### Java Math ceilDiv() Method

The `Math.ceilDiv()` method in Java is used to perform division and return the smallest (closest to negative infinity) value that is greater than or equal to the algebraic quotient. This guide will cover the method's usage, explain how it works, and provide examples to demonstrate its functionality for each of its overloaded versions.

1. Introduction
2. `ceilDiv()` Method Syntax
3. Overloaded `ceilDiv()` Methods
4. Examples
• `ceilDiv(int x, int y)`
• `ceilDiv(long x, int y)`
• `ceilDiv(long x, long y)`
5. Real-World Use Case
6. Conclusion

## Introduction

The `Math.ceilDiv()` method provides a way to perform division and ensure that the result is rounded up to the nearest integer value. This is useful in scenarios where you need to divide two numbers and ensure that the result is always rounded up, even if there is a remainder.

## ceilDiv() Method Syntax

The syntax for the `ceilDiv()` method varies depending on the types of the arguments:

### `ceilDiv(int x, int y)`

``````public static int ceilDiv(int x, int y)
``````

### `ceilDiv(long x, int y)`

``````public static long ceilDiv(long x, int y)
``````

### `ceilDiv(long x, long y)`

``````public static long ceilDiv(long x, long y)
``````

### Parameters:

• `x`: The dividend.
• `y`: The divisor.

### Returns:

• The smallest value that is greater than or equal to the algebraic quotient.

### Throws:

• `ArithmeticException` if the divisor `y` is zero.

The `Math.ceilDiv()` method is overloaded to handle different primitive data types: `int` and `long`. Each version returns the quotient of the division, rounded up to the nearest integer value.

## Examples

### `ceilDiv(int x, int y)`

The `ceilDiv(int x, int y)` method returns the quotient of two `int` values, rounded up to the nearest integer value.

#### Example

``````public class CeilDivIntExample {
public static void main(String[] args) {
int x1 = 7, y1 = 3;
int x2 = -7, y2 = 3;

int result1 = Math.ceilDiv(x1, y1);
int result2 = Math.ceilDiv(x2, y2);

System.out.println("Ceiling division of " + x1 + " / " + y1 + " is " + result1);
System.out.println("Ceiling division of " + x2 + " / " + y2 + " is " + result2);
}
}
``````

Output:

``````Ceiling division of 7 / 3 is 3
Ceiling division of -7 / 3 is -2
``````

### `ceilDiv(long x, int y)`

The `ceilDiv(long x, int y)` method returns the quotient of a `long` and an `int` value, rounded up to the nearest integer value.

#### Example

``````public class CeilDivLongIntExample {
public static void main(String[] args) {
long x1 = 10L, y1 = 3;
long x2 = -10L, y2 = 3;

long result1 = Math.ceilDiv(x1, y1);
long result2 = Math.ceilDiv(x2, y2);

System.out.println("Ceiling division of " + x1 + " / " + y1 + " is " + result1);
System.out.println("Ceiling division of " + x2 + " / " + y2 + " is " + result2);
}
}
``````

Output:

``````Ceiling division of 10 / 3 is 4
Ceiling division of -10 / 3 is -3
``````

### `ceilDiv(long x, long y)`

The `ceilDiv(long x, long y)` method returns the quotient of two `long` values, rounded up to the nearest integer value.

#### Example

``````public class CeilDivLongLongExample {
public static void main(String[] args) {
long x1 = 20L, y1 = 4L;
long x2 = 21L, y2 = 4L;

long result1 = Math.ceilDiv(x1, y1);
long result2 = Math.ceilDiv(x2, y2);

System.out.println("Ceiling division of " + x1 + " / " + y1 + " is " + result1);
System.out.println("Ceiling division of " + x2 + " / " + y2 + " is " + result2);
}
}
``````

Output:

``````Ceiling division of 20 / 4 is 5
Ceiling division of 21 / 4 is 6
``````

## Real-World Use Case

In real-world scenarios, the `Math.ceilDiv()` method can be used to evenly distribute tasks among workers, ensuring that each worker gets at least one task if there are any remaining tasks.

#### Example

``````public class TaskDistributionExample {
public static void main(String[] args) {
int workers = 3;

}
}
``````

Output:

``````Each worker should handle 4 tasks.
``````

## Conclusion

The `Math.ceilDiv()` method in Java provides a way to perform division with rounding up, ensuring that the result is the smallest integer greater than or equal to the algebraic quotient.