448. Find All Numbers Disappeared in an Array

https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array/

Problem

Given an array of integers where 1 ≤ a[i] ≤ n (n = size of array), some elements appear twice and others appear once.

Find all the elements of [1, n] inclusive that do not appear in this array.

Could you do it without extra space and in O(n) runtime? You may assume the returned list does not count as extra space.

Example:

Input:
[4,3,2,7,8,2,3,1]

Output:
[5,6]

Solution

1. $O(N)$ Space using Hash Map

class Solution {
public:
    vector<int> findDisappearedNumbers(vector<int>& nums) {
        vector<int> ans;
        if (nums.empty()) return ans;
        const int size = nums.size();
        int counter[size];
        for (int i = 0; i < size; ++i) counter[i] = 0;
        
        ans.reserve(size);
        for (const auto& n: nums) counter[n - 1]++;
        for (int i = 0; i < size; ++i) {
            if (counter[i] == 0) ans.push_back(i + 1);
        }
        return ans;
    }
};

2. $O(1)$ Space using encoding

class Solution {
public:
    vector<int> findDisappearedNumbers(vector<int>& nums) {
        vector<int> ans;
        if (nums.empty()) return ans;
        for (int i = 0; i < nums.size(); ++i) {
            const int idx = abs(nums[i]) - 1;
            if (nums[idx] > 0) nums[idx] *= -1; 
        }
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] < 0) continue;
            ans.push_back(i + 1);
        }
        return ans;
    }
};

• #encoding

• #hash