Merge pull request #899 from debangi29/sort-colors

Sort colors - Added solution to leetcode 75

Author: ajay-dhangar

dsa-solutions/lc-solutions/0000-0099/0075-sort-colors.md

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+---
+id: sort-colors
+title: Sort Colors
+difficulty: Medium
+sidebar_label: 0075-sortcolors
+tags:
+  - Arrays
+  - Two Pointers
+  - Sorting
+---
+
+## Problem
+
+| Problem Statement | Solution Link | LeetCode Profile |
+| :---------------- | :------------ | :--------------- |
+| [Sort Colors](https://leetcode.com/problems/sort-colors/description/) | [Sort Colors Solution on LeetCode](https://leetcode.com/problems/sort-colors/solutions/) |  [Leetcode Profile](https://leetcode.com/u/debangi_29/) |
+
+## Problem Description
+
+Given an array nums with n objects colored red, white, or blue, sort them in-place so that objects of the same color are adjacent, with the colors in the order red, white, and blue.
+
+We will use the integers 0, 1, and 2 to represent the color red, white, and blue, respectively.
+
+You must solve this problem without using the library's sort function.
+ 
+
+### Examples
+
+### Example 1:
+
+**Input**: nums = [2,0,2,1,1,0]
+
+**Output**: [0,0,1,1,2,2]
+
+
+### Example 2:
+
+**Input**: nums = [2,0,1]
+
+**Output**: [0,1,2]
+
+ 
+
+### Constraints
+
+- $n = \text{nums.length}$
+- $1 \leq n \leq 300$
+- $\text{nums}[i] \in \{0, 1, 2\}$
+
+### Approach
+This problem is a variation of the popular Dutch National flag algorithm. 
+
+The steps will be the following:
+
+- First, we will run a loop that will continue until `mid <= high.`
+- There can be three different values of mid pointer i.e. arr[mid]
+    - If arr[mid] == 0, we will swap arr[low] and arr[mid] and will increment both low and mid. Now the subarray from index 0 to (low-1) only contains 0.
+    - If arr[mid] == 1, we will just increment the mid pointer and then the index (mid-1) will point to 1 as it should according to the rules.
+    - If arr[mid] == 2, we will swap arr[mid] and arr[high] and will decrement high. Now the subarray from index high+1 to (n-1) only contains 2.In this step, we will do nothing to the mid-pointer as even after swapping, the subarray from mid to high(after decrementing high) might be unsorted. So, we will check the value of mid again in the next iteration.
+- Finally, our array should be sorted.
+### Solution Code
+
+#### Python
+
+```
+class Solution:
+ def sortArray(arr):
+    low = 0
+    mid = 0
+    high = len(arr) - 1
+
+    while mid <= high:
+        if arr[mid] == 0:
+            arr[low], arr[mid] = arr[mid], arr[low]
+            low += 1
+            mid += 1
+        elif arr[mid] == 1:
+            mid += 1
+        else:
+            arr[mid], arr[high] = arr[high], arr[mid]
+            high -= 1
+```
+
+#### Java
+
+```
+class Solution {
+  public static void sortArray(ArrayList<Integer> arr, int n) {
+        int low = 0, mid = 0, high = n - 1; // 3 pointers
+
+        while (mid <= high) {
+            if (arr.get(mid) == 0) {
+                // swapping arr[low] and arr[mid]
+                int temp = arr.get(low);
+                arr.set(low, arr.get(mid));
+                arr.set(mid, temp);
+
+                low++;
+                mid++;
+
+            } else if (arr.get(mid) == 1) {
+                mid++;
+
+            } else {
+                // swapping arr[mid] and arr[high]
+                int temp = arr.get(mid);
+                arr.set(mid, arr.get(high));
+                arr.set(high, temp);
+
+                high--;
+            }
+        }
+    }
+}
+```
+
+#### C++
+
+```
+class Solution {
+ public:
+  void sortArray(vector<int>& arr, int n) {
+
+    int low = 0, mid = 0, high = n - 1; // 3 pointers
+
+    while (mid <= high) {
+        if (arr[mid] == 0) {
+            swap(arr[low], arr[mid]);
+            low++;
+            mid++;
+        }
+        else if (arr[mid] == 1) {
+            mid++;
+        }
+        else {
+            swap(arr[mid], arr[high]);
+            high--;
+        }
+    }
+}
+};
+
+```
+
+### Conclusion
+
+- Time Complexity: $O(N)$, where N = size of the given array.
+    
+    Reason: We are using a single loop that can run at most N times.
+
+- Space Complexity: $O(1)$ as we are not using any extra space.