Sort Colors
Given an array with n objects colored red (0), white (1), or blue (2), sort them in-place so same colors are adjacent in order 0, 1, 2.
Output space-separated.
Example:
2,0,2,1,1,0
0 0 1 1 2 2
- The input array is
2, 0, 2, 1, 1, 0, which needs to be sorted in-place with same colors adjacent in order 0, 1, 2. - We initialize three pointers: one at the start, one at the end, and one for scanning the array, to track the positions of 0, 1, and 2.
- As we scan the array, we swap elements to maintain the order: if the current element is 0, we swap it with the element at the start pointer and move both pointers forward; if it's 2, we swap it with the element at the end pointer and move the end pointer backward.
- After scanning the entire array, the elements are sorted in-place as
0, 0, 1, 1, 2, 2, which is then output as space-separated values:0 0 1 1 2 2.
Constraints:
- 1 <= len(nums) <= 300
- nums[i] is 0, 1, or 2
Background Knowledge
The "Sort Colors" problem is a classic example of a problem that can be solved using the Dutch National Flag algorithm, which is a variation of the three-way partitioning technique. This technique is used to sort an array of objects into three categories. In this case, the objects are colored red (0), white (1), or blue (2), and we need to sort them in-place so that the same colors are adjacent in the order 0, 1, 2. The key concept here is to use two pointers to keep track of the positions where the next 0 and 2 should be placed.
The two pointers technique is a fundamental concept in array and string problems. It involves using two pointers, usually starting from the beginning and end of the array, to traverse the array and solve the problem. In this case, we can use two pointers to keep track of the positions where the next 0 and 2 should be placed. This technique is useful when we need to solve problems that involve partitioning or sorting arrays.
The in-place requirement means that we need to solve the problem without using any extra space that scales with the input size. This means that we cannot use any additional arrays or data structures that scale with the input size. We need to use the given array itself to solve the problem. This requirement makes the problem more challenging and requires us to think creatively about how to use the given array to solve the problem.
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