Sort Colors
Sure! This problem is known as the Dutch national flag problem, and it can be solved using a threepointer approach. The idea is to maintain three pointers to divide the array into four sections: red, white, unknown, and blue.
Here’s how you can implement this in the Solution
class:


Here’s a breakdown of the logic:
 If the current element
nums[white]
is 0 (red), we swap it with the element at thered
pointer and move bothred
andwhite
pointers forward.  If the current element is 1 (white), we don’t need to swap, and we just move the
white
pointer forward.  If the current element is 2 (blue), we swap it with the element at the
blue
pointer and move theblue
pointer backward.
This approach ensures that the colors are sorted inplace, and the time complexity is (O(n)), where (n) is the length of the array nums
.
Identifying Problem Isomorphism
“Sort Colors” involves sorting an array of integers where each element is either 0, 1, or 2. It’s an application of the Dutch national flag problem and requires understanding of inplace array manipulation.
An easier problem is “Move Zeroes”, where you need to move all the 0’s to the end of an array while maintaining the relative order of the nonzero elements. It’s simpler than “Sort Colors” as it only involves two types of elements, zeroes and nonzeroes, rather than three distinct values. However, both problems require a similar approach of swapping elements in the array to achieve the required order.
A more complex problem is “Sort an Array”, where you have to sort an array of integers. This problem does not limit the array’s values to just 0, 1, and 2, meaning a more general sorting algorithm is required. This elevates the complexity as it requires a broad understanding of sorting algorithms and their efficiency.
In increasing complexity:
 “Move Zeroes”
 “Sort Colors”
 “Sort an Array”.
These problems all involve reordering elements in an array to fulfill certain conditions.
10 Prerequisite LeetCode Problems
Understand concepts like array manipulation, two pointers, and sorting. Here are 10 problems to prepare for “75. Sort Colors”.
283. Move Zeroes: This problem is about rearranging an array, which is a simpler version of the “Sort Colors” problem.
27. Remove Element: This problem is also about array manipulation and will help you practice using two pointers to maintain the original order of an array.
88. Merge Sorted Array: This problem will help you learn how to merge two sorted arrays into one.
26. Remove Duplicates from Sorted Array: It’s a problem to help understand the use of pointers in array manipulation.
167. Two Sum II  Input array is sorted: This problem will help you understand the use of two pointers.
344. Reverse String: This problem is about inplace reversal using two pointers.
349. Intersection of Two Arrays: This problem helps understand basic set operations, a foundational concept.
268. Missing Number: This problem is about finding missing elements in an array, a similar concept to arranging or sorting.
414. Third Maximum Number: This problem involves finding the third maximum number in a nonsorted array, which can provide good practice with sorting concepts.
283. Move Zeroes: This problem involves moving all zeros in an array to the end while maintaining the relative order of the nonzero elements, which is a similar concept to sorting colors.
Given an array nums with n objects colored red, white, or blue, sort them inplace so that objects of the same color are adjacent, with the colors in the order red, white, and blue.
Here, we will use the integers 0, 1, and 2 to represent the color red, white, and blue respectively.
Note: You are not suppose to use the library’s sort function for this problem.
Here is Python code that solves the problem:


This code uses a variation of the Dutch national flag problem’s solution by Edsger Dijkstra. The idea is to move all 0s to the beginning, and all 2s to the end. We maintain three pointers: one for the current element (white), one for the next position where the 0 should be put (red), and one for the next position where the 2 should be put (blue). The white pointer is used to scan the array from the start to the end.
Problem Classification
Given an array nums with n objects colored red, white, or blue, sort them inplace 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.
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 == nums.length 1 <= n <= 300 nums[i] is either 0, 1, or 2.
Follow up: Could you come up with a onepass algorithm using only constant extra space?
Language Agnostic Coding Drills
This is an implementation of the Dutch national flag problem, which involves sorting an array of 0s, 1s, and 2s (which represent the three colors in the Dutch national flag). This is solved using a twopointer approach.
Variable Declarations and Initialization: Understand the purpose of each variable and how they’re initialized (red, white, blue).
Control Structures (While Loop): Understand how to use a while loop and when to use it. The loop here continues until the
white
pointer has passed theblue
pointer.Control Structures (Ifelifelse statements): Understand how to use ifelifelse statements to control program flow. In this code, different actions are taken based on the value at the current index pointed to by
white
.Working with Lists: Understand how to manipulate lists, in this case, swapping elements in a list.
Incrementing and decrementing pointers: Know how and when to increment or decrement pointers, in this case,
red
,white
andblue
.Combining the above: The ultimate problemsolving drill would be to understand the twopointer method and how it is applied in sorting this array. You start with
red
andwhite
at the beginning of the array andblue
at the end. You go through each element (white
), and if it’s 0, swap it withred
and move bothred
andwhite
forward. If it’s 1, just movewhite
forward. If it’s 2, swap it withblue
and moveblue
backward.
This algorithm allows you to sort the array in a single pass with constant space complexity. The general problemsolving approach here is understanding the behavior of the elements you are sorting and setting up pointers that help you track the position of these elements as you go through the array.
Targeted Drills in Python
Drill 1: Variable Declarations and Initialization
Create three variables, red
, white
, blue
, and initialize them with the values 0, 0, and 9 respectively. Print the variables.


Drill 2: Control Structures (While Loop)
Create a while loop that continues running until the variable white
is greater than blue
. In each iteration, increment white
by one. Print white
in each iteration.


Drill 3: Control Structures (Ifelifelse statements)
In a for loop from 0 to 10, check each number. If the number is divisible by 3, print “Divisible by 3”. If it’s divisible by 2, print “Divisible by 2”. Else, print the number.


Drill 4: Working with Lists
Given a list nums = [1, 2, 3, 4, 5]
, swap the first and last elements.


Drill 5: Incrementing and decrementing pointers
Start with variables left
and right
at values 0 and 10 respectively. In a while loop, continue until left
is equal to or greater than right
. In each iteration, increment left
and decrement right
.


Drill 6: Combining the above
For the final drill, implement the sortColors
function on a sample list and print the result.


These drills should help in understanding each concept separately. By combining them, one can grasp the entire algorithm.