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Code Implementation

Square Number Decomposition Implementation

Below is the implementation of the square number decomposition:

solution.js

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/**
 * Two Pointers Approach
 * Time Complexity: O(√c) - We iterate through at most √c pairs of numbers
 * Space Complexity: O(1) - We only use a constant amount of space
 *
 * @param {number} c - The target number
 * @return {boolean} - Whether c can be expressed as the sum of two squares
 */
function judgeSquareSum(c) {
  let a = 0;
  let b = Math.floor(Math.sqrt(c));
 
  while (a <= b) {
    const sum = a * a + b * b;
 
    if (sum === c) {
      return true;
    } else if (sum < c) {
      a++;
    } else {
      b--;
    }
  }
 
  return false;
}

Step-by-Step Explanation

Let's break down the implementation:

1. Understand the Problem: First, understand that we need to determine if a given non-negative integer c can be expressed as the sum of two perfect squares.
2. Set Up Two Pointers: Initialize two pointers: a starting from 0 and b starting from the square root of c.
3. Implement the Two-Pointer Approach: Use a while loop to iterate while a ≤ b, calculating the sum of squares at each step and adjusting the pointers accordingly.
4. Check for a Solution: If the sum of squares equals c, return true. If it's less than c, increment a. If it's greater than c, decrement b.
5. Handle Edge Cases: Consider edge cases such as c = 0 or c = 1, which have straightforward solutions.
6. Optimize for Large Inputs: Ensure that the solution works efficiently for large values of c by using appropriate data types and algorithms.
7. Test the Solution: Verify the solution with the provided examples and additional test cases.

Previous Next

String Problems

Palindrome Checker

Determine if a string reads the same forward and backward.

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Message Encryption

Reverse a string to create a simple encryption system.

EasyString Manipulation

Word Puzzle Challenge

Check if two strings are anagrams of each other.

EasyString Manipulation

Learning Objective

Implement the square number decomposition solution in different programming languages.

Square Number Decomposition Implementation

Below is the implementation of the square number decomposition in different programming languages. Select a language tab to view the corresponding code.

solution.js

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/**
 * Two Pointers Approach
 * Time Complexity: O(√c) - We iterate through at most √c pairs of numbers
 * Space Complexity: O(1) - We only use a constant amount of space
 *
 * @param {number} c - The target number
 * @return {boolean} - Whether c can be expressed as the sum of two squares
 */
function judgeSquareSum(c) {
  let a = 0;
  let b = Math.floor(Math.sqrt(c));
 
  while (a <= b) {
    const sum = a * a + b * b;
 
    if (sum === c) {
      return true;
    } else if (sum < c) {
      a++;
    } else {
      b--;
    }
  }
 
  return false;
}

Step-by-Step Explanation

11. Understand the Problem

First, understand that we need to determine if a given non-negative integer c can be expressed as the sum of two perfect squares.

22. Set Up Two Pointers

Initialize two pointers: a starting from 0 and b starting from the square root of c.

33. Implement the Two-Pointer Approach

Use a while loop to iterate while a ≤ b, calculating the sum of squares at each step and adjusting the pointers accordingly.

44. Check for a Solution

If the sum of squares equals c, return true. If it's less than c, increment a. If it's greater than c, decrement b.

55. Handle Edge Cases

Consider edge cases such as c = 0 or c = 1, which have straightforward solutions.

66. Optimize for Large Inputs

Ensure that the solution works efficiently for large values of c by using appropriate data types and algorithms.

77. Test the Solution

Verify the solution with the provided examples and additional test cases.

Language-Specific Notes

javascript

JavaScript's Math.sqrt() function is used to calculate the square root of c.
Math.floor() is used to ensure that b is an integer, as the square root might not be an integer.
The solution uses strict equality (===) to check if the sum of squares equals c.

python

Python's ** operator is used to calculate the square root (c ** 0.5).
The int() function is used to convert the square root to an integer.
Python's clean syntax makes the two-pointer approach easy to implement and understand.

java

Java's Math.sqrt() method is used to calculate the square root of c.
Long data type is used to avoid integer overflow when calculating a² + b².
Type casting is used to convert the square root to a long value.

cpp

C++'s sqrt() function from the cmath library is used to calculate the square root of c.
Long data type is used to avoid integer overflow when calculating a² + b².
Type casting is used to convert the square root to a long value.

Key Takeaways

The two-pointer approach is an efficient way to solve this problem, with a time complexity of O(√c).
The maximum value of a or b cannot exceed the square root of c, which helps limit the search space.
The problem is related to Fermat's theorem on the sum of two squares, which states that a positive integer can be expressed as the sum of two squares if and only if its prime factorization contains even powers of primes of the form 4k+3.
Binary search can also be used to solve this problem, but the two-pointer approach is generally more intuitive and efficient.
When implementing the solution, be careful about integer overflow for large values of c.
The problem has applications in number theory, geometry, and cryptography.

Try It Yourself

Modify the code to implement an alternative approach and test it with the same examples.

Challenge:

Implement a function that solves the square number decomposition problem using a different approach than shown above.

Common Edge Cases

c = 0

The number 0 can be expressed as 0² + 0² = 0.

judgeSquareSum(0) → true

c = 1

The number 1 can be expressed as 0² + 1² = 1.

judgeSquareSum(1) → true

c = 2

The number 2 can be expressed as 1² + 1² = 2.

judgeSquareSum(2) → true

c = 3

The number 3 cannot be expressed as the sum of two squares.

judgeSquareSum(3) → false

Large Values of c

For large values of c, we need to be careful about integer overflow when calculating a² + b².

judgeSquareSum(2147483647) should handle potential overflow.

Solution Approach All Problems

Problem Solution Code

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Square Number Decomposition - Implementation

Code Implementation

Square Number Decomposition Implementation

Below is the implementation of the square number decomposition:

solution.js

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/**
 * Two Pointers Approach
 * Time Complexity: O(√c) - We iterate through at most √c pairs of numbers
 * Space Complexity: O(1) - We only use a constant amount of space
 *
 * @param {number} c - The target number
 * @return {boolean} - Whether c can be expressed as the sum of two squares
 */
function judgeSquareSum(c) {
  let a = 0;
  let b = Math.floor(Math.sqrt(c));
 
  while (a <= b) {
    const sum = a * a + b * b;
 
    if (sum === c) {
      return true;
    } else if (sum < c) {
      a++;
    } else {
      b--;
    }
  }
 
  return false;
}

Step-by-Step Explanation

Let's break down the implementation:

1. Understand the Problem: First, understand that we need to determine if a given non-negative integer c can be expressed as the sum of two perfect squares.
2. Set Up Two Pointers: Initialize two pointers: a starting from 0 and b starting from the square root of c.
3. Implement the Two-Pointer Approach: Use a while loop to iterate while a ≤ b, calculating the sum of squares at each step and adjusting the pointers accordingly.
4. Check for a Solution: If the sum of squares equals c, return true. If it's less than c, increment a. If it's greater than c, decrement b.
5. Handle Edge Cases: Consider edge cases such as c = 0 or c = 1, which have straightforward solutions.
6. Optimize for Large Inputs: Ensure that the solution works efficiently for large values of c by using appropriate data types and algorithms.
7. Test the Solution: Verify the solution with the provided examples and additional test cases.

Previous Next

String Problems

Palindrome Checker

Determine if a string reads the same forward and backward.

EasyString Manipulation

Message Encryption

Reverse a string to create a simple encryption system.

EasyString Manipulation

Word Puzzle Challenge

Check if two strings are anagrams of each other.

EasyString Manipulation

Learning Objective

Implement the square number decomposition solution in different programming languages.

Square Number Decomposition Implementation

Below is the implementation of the square number decomposition in different programming languages. Select a language tab to view the corresponding code.

solution.js

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
/**
 * Two Pointers Approach
 * Time Complexity: O(√c) - We iterate through at most √c pairs of numbers
 * Space Complexity: O(1) - We only use a constant amount of space
 *
 * @param {number} c - The target number
 * @return {boolean} - Whether c can be expressed as the sum of two squares
 */
function judgeSquareSum(c) {
  let a = 0;
  let b = Math.floor(Math.sqrt(c));
 
  while (a <= b) {
    const sum = a * a + b * b;
 
    if (sum === c) {
      return true;
    } else if (sum < c) {
      a++;
    } else {
      b--;
    }
  }
 
  return false;
}

Step-by-Step Explanation

11. Understand the Problem

First, understand that we need to determine if a given non-negative integer c can be expressed as the sum of two perfect squares.

22. Set Up Two Pointers

Initialize two pointers: a starting from 0 and b starting from the square root of c.

33. Implement the Two-Pointer Approach

Use a while loop to iterate while a ≤ b, calculating the sum of squares at each step and adjusting the pointers accordingly.

44. Check for a Solution

If the sum of squares equals c, return true. If it's less than c, increment a. If it's greater than c, decrement b.

55. Handle Edge Cases

Consider edge cases such as c = 0 or c = 1, which have straightforward solutions.

66. Optimize for Large Inputs

Ensure that the solution works efficiently for large values of c by using appropriate data types and algorithms.

77. Test the Solution

Verify the solution with the provided examples and additional test cases.

Language-Specific Notes

javascript

JavaScript's Math.sqrt() function is used to calculate the square root of c.
Math.floor() is used to ensure that b is an integer, as the square root might not be an integer.
The solution uses strict equality (===) to check if the sum of squares equals c.

python

Python's ** operator is used to calculate the square root (c ** 0.5).
The int() function is used to convert the square root to an integer.
Python's clean syntax makes the two-pointer approach easy to implement and understand.

java

Java's Math.sqrt() method is used to calculate the square root of c.
Long data type is used to avoid integer overflow when calculating a² + b².
Type casting is used to convert the square root to a long value.

cpp

C++'s sqrt() function from the cmath library is used to calculate the square root of c.
Long data type is used to avoid integer overflow when calculating a² + b².
Type casting is used to convert the square root to a long value.

Key Takeaways

The two-pointer approach is an efficient way to solve this problem, with a time complexity of O(√c).
The maximum value of a or b cannot exceed the square root of c, which helps limit the search space.
The problem is related to Fermat's theorem on the sum of two squares, which states that a positive integer can be expressed as the sum of two squares if and only if its prime factorization contains even powers of primes of the form 4k+3.
Binary search can also be used to solve this problem, but the two-pointer approach is generally more intuitive and efficient.
When implementing the solution, be careful about integer overflow for large values of c.
The problem has applications in number theory, geometry, and cryptography.

Try It Yourself

Modify the code to implement an alternative approach and test it with the same examples.

Challenge:

Implement a function that solves the square number decomposition problem using a different approach than shown above.

Common Edge Cases

c = 0

The number 0 can be expressed as 0² + 0² = 0.

judgeSquareSum(0) → true

c = 1

The number 1 can be expressed as 0² + 1² = 1.

judgeSquareSum(1) → true

c = 2

The number 2 can be expressed as 1² + 1² = 2.

judgeSquareSum(2) → true

c = 3

The number 3 cannot be expressed as the sum of two squares.

judgeSquareSum(3) → false

Large Values of c

For large values of c, we need to be careful about integer overflow when calculating a² + b².

judgeSquareSum(2147483647) should handle potential overflow.

Solution Approach All Problems

Code Implementation

Square Number Decomposition Implementation

Step-by-Step Explanation

String ProblemsShow All

Palindrome Checker

Message Encryption

Word Puzzle Challenge

Learning Objective

Square Number Decomposition Implementation

Step-by-Step Explanation

11. Understand the Problem

22. Set Up Two Pointers

33. Implement the Two-Pointer Approach

44. Check for a Solution

55. Handle Edge Cases

66. Optimize for Large Inputs

77. Test the Solution

Language-Specific Notes

javascript

python

java

cpp

Key Takeaways

Try It Yourself

Challenge:

Common Edge Cases

c = 0

c = 1

c = 2

c = 3

Large Values of c

Square Number Decomposition - Implementation

Code Implementation

Square Number Decomposition Implementation

Step-by-Step Explanation

String ProblemsShow All

Palindrome Checker

Message Encryption

Word Puzzle Challenge

Learning Objective

Square Number Decomposition Implementation

Step-by-Step Explanation

11. Understand the Problem

22. Set Up Two Pointers

33. Implement the Two-Pointer Approach

44. Check for a Solution

55. Handle Edge Cases

66. Optimize for Large Inputs

77. Test the Solution

Language-Specific Notes

javascript

python

java

cpp

Key Takeaways

Try It Yourself

Challenge:

Common Edge Cases

c = 0

c = 1

c = 2

c = 3

Large Values of c

String Problems

String Problems