Add Gaussian Elimination (TheAlgorithms#2810)

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Andrii Siriak <[email protected]>

Author: 3 people

DIRECTORY.md

@@ -10,14 +10,13 @@
 ## Ciphers
   * [AES](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/AES.java)
   * [AESEncryption](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/AESEncryption.java)
-  * [affineCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/affineCipher.java)
   * [AffineCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/AffineCipher.java)
   * [Caesar](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/Caesar.java)
   * [ColumnarTranspositionCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/ColumnarTranspositionCipher.java)
   * [HillCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/HillCipher.java)
   * [ProductCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/ProductCipher.java)
   * [RSA](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/RSA.java)
-  * [simpleSubCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/simpleSubCipher.java)
+  * [SimpleSubCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/SimpleSubCipher.java)
   * [SimpleSubstitutionCipher](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/SimpleSubstitutionCipher.java)
   * [Vigenere](https://github.com/TheAlgorithms/Java/blob/master/Ciphers/Vigenere.java)
 
@@ -102,6 +101,7 @@
   * Stacks
     * [BalancedBrackets](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Stacks/BalancedBrackets.java)
     * [DecimalToAnyUsingStack](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Stacks/DecimalToAnyUsingStack.java)
+    * [DuplicateBrackets](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Stacks/DuplicateBrackets.java)
     * [InfixToPostfix](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Stacks/InfixToPostfix.java)
     * [MaximumMinimumWindow](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Stacks/MaximumMinimumWindow.java)
     * [NodeStack](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Stacks/NodeStack.java)
@@ -116,6 +116,7 @@
     * [BSTRecursive](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/BSTRecursive.java)
     * [BSTRecursiveGeneric](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/BSTRecursiveGeneric.java)
     * [CeilInBinarySearchTree](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/CeilInBinarySearchTree.java)
+    * [CheckIfBinaryTreeBalanced](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/CheckIfBinaryTreeBalanced.java)
     * [CreateBinaryTreeFromInorderPreorder](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/CreateBinaryTreeFromInorderPreorder.java)
     * [CreateBSTFromSortedArray](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/CreateBSTFromSortedArray.java)
     * [FenwickTree](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/FenwickTree.java)
@@ -132,6 +133,16 @@
     * [ValidBSTOrNot](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/ValidBSTOrNot.java)
     * [VerticalOrderTraversal](https://github.com/TheAlgorithms/Java/blob/master/DataStructures/Trees/VerticalOrderTraversal.java)
 
+## DevUtils
+  * Nodes
+    * [LargeTreeNode](https://github.com/TheAlgorithms/Java/blob/master/DevUtils/Nodes/LargeTreeNode.java)
+    * [Node](https://github.com/TheAlgorithms/Java/blob/master/DevUtils/Nodes/Node.java)
+    * [SimpleNode](https://github.com/TheAlgorithms/Java/blob/master/DevUtils/Nodes/SimpleNode.java)
+    * [SimpleTreeNode](https://github.com/TheAlgorithms/Java/blob/master/DevUtils/Nodes/SimpleTreeNode.java)
+    * [TreeNode](https://github.com/TheAlgorithms/Java/blob/master/DevUtils/Nodes/TreeNode.java)
+  * Searches
+    * [SearchAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/DevUtils/Searches/SearchAlgorithm.java)
+
 ## DivideAndConquer
   * [BinaryExponentiation](https://github.com/TheAlgorithms/Java/blob/master/DivideAndConquer/BinaryExponentiation.java)
   * [ClosestPair](https://github.com/TheAlgorithms/Java/blob/master/DivideAndConquer/ClosestPair.java)
@@ -153,6 +164,7 @@
   * [Knapsack](https://github.com/TheAlgorithms/Java/blob/master/DynamicProgramming/Knapsack.java)
   * [KnapsackMemoization](https://github.com/TheAlgorithms/Java/blob/master/DynamicProgramming/KnapsackMemoization.java)
   * [LevenshteinDistance](https://github.com/TheAlgorithms/Java/blob/master/DynamicProgramming/LevenshteinDistance.java)
+  * [LongestAlternatingSubsequence](https://github.com/TheAlgorithms/Java/blob/master/DynamicProgramming/LongestAlternatingSubsequence.java)
   * [LongestCommonSubsequence](https://github.com/TheAlgorithms/Java/blob/master/DynamicProgramming/LongestCommonSubsequence.java)
   * [LongestIncreasingSubsequence](https://github.com/TheAlgorithms/Java/blob/master/DynamicProgramming/LongestIncreasingSubsequence.java)
   * [LongestPalindromicSubsequence](https://github.com/TheAlgorithms/Java/blob/master/DynamicProgramming/LongestPalindromicSubsequence.java)
@@ -203,15 +215,18 @@
   * [FindMin](https://github.com/TheAlgorithms/Java/blob/master/Maths/FindMin.java)
   * [FindMinRecursion](https://github.com/TheAlgorithms/Java/blob/master/Maths/FindMinRecursion.java)
   * [Floor](https://github.com/TheAlgorithms/Java/blob/master/Maths/Floor.java)
+  * [Gaussian](https://github.com/TheAlgorithms/Java/blob/master/Maths/Gaussian.java)
   * [GCD](https://github.com/TheAlgorithms/Java/blob/master/Maths/GCD.java)
   * [GCDRecursion](https://github.com/TheAlgorithms/Java/blob/master/Maths/GCDRecursion.java)
   * [GenericRoot](https://github.com/TheAlgorithms/Java/blob/master/Maths/GenericRoot.java)
   * [HarshadNumber](https://github.com/TheAlgorithms/Java/blob/master/Maths/HarshadNumber.java)
   * [KeithNumber](https://github.com/TheAlgorithms/Java/blob/master/Maths/KeithNumber.java)
   * [KrishnamurthyNumber](https://github.com/TheAlgorithms/Java/blob/master/Maths/KrishnamurthyNumber.java)
   * [LeonardoNumber](https://github.com/TheAlgorithms/Java/blob/master/Maths/LeonardoNumber.java)
+  * [LinearDiophantineEquationsSolver](https://github.com/TheAlgorithms/Java/blob/master/Maths/LinearDiophantineEquationsSolver.java)
   * [LucasSeries](https://github.com/TheAlgorithms/Java/blob/master/Maths/LucasSeries.java)
   * [MagicSquare](https://github.com/TheAlgorithms/Java/blob/master/Maths/MagicSquare.java)
+  * [MatrixUtil](https://github.com/TheAlgorithms/Java/blob/master/Maths/MatrixUtil.java)
   * [MaxValue](https://github.com/TheAlgorithms/Java/blob/master/Maths/MaxValue.java)
   * [Median](https://github.com/TheAlgorithms/Java/blob/master/Maths/Median.java)
   * [MinValue](https://github.com/TheAlgorithms/Java/blob/master/Maths/MinValue.java)
@@ -231,13 +246,15 @@
   * [PrimeCheck](https://github.com/TheAlgorithms/Java/blob/master/Maths/PrimeCheck.java)
   * [PrimeFactorization](https://github.com/TheAlgorithms/Java/blob/master/Maths/PrimeFactorization.java)
   * [PythagoreanTriple](https://github.com/TheAlgorithms/Java/blob/master/Maths/PythagoreanTriple.java)
+  * [ReverseNumber](https://github.com/TheAlgorithms/Java/blob/master/Maths/ReverseNumber.java)
   * [RomanNumeralUtil](https://github.com/TheAlgorithms/Java/blob/master/Maths/RomanNumeralUtil.java)
   * [SimpsonIntegration](https://github.com/TheAlgorithms/Java/blob/master/Maths/SimpsonIntegration.java)
   * [SumOfArithmeticSeries](https://github.com/TheAlgorithms/Java/blob/master/Maths/SumOfArithmeticSeries.java)
   * [SumOfDigits](https://github.com/TheAlgorithms/Java/blob/master/Maths/SumOfDigits.java)
   * [TrinomialTriangle](https://github.com/TheAlgorithms/Java/blob/master/Maths/TrinomialTriangle.java)
   * [VampireNumber](https://github.com/TheAlgorithms/Java/blob/master/Maths/VampireNumber.java)
   * [VectorCrossProduct](https://github.com/TheAlgorithms/Java/blob/master/Maths/VectorCrossProduct.java)
+  * [Volume](https://github.com/TheAlgorithms/Java/blob/master/Maths/Volume.java)
 
 ## MatrixExponentiation
   * [Fibonacci](https://github.com/TheAlgorithms/Java/blob/master/MatrixExponentiation/Fibonacci.java)
@@ -251,12 +268,16 @@
   * [matrixTranspose](https://github.com/TheAlgorithms/Java/blob/master/Misc/matrixTranspose.java)
   * [MedianOfRunningArray](https://github.com/TheAlgorithms/Java/blob/master/Misc/MedianOfRunningArray.java)
   * [PalindromePrime](https://github.com/TheAlgorithms/Java/blob/master/Misc/PalindromePrime.java)
+  * [PalindromeSinglyLinkedList](https://github.com/TheAlgorithms/Java/blob/master/Misc/PalindromeSinglyLinkedList.java)
   * [RangeInSortedArray](https://github.com/TheAlgorithms/Java/blob/master/Misc/RangeInSortedArray.java)
+  * [Sort012D](https://github.com/TheAlgorithms/Java/blob/master/Misc/Sort012D.java)
   * [Sparcity](https://github.com/TheAlgorithms/Java/blob/master/Misc/Sparcity.java)
+  * [ThreeSumProblem](https://github.com/TheAlgorithms/Java/blob/master/Misc/ThreeSumProblem.java)
   * [TwoSumProblem](https://github.com/TheAlgorithms/Java/blob/master/Misc/TwoSumProblem.java)
   * [WordBoggle](https://github.com/TheAlgorithms/Java/blob/master/Misc/WordBoggle.java)
 
 ## Others
+  * [BankersAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/Others/BankersAlgorithm.java)
   * [BestFit](https://github.com/TheAlgorithms/Java/blob/master/Others/BestFit.java)
   * [BFPRT](https://github.com/TheAlgorithms/Java/blob/master/Others/BFPRT.java)
   * [BoyerMoore](https://github.com/TheAlgorithms/Java/blob/master/Others/BoyerMoore.java)
@@ -271,6 +292,7 @@
   * [FirstFit](https://github.com/TheAlgorithms/Java/blob/master/Others/FirstFit.java)
   * [FloydTriangle](https://github.com/TheAlgorithms/Java/blob/master/Others/FloydTriangle.java)
   * [GuassLegendre](https://github.com/TheAlgorithms/Java/blob/master/Others/GuassLegendre.java)
+  * [Huffman](https://github.com/TheAlgorithms/Java/blob/master/Others/Huffman.java)
   * [Implementing auto completing features using trie](https://github.com/TheAlgorithms/Java/blob/master/Others/Implementing_auto_completing_features_using_trie.java)
   * [InsertDeleteInArray](https://github.com/TheAlgorithms/Java/blob/master/Others/InsertDeleteInArray.java)
   * [KMP](https://github.com/TheAlgorithms/Java/blob/master/Others/KMP.java)
@@ -304,10 +326,13 @@
   * [TopKWords](https://github.com/TheAlgorithms/Java/blob/master/Others/TopKWords.java)
   * [TowerOfHanoi](https://github.com/TheAlgorithms/Java/blob/master/Others/TowerOfHanoi.java)
   * [TwoPointers](https://github.com/TheAlgorithms/Java/blob/master/Others/TwoPointers.java)
+  * [Verhoeff](https://github.com/TheAlgorithms/Java/blob/master/Others/Verhoeff.java)
   * [WorstFit](https://github.com/TheAlgorithms/Java/blob/master/Others/WorstFit.java)
 
 ## Searches
   * [BinarySearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/BinarySearch.java)
+  * [BreadthFirstSearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/BreadthFirstSearch.java)
+  * [DepthFirstSearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/DepthFirstSearch.java)
   * [ExponentalSearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/ExponentalSearch.java)
   * [FibonacciSearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/FibonacciSearch.java)
   * [HowManyTimesRotated](https://github.com/TheAlgorithms/Java/blob/master/Searches/HowManyTimesRotated.java)
@@ -320,7 +345,6 @@
   * [MonteCarloTreeSearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/MonteCarloTreeSearch.java)
   * [PerfectBinarySearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/PerfectBinarySearch.java)
   * [SaddlebackSearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/SaddlebackSearch.java)
-  * [SearchAlgorithm](https://github.com/TheAlgorithms/Java/blob/master/Searches/SearchAlgorithm.java)
   * [SquareRootBinarySearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/SquareRootBinarySearch.java)
   * [TernarySearch](https://github.com/TheAlgorithms/Java/blob/master/Searches/TernarySearch.java)
   * [UnionFind](https://github.com/TheAlgorithms/Java/blob/master/Searches/UnionFind.java)

Maths/Gaussian.java

@@ -0,0 +1,68 @@
+/**
+ * \file
+ * \brief [Gaussian elimination
+ * method](https://en.wikipedia.org/wiki/Gaussian_elimination)
+ */
+package Maths;
+import java.util.*;
+
+/** Main function */
+public class Gaussian {
+
+  public static void main(String[] args) {
+    int mat_size, i, j, step;
+    Scanner sc = new Scanner(System.in);
+    
+    System.out.println("Matrix Size : ");
+    mat_size = sc.nextInt();
+
+    double [][] mat = new double[mat_size+1][mat_size+1];
+    double [][] x = new double[mat_size][mat_size+1];
+
+    System.out.println("Enter value of the matrix");
+    System.out.println(' ');
+    for (i = 0; i < mat_size; i++) {
+        for (j = 0; j <= mat_size; j++) {
+            mat[i][j] = sc.nextInt();
+        }
+    }
+
+    // perform Gaussian elimination
+    for (step = 0; step < mat_size - 1; step++) {
+        for (i = step; i < mat_size - 1; i++) {
+            double a = (mat[i + 1][step] / mat[step][step]);
+
+            for (j = step; j <= mat_size; j++)
+                mat[i + 1][j] = mat[i + 1][j] - (a * mat[step][j]);
+        }
+    }
+    
+    System.out.println("Matrix using Gaussian Elimination method: ");
+    System.out.println(" ");
+    for (i = 0; i < mat_size; i++) {
+        for (j = 0; j <= mat_size; j++) {
+            x[i][j] = mat[i][j];
+            System.out.print(mat[i][j] + " ");
+        }
+        System.out.println();
+    }
+    System.out.println( "Value of the Gaussian Elimination method: ");
+    System.out.println(" ");
+    
+    for (i = mat_size - 1; i >= 0; i--) {
+        double sum = 0;
+        for (j = mat_size - 1; j > i; j--) {
+            x[i][j] = x[j][j] * x[i][j];
+            sum = x[i][j] + sum;
+        }
+        if (x[i][i] == 0){
+            x[i][i] = 0;
+        }
+        else{
+            x[i][i] = (x[i][mat_size] - sum) / (x[i][i]);
+        }
+        System.out.print("x" + i + "=" + x[i][i]);
+        System.out.println(" ");
+    }
+  }
+}