442. Find All Duplicates in an Array - Explanation

Description

The array nums has length n. Each value is between 1 and n, and no value occurs more than twice. Return every value that occurs twice, listing each repeated value once. You may return the values in any order. Your algorithm should run in O(n) time and use O(1) auxiliary space, excluding the returned array. You may modify nums.

Example 1:

Input: nums = [3,1,3,2,2]

Output: [2,3]

Explanation: Values 2 and 3 each appear twice, while 1 appears once. Return [2,3]; [3,2] is also valid.

Example 2:

Input: nums = [2,1,3]

Output: []

Explanation: Every value appears exactly once, so there are no duplicates and the result is empty.

Example 3:

Input: nums = [1,1]

Output: [1]

Explanation: The value 1 appears twice. Include it once in the returned array.

Constraints:

1 <= n <= 100000
1 <= nums[i] <= n
Every value occurs at most twice.

Topics

Array Hash Table

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Prerequisites

Before attempting this problem, you should be comfortable with:

Hash Sets and Hash Maps - Used for O(1) lookup to track seen elements or count frequencies
Array Index Manipulation - Understanding how values in range [1, n] can map to indices [0, n-1]
In-Place Array Modification - The optimal solution uses negative marking to avoid extra space

1. Brute Force

Intuition

The most direct approach is to compare every element with every other element that comes after it. If we find two elements that are equal, we know that value appears twice (since the problem states each element appears at most twice).

Algorithm

For each element at index i:
- Compare it with every element at index j where j > i.
- If nums[i] == nums[j], add nums[i] to the result and break (no need to check further for this value).
Return the result list.

class Solution:
    def findDuplicates(self, nums: List[int]) -> List[int]:
        n = len(nums)
        res = []

        for i in range(n):
            for j in range(i + 1, n):
                if nums[i] == nums[j]:
                    res.append(nums[i])
                    break

        return res

public class Solution {
    public List<Integer> findDuplicates(int[] nums) {
        int n = nums.length;
        List<Integer> res = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (nums[i] == nums[j]) {
                    res.add(nums[i]);
                    break;
                }
            }
        }

        return res;
    }
}

class Solution {
public:
    vector<int> findDuplicates(vector<int>& nums) {
        int n = nums.size();
        vector<int> res;

        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (nums[i] == nums[j]) {
                    res.push_back(nums[i]);
                    break;
                }
            }
        }

        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number[]}
     */
    findDuplicates(nums) {
        const n = nums.length;
        const res = [];

        for (let i = 0; i < n; i++) {
            for (let j = i + 1; j < n; j++) {
                if (nums[i] === nums[j]) {
                    res.push(nums[i]);
                    break;
                }
            }
        }

        return res;
    }
}

public class Solution {
    public IList<int> FindDuplicates(int[] nums) {
        int n = nums.Length;
        List<int> res = new List<int>();

        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (nums[i] == nums[j]) {
                    res.Add(nums[i]);
                    break;
                }
            }
        }

        return res;
    }
}

func findDuplicates(nums []int) []int {
    n := len(nums)
    res := []int{}

    for i := 0; i < n; i++ {
        for j := i + 1; j < n; j++ {
            if nums[i] == nums[j] {
                res = append(res, nums[i])
                break
            }
        }
    }

    return res
}

class Solution {
    fun findDuplicates(nums: IntArray): List<Int> {
        val n = nums.size
        val res = mutableListOf<Int>()

        for (i in 0 until n) {
            for (j in i + 1 until n) {
                if (nums[i] == nums[j]) {
                    res.add(nums[i])
                    break
                }
            }
        }

        return res
    }
}

class Solution {
    func findDuplicates(_ nums: [Int]) -> [Int] {
        let n = nums.count
        var res = [Int]()

        for i in 0..<n {
            for j in (i + 1)..<n {
                if nums[i] == nums[j] {
                    res.append(nums[i])
                    break
                }
            }
        }

        return res
    }
}

impl Solution {
    pub fn find_duplicates(nums: Vec<i32>) -> Vec<i32> {
        let n = nums.len();
        let mut res = vec![];

        for i in 0..n {
            for j in (i + 1)..n {
                if nums[i] == nums[j] {
                    res.push(nums[i]);
                    break;
                }
            }
        }

        res
    }
}

Time & Space Complexity

Time complexity: $O(n ^ 2)$
Space complexity: $O(1)$ extra space.

2. Sorting

Intuition

After sorting, duplicate values will be adjacent to each other. We can simply scan through the sorted array and check if any element equals its neighbor. This is more efficient than the brute force approach since we only need one pass after sorting.

Algorithm

Sort the array.
Iterate through the array from index 0 to n-2:
- If nums[i] == nums[i+1], add nums[i] to the result.
Return the result list.

class Solution:
    def findDuplicates(self, nums: List[int]) -> List[int]:
        nums.sort()
        res = []

        for i in range(len(nums) - 1):
            if nums[i] == nums[i + 1]:
                res.append(nums[i])

        return res

public class Solution {
    public List<Integer> findDuplicates(int[] nums) {
        Arrays.sort(nums);
        List<Integer> res = new ArrayList<>();

        for (int i = 0; i < nums.length - 1; i++) {
            if (nums[i] == nums[i + 1]) {
                res.add(nums[i]);
            }
        }

        return res;
    }
}

class Solution {
public:
    vector<int> findDuplicates(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        vector<int> res;

        for (int i = 0; i < nums.size() - 1; i++) {
            if (nums[i] == nums[i + 1]) {
                res.push_back(nums[i]);
            }
        }

        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number[]}
     */
    findDuplicates(nums) {
        nums.sort((a, b) => a - b);
        const res = [];

        for (let i = 0; i < nums.length - 1; i++) {
            if (nums[i] === nums[i + 1]) {
                res.push(nums[i]);
            }
        }

        return res;
    }
}

public class Solution {
    public IList<int> FindDuplicates(int[] nums) {
        Array.Sort(nums);
        List<int> res = new List<int>();

        for (int i = 0; i < nums.Length - 1; i++) {
            if (nums[i] == nums[i + 1]) {
                res.Add(nums[i]);
            }
        }

        return res;
    }
}

func findDuplicates(nums []int) []int {
    sort.Ints(nums)
    res := []int{}

    for i := 0; i < len(nums)-1; i++ {
        if nums[i] == nums[i+1] {
            res = append(res, nums[i])
        }
    }

    return res
}

class Solution {
    fun findDuplicates(nums: IntArray): List<Int> {
        nums.sort()
        val res = mutableListOf<Int>()

        for (i in 0 until nums.size - 1) {
            if (nums[i] == nums[i + 1]) {
                res.add(nums[i])
            }
        }

        return res
    }
}

class Solution {
    func findDuplicates(_ nums: [Int]) -> [Int] {
        var nums = nums.sorted()
        var res = [Int]()

        for i in 0..<nums.count - 1 {
            if nums[i] == nums[i + 1] {
                res.append(nums[i])
            }
        }

        return res
    }
}

impl Solution {
    pub fn find_duplicates(mut nums: Vec<i32>) -> Vec<i32> {
        nums.sort();
        let mut res = vec![];

        for i in 0..nums.len() - 1 {
            if nums[i] == nums[i + 1] {
                res.push(nums[i]);
            }
        }

        res
    }
}

Time & Space Complexity

Time complexity: $O(n \log n)$
Space complexity: $O(1)$ or $O(n)$ depending on the sorting algorithm.

3. Hash Set

Intuition

We can use a hash set to track which numbers we have already seen. As we iterate through the array, if a number is already in the set, it must be a duplicate. Otherwise, we add it to the set. This gives us O(1) lookup time for each element.

Algorithm

Initialize an empty hash set seen and an empty result list.
For each number in the array:
- If it is already in seen, add it to the result.
- Otherwise, add it to seen.
Return the result list.

class Solution:
    def findDuplicates(self, nums: List[int]) -> List[int]:
        seen = set()
        res = []
        for num in nums:
            if num in seen:
                res.append(num)
            else:
                seen.add(num)
        return res

public class Solution {
    public List<Integer> findDuplicates(int[] nums) {
        Set<Integer> seen = new HashSet<>();
        List<Integer> res = new ArrayList<>();

        for (int num : nums) {
            if (seen.contains(num)) {
                res.add(num);
            } else {
                seen.add(num);
            }
        }

        return res;
    }
}

class Solution {
public:
    vector<int> findDuplicates(vector<int>& nums) {
        unordered_set<int> seen;
        vector<int> res;

        for (int num : nums) {
            if (seen.count(num)) {
                res.push_back(num);
            } else {
                seen.insert(num);
            }
        }

        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number[]}
     */
    findDuplicates(nums) {
        const seen = new Set();
        const res = [];

        for (const num of nums) {
            if (seen.has(num)) {
                res.push(num);
            } else {
                seen.add(num);
            }
        }

        return res;
    }
}

public class Solution {
    public IList<int> FindDuplicates(int[] nums) {
        HashSet<int> seen = new HashSet<int>();
        List<int> res = new List<int>();

        foreach (int num in nums) {
            if (seen.Contains(num)) {
                res.Add(num);
            } else {
                seen.Add(num);
            }
        }

        return res;
    }
}

func findDuplicates(nums []int) []int {
    seen := make(map[int]bool)
    res := []int{}

    for _, num := range nums {
        if seen[num] {
            res = append(res, num)
        } else {
            seen[num] = true
        }
    }

    return res
}

class Solution {
    fun findDuplicates(nums: IntArray): List<Int> {
        val seen = HashSet<Int>()
        val res = mutableListOf<Int>()

        for (num in nums) {
            if (num in seen) {
                res.add(num)
            } else {
                seen.add(num)
            }
        }

        return res
    }
}

class Solution {
    func findDuplicates(_ nums: [Int]) -> [Int] {
        var seen = Set<Int>()
        var res = [Int]()

        for num in nums {
            if seen.contains(num) {
                res.append(num)
            } else {
                seen.insert(num)
            }
        }

        return res
    }
}

impl Solution {
    pub fn find_duplicates(nums: Vec<i32>) -> Vec<i32> {
        let mut seen = HashSet::new();
        let mut res = vec![];

        for num in nums {
            if seen.contains(&num) {
                res.push(num);
            } else {
                seen.insert(num);
            }
        }

        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(n)$

4. Hash Map

Intuition

Instead of just tracking presence, we can count how many times each number appears using a hash map. After counting, we iterate through the map and collect all numbers that appear exactly 2.

Algorithm

Build a frequency map counting occurrences of each number.
Iterate through the map:
- If a number has a count of 2, add it to the result.
Return the result list.

class Solution:
    def findDuplicates(self, nums: List[int]) -> List[int]:
        count = Counter(nums)
        res = []

        for num in count:
            if count[num] == 2:
                res.append(num)

        return res

public class Solution {
    public List<Integer> findDuplicates(int[] nums) {
        Map<Integer, Integer> count = new HashMap<>();
        List<Integer> res = new ArrayList<>();

        for (int num : nums) {
            count.put(num, count.getOrDefault(num, 0) + 1);
        }

        for (int num : count.keySet()) {
            if (count.get(num) == 2) {
                res.add(num);
            }
        }

        return res;
    }
}

class Solution {
public:
    vector<int> findDuplicates(vector<int>& nums) {
        unordered_map<int, int> count;
        vector<int> res;

        for (int num : nums) {
            count[num]++;
        }

        for (auto& [num, freq] : count) {
            if (freq == 2) {
                res.push_back(num);
            }
        }

        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number[]}
     */
    findDuplicates(nums) {
        const count = new Map();
        const res = [];

        for (const num of nums) {
            count.set(num, (count.get(num) || 0) + 1);
        }

        for (const [num, freq] of count.entries()) {
            if (freq === 2) {
                res.push(num);
            }
        }

        return res;
    }
}

public class Solution {
    public IList<int> FindDuplicates(int[] nums) {
        Dictionary<int, int> count = new Dictionary<int, int>();
        List<int> res = new List<int>();

        foreach (int num in nums) {
            if (count.ContainsKey(num)) {
                count[num]++;
            } else {
                count[num] = 1;
            }
        }

        foreach (var kvp in count) {
            if (kvp.Value == 2) {
                res.Add(kvp.Key);
            }
        }

        return res;
    }
}

func findDuplicates(nums []int) []int {
    count := make(map[int]int)
    res := []int{}

    for _, num := range nums {
        count[num]++
    }

    for num, freq := range count {
        if freq == 2 {
            res = append(res, num)
        }
    }

    return res
}

class Solution {
    fun findDuplicates(nums: IntArray): List<Int> {
        val count = HashMap<Int, Int>()
        val res = mutableListOf<Int>()

        for (num in nums) {
            count[num] = count.getOrDefault(num, 0) + 1
        }

        for ((num, freq) in count) {
            if (freq == 2) {
                res.add(num)
            }
        }

        return res
    }
}

class Solution {
    func findDuplicates(_ nums: [Int]) -> [Int] {
        var count = [Int: Int]()
        var res = [Int]()

        for num in nums {
            count[num, default: 0] += 1
        }

        for (num, freq) in count {
            if freq == 2 {
                res.append(num)
            }
        }

        return res
    }
}

impl Solution {
    pub fn find_duplicates(nums: Vec<i32>) -> Vec<i32> {
        let mut count = HashMap::new();
        let mut res = vec![];

        for &num in &nums {
            *count.entry(num).or_insert(0) += 1;
        }

        for (&num, &freq) in &count {
            if freq == 2 {
                res.push(num);
            }
        }

        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(n)$

5. Negative Marking

Intuition

Since all values are in the range [1, n] where n is the array length, we can use the array itself as a hash map. The key insight is that each value v can be mapped to index v-1. When we encounter a value, we mark the element at its corresponding index as negative. If we encounter a value whose corresponding index is already negative, that value must be a duplicate.

Algorithm

For each number in the array:
- Compute the index as abs(num) - 1.
- If nums[idx] is already negative, add abs(num) to the result (this value was seen before).
- Negate nums[idx] to mark that we have seen the value idx + 1.
Return the result list.

class Solution:
    def findDuplicates(self, nums: List[int]) -> List[int]:
        res = []

        for num in nums:
            idx = abs(num) - 1
            if nums[idx] < 0:
                res.append(abs(num))
            nums[idx] = -nums[idx]

        return res

public class Solution {
    public List<Integer> findDuplicates(int[] nums) {
        List<Integer> res = new ArrayList<>();

        for (int num : nums) {
            int idx = Math.abs(num) - 1;
            if (nums[idx] < 0) {
                res.add(Math.abs(num));
            }
            nums[idx] = -nums[idx];
        }

        return res;
    }
}

class Solution {
public:
    vector<int> findDuplicates(vector<int>& nums) {
        vector<int> res;

        for (int num : nums) {
            int idx = abs(num) - 1;
            if (nums[idx] < 0) {
                res.push_back(abs(num));
            }
            nums[idx] = -nums[idx];
        }

        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number[]}
     */
    findDuplicates(nums) {
        const res = [];

        for (let num of nums) {
            const idx = Math.abs(num) - 1;
            if (nums[idx] < 0) {
                res.push(Math.abs(num));
            }
            nums[idx] = -nums[idx];
        }

        return res;
    }
}

public class Solution {
    public IList<int> FindDuplicates(int[] nums) {
        List<int> res = new List<int>();

        foreach (int num in nums) {
            int idx = Math.Abs(num) - 1;
            if (nums[idx] < 0) {
                res.Add(Math.Abs(num));
            }
            nums[idx] = -nums[idx];
        }

        return res;
    }
}

func findDuplicates(nums []int) []int {
    res := []int{}

    for _, num := range nums {
        idx := abs(num) - 1
        if nums[idx] < 0 {
            res = append(res, abs(num))
        }
        nums[idx] = -nums[idx]
    }

    return res
}

func abs(x int) int {
    if x < 0 {
        return -x
    }
    return x
}

class Solution {
    fun findDuplicates(nums: IntArray): List<Int> {
        val res = mutableListOf<Int>()

        for (num in nums) {
            val idx = kotlin.math.abs(num) - 1
            if (nums[idx] < 0) {
                res.add(kotlin.math.abs(num))
            }
            nums[idx] = -nums[idx]
        }

        return res
    }
}

class Solution {
    func findDuplicates(_ nums: [Int]) -> [Int] {
        var nums = nums
        var res = [Int]()

        for num in nums {
            let idx = abs(num) - 1
            if nums[idx] < 0 {
                res.append(abs(num))
            }
            nums[idx] = -nums[idx]
        }

        return res
    }
}

impl Solution {
    pub fn find_duplicates(mut nums: Vec<i32>) -> Vec<i32> {
        let mut res = vec![];

        for i in 0..nums.len() {
            let idx = (nums[i].abs() - 1) as usize;
            if nums[idx] < 0 {
                res.push(nums[i].abs());
            }
            nums[idx] = -nums[idx];
        }

        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(1)$ extra space.

Common Pitfalls

Forgetting to Use Absolute Value When Accessing Indices

In the negative marking approach, once a value at an index is negated, subsequent accesses using that value as an index will fail. Always use abs(num) - 1 to compute the correct index, as the value itself may have been negated in a previous iteration.

Off-by-One Index Errors

Since array values are in the range [1, n] but indices are [0, n-1], you must subtract 1 when converting a value to an index. Forgetting this adjustment causes index out of bounds errors or marks the wrong positions.

Modifying the Array When It Should Be Preserved

The negative marking approach modifies the input array in place. If the problem requires the original array to remain unchanged, or if the array is used elsewhere after the function call, you should either restore the array afterward or use a different approach like a hash set.