https://github.com/shaldonbarnes10/sorting_0_1_2s
Sort an Array of 0s, 1s, and 2s in a Single Scan. This project provides an efficient solution to sort an array consisting only of 0s, 1s, and 2s using a single-pass algorithm (Dutch National Flag Algorithm) Three pointer. Given multiple test cases, the algorithm ensures optimal performance with a time complexity of O(N) and space complexity of O(1)
https://github.com/shaldonbarnes10/sorting_0_1_2s
algorithms-and-data-structures codestudio cpp dsa-algorithm dutch-nationalflag-problem
Last synced: 2 months ago
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Sort an Array of 0s, 1s, and 2s in a Single Scan. This project provides an efficient solution to sort an array consisting only of 0s, 1s, and 2s using a single-pass algorithm (Dutch National Flag Algorithm) Three pointer. Given multiple test cases, the algorithm ensures optimal performance with a time complexity of O(N) and space complexity of O(1)
- Host: GitHub
- URL: https://github.com/shaldonbarnes10/sorting_0_1_2s
- Owner: Shaldonbarnes10
- Created: 2025-01-30T16:55:54.000Z (4 months ago)
- Default Branch: main
- Last Pushed: 2025-02-02T17:31:31.000Z (4 months ago)
- Last Synced: 2025-03-29T06:44:55.703Z (2 months ago)
- Topics: algorithms-and-data-structures, codestudio, cpp, dsa-algorithm, dutch-nationalflag-problem
- Language: C++
- Homepage:
- Size: 44.9 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Sorting an Array of 0s, 1s, and 2s using the Three-Pointer Approach (Dutch National Flag Algorithm)
## Overview
This repository implements an efficient algorithm to sort an array consisting of only `0`s, `1`s, and `2`s. The algorithm follows the **Dutch National Flag Algorithm**, which uses three pointers to partition the array in a single pass, ensuring an optimal time complexity of **O(n)**.
## Problem Statement
Given an array consisting only of the numbers `0`, `1`, and `2`, sort it in ascending order **in-place** without using any extra space.
### Example
#### **Input:**
```
arr[] = {0, 1, 2, 1, 2, 1, 2}
```
#### **Output:**
```
0 1 1 1 2 2 2
```
## Approach: Three-Pointer Technique
We use three pointers:
1. **Low Pointer (`low`)**: Marks the boundary where `0`s should be placed.
2. **Mid Pointer (`mid`)**: Iterates through the array, processing elements.
3. **High Pointer (`high`)**: Marks the boundary where `2`s should be placed.
### **Algorithm Steps:**
1. Initialize three pointers:
- `low = 0` (beginning of array)
- `mid = 0` (current element being processed)
- `high = n - 1` (end of array)
2. Traverse the array while `mid <= high`:
- **If `arr[mid] == 0`**:
- Swap `arr[mid]` and `arr[low]`
- Increment `low` and `mid`
- **If `arr[mid] == 1`**:
- Leave as is, simply increment `mid`
- **If `arr[mid] == 2`**:
- Swap `arr[mid]` and `arr[high]`
- Decrement `high` (do not increment `mid` immediately, as swapped value needs processing)
### **Code Implementation (C++)**
```cpp
#include
#include
using namespace std;
void sort012(array& arr) {
int low = 0, mid = 0, high = arr.size() - 1;
while (mid <= high) {
if (arr[mid] == 0) {
swap(arr[low], arr[mid]);
low++;
mid++;
} else if (arr[mid] == 1) {
mid++;
} else { // arr[mid] == 2
swap(arr[mid], arr[high]);
high--;
}
}
}
int main() {
array arr = {0, 1, 2, 1, 2, 1, 2};
sort012(arr);
cout << "Sorted array: ";
for (int i = 0; i < arr.size(); i++) {
cout << arr[i] << " ";
}
cout << endl;
return 0;
}
```
### **Time Complexity Analysis**
- **Best Case:** O(n)
- **Worst Case:** O(n)
- **Average Case:** O(n)
### **Space Complexity**
- **O(1)** (Sorting is performed in-place without extra space)
## Why Use the Three-Pointer Approach?
✅ **Single pass (O(n) complexity)** – Efficient for large datasets.
✅ **In-place sorting (O(1) space)** – No extra memory required.
✅ **Easy to implement and understand.**
## Conclusion
This algorithm is one of the most efficient ways to sort an array of `0`s, `1`s, and `2`s, ensuring optimal performance. The three-pointer approach minimizes swaps and avoids unnecessary operations, making it an excellent choice for real-world scenarios.
---
### **Contributions**
Feel free to fork this repository, suggest improvements, or report any issues!
---
**Author:** Shaldon Barnes
**License:** MIT