Time complexity is O(N^target) where N is a length of candidates array.
Space complexity is O(target).
This is worst case and without any optimization, like moving position forward and sorting to stop early. Just assuming that each recursive step we go over all existing candidates, so base N. And go as deep as target in our recursive calls (if candidates are close to 1), so power of target. You can mention that this is worst case and optimizations can make time complexity a little better, for interview I think this should be enough
###Structure
This structure might apply to many other backtracking questions, but here I am just going to demonstrate Subsets, Permutations, and Combination Sum.
When to Choose i=0 vs i=index
In case of Subset problem subset always grow forwards it never comes back unlike permutation
So Rule of Thumb Subset always take i=index and for permutation i=0;
[1,2,3]
[1]
[1 2]
[2 3]
[1,2.3] ---> These are all subset
whereas
[1,2,3]
[2,1,3]
[3,1,2] ---> These are all permutations
Subsets : https://leetcode.com/problems/subsets/
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);
}
}
Subsets II (contains duplicates) : https://leetcode.com/problems/subsets-ii/
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);
}
}
Permutations : https://leetcode.com/problems/permutations/
public List<List<Integer>> permute(int[] nums) {
List<List<Integer>> list = new ArrayList<>();
// Arrays.sort(nums); // not necessary
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);
}
}
}
Permutations II (contains duplicates) : https://leetcode.com/problems/permutations-ii/
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);
}
}
}
Combination Sum : https://leetcode.com/problems/combination-sum/
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);
}
}
}
Combination Sum II (can't reuse same element) : https://leetcode.com/problems/combination-sum-ii/
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);
}
}
}
Palindrome Partitioning : https://leetcode.com/problems/palindrome-partitioning/
public List<List<String>> partition(String s) {
List<List<String>> list = new ArrayList<>();
backtrack(list, new ArrayList<>(), s, 0);
return list;
}
public void backtrack(List<List<String>> list, List<String> tempList, String s, int start){
if(start == s.length())
list.add(new ArrayList<>(tempList));
else{
for(int i = start; i < s.length(); i++){
if(isPalindrome(s, start, i)){
tempList.add(s.substring(start, i + 1));
backtrack(list, tempList, s, i + 1);
tempList.remove(tempList.size() - 1);
}
}
}
}
public boolean isPalindrome(String s, int low, int high){
while(low < high)
if(s.charAt(low++) != s.charAt(high--)) return false;
return true;
}