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Write a program that, for all positive integers i, j, k, and l from 1 through 500, finds and prints all possible combinations of i, j, k and l such that i + j + k = l and i < j < k < l ?
Unique combinations of i, j, k, and l
public class FindCombinations {
public static void main(String[] args) {
int max = 500;
for (int i = 1; i <= max - 3; i++) {
for (int j = i + 1; j <= max - 2; j++) {
for (int k = j + 1; k <= max - 1; k++) {
int l = i + j + k;
if (l > k && l <= max) {
System.out.println(i + " " + j + " " + k + " " + l);
}
}
}
}
}
}
Out Put
i = 1, j = 2, k = 3, l = 6
i = 1, j = 3, k = 4, l = 8
i = 1, j = 4, k = 5, l = 10
i = 1, j = 5, k = 6, l = 12
i = 1, j = 6, k = 7, l = 14
i = 1, j = 7, k = 8, l = 16
...
i = 121, j = 189, k = 189, l = 499
i = 123, j = 189, k = 189, l = 501
...
javac CombinationFinder.java
java CombinationFinder
Explanation:
- Loop Structure:
- The outermost loop iterates through possible values of from 1 to −3 (since must be less than , , and ).
- The second loop iterates through possible values of from +1 to −2.
- The third loop iterates through possible values of from +1 to −1.
- Calculate :
- For each combination of , , and , is calculated as .
- Condition Check:
- The condition
if (l > k && l <= max)ensures that is greater than (to satisfy ) and that is within the range (1 to 500).
- The condition
- Print the Combination:
- If the condition is met, the combination is printed.
Performance Considerations:
- The nested loops ensure that the condition is inherently satisfied by the order of iteration.
- This brute-force approach is feasible within the given constraints (1 to 500) due to modern computational power, but for larger ranges, optimizations might be necessary.
This program efficiently finds and prints all valid combinations of , , , and within the specified range.
Running the Program:
To run this program, save it in a file named CombinationFinder.java and use the following commands in a terminal or command prompt:
This will output all the valid combinations of i, j, k, and l as per the given conditions. Note that the actual output will be very extensive, considering all possible combinations from 1 to 500.
Another example scanner class
Below is a Java program that uses the Scanner class to allow for dynamic input of the upper limit (though by default it can be set to 500). The program finds and prints all combinations of positive integers i, j, k, and l from 1 through the user-provided limit such that i + j + k = l and i < j < k < l.
import java.util.Scanner;
public class CombinationFinder {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
// Prompt the user for the upper limit
System.out.print("Enter the upper limit (e.g., 500): ");
int max = scanner.nextInt();
scanner.close();
// Find and print the combinations
for (int l = 4; l <= max; l++) { // l starts from 4 because i, j, k are at least 1
for (int k = 3; k < l; k++) { // k starts from 3 to ensure i + j + k = l and i < j < k
for (int j = 2; j < k; j++) { // j starts from 2 to ensure i < j
for (int i = 1; i < j; i++) { // i starts from 1 and must be less than j
if (i + j + k == l) {
System.out.println("i = " + i + ", j = " + j + ", k = " + k + ", l = " + l);
}
}
}
}
}
}
}
Explanation:
User Input:
- The
Scannerclass is used to take user input for the upper limit. - This allows the program to be flexible and not hard-coded to 500.
- The
Loop Structure:
- The outermost loop iterates
lfrom 4 to the user-provided limit. - The next loop iterates
kfrom 3 to one less thanl. - The subsequent loop iterates
jfrom 2 to one less thank. - The innermost loop iterates
ifrom 1 to one less thanj.
- The outermost loop iterates
Condition Check:
- The condition
i + j + k == lensures that the sum ofi,j, andkequalsl. - The condition
i < j < k < lis maintained by the structure of the loops.
- The condition
Printing Results:
- When the condition is met, the program prints the values of
i,j,k, andl. Sample Output:
Here’s what a portion of the output might look like for an upper limit of 10:
- When the condition is met, the program prints the values of
Enter the upper limit (e.g., 500): 10
i = 1, j = 2, k = 3, l = 6
i = 1, j = 3, k = 4, l = 8
i = 1, j = 4, k = 5, l = 10
Running the Program:
To run this program, follow these steps:
- Save the program in a file named
CombinationFinder.java. - Open a terminal or command prompt and navigate to the directory containing the file.
- Compile the program using the following command:
javac CombinationFinder.java
java CombinationFinder
