# Java: Count the number of possible triangles from a given unsorted array of positive integers

## Java Array: Exercise-44 with Solution

Write a Java program to count the number of possible triangles from a given unsorted array of positive integers.

Note: The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side.

**Sample Solution**:

**Java Code:**

```
// Import necessary Java libraries.
import java.util.*;
import java.lang.*;
// Define a class named Main.
public class Main
{
// The main method for executing the program.
public static void main(String[] args)
{
// Define an array of integers.
int nums[] = {6, 7, 9, 16, 25, 12, 30, 40};
int n = nums.length;
System.out.println("Original Array : " + Arrays.toString(nums));
// Sort the array elements in non-decreasing order.
Arrays.sort(nums);
// Initialize count of triangles.
int ctr = 0;
// Iterate through the array elements to count the number of triangles.
for (int i = 0; i < n - 2; ++i)
{
int x = i + 2;
for (int j = i + 1; j < n; ++j)
{
while (x < n && nums[i] + nums[j] > nums[x])
++x;
ctr += x - j - 1;
}
}
System.out.println("Total number of triangles: " + ctr);
}
}
```

Sample Output:

Original Array : [6, 7, 9, 16, 25, 12, 30, 40] Total number of triangles: 17

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