Valid Number Problem in Java
In this tutorial, we will learn about valid numbers in Java. A valid number is a numeric representation that satisfies specified criteria, such as being an integer or floating-point value, getting within a defined range, and following any formatting or mathematical rules required in a given context.
Examples of valid numbers vary depending on the context and criteria for validity.
The Mathematical representation of a valid number is dependent on the specific conditions or criteria that determine its validity in a given context which includes integer validity, even number validity, divisibility by n, combination of conditions.
In general, a valid number can be represented by mathematical expressions, inequalities, or equations that determine the number's required properties. A few properties of a valid number includes that the number should fall in a certain range, the number should satisfy multiple conditions, the number should be non-zero, the number should be divisible by a specific divisor, the number should be either even or odd and also a prime number.
Example 1:
Input Condition: Even and Divisible by 4
Output: 4, 8, 12, 16 etc.
Example 2:
Input Condition: Odd and Prime
Output: 3, 5, 7, 11, 13 etc.
Example 3:
Input Condition: Multiple of 3 and 7
Output: 21, 42, 63, 84 etc.
Brute Force Approach:
A brute-force approach to identifying a valid number involves systematically checking a range of values until a valid number is found. This method is simple but may not be efficient, particularly if the valid number falls within a wide range.
FileName:BruteForceValidNumber.java
public class BruteForceValidNumber {
public static void main(String args[]) {
int result = findValidNumber();
if (result != -1) {
System.out.println("The valid number is: " + result);
} else {
System.out.println("No valid number found in the specified range.");
}
}
public static int findValidNumber() {
// Brute force approach to find a valid number
int startRange = 1;
int endRange = 100;
for (int number = startRange; number <= endRange; number++) {
if (isValidNumber(number)) {
return number;
}
}
return -1; // If no valid number is found in the given range
}
public static boolean isValidNumber(int number) {
// Example condition: Valid number is even and divisible by 5
return number % 2 == 0 && number % 5 == 0;
}
}
Output:
The valid number is: 10
Complexity analysis: The time complexity of the provided brute force approach is primarily determined by the number of iterations required to find a valid number within the given range. The loop runs from the beginning to the end of the range, with a time complexity of O(N), where N is the range's size. The brute force approach has minimal space complexity. It does not use any additional data structures that scale with input size. As a result, the space complexity is O(1), indicating that the space is used continually.
Optimized approach :
An optimized or efficient approach to finding a valid number is determined by the specific criteria or conditions that define validity.
The example below shows an optimized approach in which the valid number is computed directly based on certain conditions.
FileName:EfficientValidNumber.java
public class EfficientValidNumber {
public static void main(String args[]) {
int result = findValidNumber();
if (result != -1) {
System.out.println("The valid number is: " + result);
} else {
System.out.println("No valid number found based on the specified conditions.");
}
}
public static int findValidNumber() {
// Optimized approach to find a valid number
int startRange = 1;
int endRange = 100;
for (int number = startRange; number <= endRange; number++) {
if (isValidNumber(number)) {
return number;
}
}
return -1; // If no valid number is found in the given range
}
public static boolean isValidNumber(int number) {
// Example condition: Valid number is even and divisible by 5
return number % 2 == 0 && number % 5 == 0;
}
}
Output:
The valid number is: 10
Complexity analysis: The optimized approach continues to have a time complexity of O(N), where N is the range size. The loop runs from the beginning to the end of the range, and the time complexity is linear in proportion to the range's size. The optimized approach has a space complexity of O(1), indicating that it uses constant space. This is because memory requirements are minimal and independent of input size.