Find All Duplicates in Array
Given an integer array nums of length n where all integers are in the range [1, n] and each integer appears once or twice, return all integers that appear twice.
You must run in O(n) time with O(1) extra space. Output as space-separated sorted integers.
Example:
4,3,2,7,8,2,3,1
2 3
- We start by iterating over the input array
numsand for each number, we use its absolute value as an index to mark the presence of that number. - When we encounter a number, we check if the value at its corresponding index is negative. If it's not, we mark it as negative to indicate that we've seen this number before.
- We repeat this process for all numbers in the array. After that, we iterate over the array again to find the indices that are still positive, which correspond to the numbers that appear only once. The numbers that appear twice will have negative values at their corresponding indices.
- Finally, we return the indices of the negative values (excluding the sign) in sorted order, which are the numbers that appear twice in the array: 2 and 3.
Constraints:
- 1 <= n <= 10^5
- 1 <= nums[i] <= n
Background Knowledge
The problem "Find All Duplicates in Array" falls under the category of Arrays & Hashing. To tackle this problem, it's essential to understand the basics of arrays and how hashing can be applied to solve problems efficiently. In the context of arrays, hashing refers to the process of using the array indices to store and retrieve values. Given that all integers in the array are in the range [1, n], we can leverage this property to our advantage.
The constraint of running in O(n) time with O(1) extra space implies that we cannot use any additional data structures that scale with the input size, such as hash tables or sets. This means we need to rely solely on the given array to store and manipulate the data. Understanding how to utilize the given array to mark or identify duplicate elements is crucial. This can involve modifying the array in-place, using the sign or magnitude of the elements to convey additional information.
The problem also requires outputting the duplicate integers in sorted order. While this might seem like an additional complexity, it can be addressed as part of the overall solution strategy. The key is to recognize that the range of integers [1, n] allows for a straightforward sorting or ordering mechanism, potentially tied to the array indices themselves. By combining these insights—hashing, in-place modification, and the specific range of integers—we can develop an efficient solution.
Algorithm/Approach
The general approach to solving this type of problem involves using the array indices to our advantage, essentially treating the array as a hash table where the index corresponds to the value minus one (since the range is [1, n]). This technique is known as in-place hashing. By iterating through the array and using each element's value to determine an index, we can mark or modify the array at those indices to track which numbers have been seen. This method allows us to identify duplicates without using extra space that scales with the input size.
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