new ArrayList<>(), nums, 0);
return list;
}
private void backtrack(List<List<Integer>> list , List<Integer> tempList, int [] nums, int start){
list.add(new ArrayList<>(tempList));
for(int i = start; i < nums.length; i++){
tempList.add(nums[i]);
backtrack(list, tempList, nums, i + 1);
tempList.remove(tempList.size() - 1);
}
}
Given a collection of integers that might contain duplicates, nums, return all possible subsets.
Note: The solution set must not contain duplicate subsets.
For example, If nums = [1,2,2], a solution is:
[
[2],
[1],
[1,2,2],
[2,2],
[1,2],
[]
]
处理重复的数,和上面是一个思路,即只允许用前面的数字。
public List<List<Integer>> subsetsWithDup(int[] nums) {
List<List<Integer>> list = new ArrayList<>();
Arrays.sort(nums);
backtrack(list, new ArrayList<>(), nums, 0);
return list;
}
private void backtrack(List<List<Integer>> list, List<Integer> tempList, int [] nums, int start){
list.add(new ArrayList<>(tempList));
for(int i = start; i < nums.length; i++){
if(i > start && nums[i] == nums[i-1]) continue; // skip duplicates
tempList.add(nums[i]);
backtrack(list, tempList, nums, i + 1);
tempList.remove(tempList.size() - 1);
}
}
Given a set of candidate numbers (C) (without duplicates) and a target number (T), find all unique combinations in C where the candidate numbers sums to T.
The same repeated number may be chosen from C unlimited number of times.
Note: All numbers (including target) will be positive integers. The solution set must not contain duplicate combinations. For example, given candidate set [2, 3, 6, 7] and target 7, A solution set is:
[
[7],
[2, 2, 3]
]
和Subsets
是同一个思路,只不过这次不是求子集,而是加上了限制条件:和为指定的值。
public List<List<Integer>> combinationSum(int[] nums, int target) {
List<List<Integer>> list = new ArrayList<>();
Arrays.sort(nums);
backtrack(list, new ArrayList<>(), nums, target, 0);
return list;
}
private void backtrack(List<List<Integer>> list, List<Integer> tempList, int [] nums, int remain, int start){
if(remain < 0) return;
else if(remain == 0) list.add(new ArrayList<>(tempList));
else{
for(int i = start; i < nums.length; i++){
tempList.add(nums[i]);
backtrack(list, tempList, nums, remain - nums[i], i); // not i + 1 because we can reuse same elements
tempList.remove(tempList.size() - 1);
}
}
}
Given a collection of candidate numbers (C) and a target number (T), find all unique combinations in C where the candidate numbers sums to T.
Each number in C may only be used once in the combination.
Note: All numbers (including target) will be positive integers. The solution set must not contain duplicate combinations. For example, given candidate set [10, 1, 2, 7, 6, 1, 5] and target 8, A solution set is:
[
[1, 7],
[1, 2, 5],
[2, 6],
[1, 1, 6]
]
和上一题有两点不同的地方:
解决数组中可能有重复的数字:
if(i > start && nums[i] == nums[i-1]) continue; // skip duplicates
解决不能重复利用数组中的数字(上一题中最后是i,而不是i + 1):
backtrack(list, tempList, nums, remain - nums[i], i + 1);
public List<List<Integer>> combinationSum2(int[] nums, int target) {
List<List<Integer>> list = new ArrayList<>();
Arrays.sort(nums);
backtrack(list, new ArrayList<>(), nums, target, 0);
return list;
}
private void backtrack(List<List<Integer>> list, List<Integer> tempList, int [] nums, int remain, int start){
if(remain < 0) return;
else if(remain == 0) list.add(new ArrayList<>(tempList));
else{
for(int i = start; i < nums.length; i++){
if(i > start && nums[i] == nums[i-1]) continue; // skip duplicates
tempList.add(nums[i]);
backtrack(list, tempList, nums, remain - nums[i], i + 1);
tempList.remove(tempList.size() - 1);
}
}
}