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Linear Space On

Linear Space Complexity refers to algorithms where the memory usage grows linearly with the input size. This occurs when an algorithm needs to store a new copy of the input or requires auxiliary data structures proportional to the input size.

Key Characteristics

In an algorithm with space complexity:

The memory usage increases linearly with the size of the input.
Common in tasks that duplicate the input data or process each element with additional storage.

Code Example 1: Copying a String

Let’s look at an example where we create a copy of a string. This requires memory proportional to the length of the string, resulting in space complexity.

java

class Solution {

  public String copy_string(String s) {
    String copied_str = new String(s); // Creates a copy of the string
    return copied_str;
  }

  public static void main(String[] args) {
    String original = "Hello, Java!";

    Solution solution = new Solution();
    String copied = solution.copy_string(original);

    System.out.println("Original string: " + original);
    System.out.println("Copied string: " + copied);
  }
}

Explanation:
- The copy_string method takes an input string s and creates a copy copied_str.
- Since copied_str is a complete duplicate of s, it requires memory proportional to the length of s, resulting in space complexity.

Code Example 2: Copying an Array

Here’s another example that demonstrates space complexity by creating a copy of an array.

java

import java.util.Arrays;

class Solution {
    public int[] copy_array(int[] arr) {
        int[] copied_arr = arr.clone(); // Creates a copy of the array
        return copied_arr;
    }

    public static void main(String[] args) {
        int[] original = {1, 2, 3, 4, 5}; // Example array
        
        Solution solution = new Solution();
        int[] copied = solution.copy_array(original);

        // Print original and copied arrays
        System.out.println("Original array: " + Arrays.toString(original));
        System.out.println("Copied array: " + Arrays.toString(copied));
    }
}

Explanation:
- This copy_array function takes an input array arr and creates a duplicate copied_arr.
- Since copied_arr contains each element of arr, it requires memory proportional to the size of arr, resulting in space complexity.

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