Heaps are tree-like data structures that allow storing elements in a specific - * way. Each node corresponds to an element and has one parent node (except for the root) and - * at most two children nodes. Every element contains a key, and those keys - * indicate how the tree shall be built. For instance, for a min-heap, the key of a node shall - * be greater than or equal to its parent's and lower than or equal to its children's (the opposite rule applies to a - * max-heap).
- *All heap-related operations (inserting or deleting an element, extracting the min or max) are performed in - * O(log n) time.
- * @author Nicolas Renard - * - * - */ -public interface Heap { - - /** - * - * @return the top element in the heap, the one with lowest key for min-heap or with - * the highest key for max-heap - * @throws Exception if heap is empty - */ - public abstract HeapElement getElement() throws EmptyHeapException; - /** - * Inserts an element in the heap. Adds it to then end and toggle it until it finds its - * right position. - * - * @param element an instance of the HeapElement class. - */ - public abstract void insertElement(HeapElement element); - - /** - * Delete an element in the heap. - * - * @param elementIndex int containing the position in the heap of the element to be deleted. - */ - public abstract void deleteElement(int elementIndex); - -} diff --git a/Data Structures/Heaps/HeapElement.java b/Data Structures/Heaps/HeapElement.java deleted file mode 100644 index e0cc93ccbfe0..000000000000 --- a/Data Structures/Heaps/HeapElement.java +++ /dev/null @@ -1,132 +0,0 @@ -/** - * - */ -package heaps; - -import java.lang.Double; -import java.lang.Object; - -/** - * Class for heap elements.A heap element contains two attributes: a key which will be used to build the tree (int - * or double, either primitive type or object) and any kind of IMMUTABLE object the user sees fit - * to carry any information he/she likes. Be aware that the use of a mutable object might - * jeopardize the integrity of this information.
- * @author Nicolas Renard - * - */ -public class HeapElement { - private final double key; - private final Object additionalInfo; - - // Constructors - - /** - * - * @param key : a number of primitive type 'double' - * @param info : any kind of IMMUTABLE object. May be null, since the purpose is only to carry - * additional information of use for the user - */ - public HeapElement(double key, Object info) { - this.key = key; - this.additionalInfo = info; - } - - /** - * - * @param key : a number of primitive type 'int' - * @param info : any kind of IMMUTABLE object. May be null, since the purpose is only to carry - * additional information of use for the user - */ - public HeapElement(int key, Object info) { - this.key = key; - this.additionalInfo = info; - } - - /** - * - * @param key : a number of object type 'Integer' - * @param info : any kind of IMMUTABLE object. May be null, since the purpose is only to carry - * additional information of use for the user - */ - public HeapElement(Integer key, Object info) { - this.key = key; - this.additionalInfo = info; - } - - /** - * - * @param key : a number of object type 'Double' - * @param info : any kind of IMMUTABLE object. May be null, since the purpose is only to carry - * additional information of use for the user - */ - public HeapElement(Double key, Object info) { - this.key = key; - this.additionalInfo = info; - } - - /** - * - * @param key : a number of primitive type 'double' - */ - public HeapElement(double key) { - this.key = key; - this.additionalInfo = null; - } - - /** - * - * @param key : a number of primitive type 'int' - */ - public HeapElement(int key) { - this.key = key; - this.additionalInfo = null; - } - - /** - * - * @param key : a number of object type 'Integer' - */ - public HeapElement(Integer key) { - this.key = key; - this.additionalInfo = null; - } - - /** - * - * @param key : a number of object type 'Double' - */ - public HeapElement(Double key) { - this.key = key; - this.additionalInfo = null; - } - - // Getters - /** - * @return the object containing the additional info provided by the user. - */ - public Object getInfo() { - return additionalInfo; - } - /** - * @return the key value of the element - */ - public double getKey() { - return key; - } - - // Overridden object methods - - public String toString() { - return "Key: " + key + " - " +additionalInfo.toString(); - } - /** - * - * @param otherHeapElement - * @return true if the keys on both elements are identical and the additional info objects - * are identical. - */ - public boolean equals(HeapElement otherHeapElement) { - return (this.key == otherHeapElement.key) && (this.additionalInfo.equals(otherHeapElement.additionalInfo)); - } -} diff --git a/Data Structures/Heaps/MaxHeap.java b/Data Structures/Heaps/MaxHeap.java deleted file mode 100644 index 5f774e3534a8..000000000000 --- a/Data Structures/Heaps/MaxHeap.java +++ /dev/null @@ -1,115 +0,0 @@ -package heaps; - -import java.util.ArrayList; -import java.util.List; - -/** - * Heap tree where a node's key is higher than or equal to its parent's and lower than or equal - * to its children's. - * @author Nicolas Renard - * - */ -public class MaxHeap implements Heap { - - private final ListThis filter applies an exponential moving average to a sequence of audio + * signal values, making it useful for smoothing out rapid fluctuations. + * The smoothing factor (alpha) controls the degree of smoothing. + * + *
Based on the definition from
+ * Wikipedia link.
+ */
+public class EMAFilter {
+ private final double alpha;
+ private double emaValue;
+ /**
+ * Constructs an EMA filter with a given smoothing factor.
+ *
+ * @param alpha Smoothing factor (0 < alpha <= 1)
+ * @throws IllegalArgumentException if alpha is not in (0, 1]
+ */
+ public EMAFilter(double alpha) {
+ if (alpha <= 0 || alpha > 1) {
+ throw new IllegalArgumentException("Alpha must be between 0 and 1.");
+ }
+ this.alpha = alpha;
+ this.emaValue = 0.0;
+ }
+ /**
+ * Applies the EMA filter to an audio signal array.
+ *
+ * @param audioSignal Array of audio samples to process
+ * @return Array of processed (smoothed) samples
+ */
+ public double[] apply(double[] audioSignal) {
+ if (audioSignal.length == 0) {
+ return new double[0];
+ }
+ double[] emaSignal = new double[audioSignal.length];
+ emaValue = audioSignal[0];
+ emaSignal[0] = emaValue;
+ for (int i = 1; i < audioSignal.length; i++) {
+ emaValue = alpha * audioSignal[i] + (1 - alpha) * emaValue;
+ emaSignal[i] = emaValue;
+ }
+ return emaSignal;
+ }
+}
diff --git a/src/main/java/com/thealgorithms/audiofilters/IIRFilter.java b/src/main/java/com/thealgorithms/audiofilters/IIRFilter.java
new file mode 100644
index 000000000000..fbc095909541
--- /dev/null
+++ b/src/main/java/com/thealgorithms/audiofilters/IIRFilter.java
@@ -0,0 +1,93 @@
+package com.thealgorithms.audiofilters;
+
+/**
+ * N-Order IIR Filter Assumes inputs are normalized to [-1, 1]
+ *
+ * Based on the difference equation from
+ * Wikipedia link
+ */
+public class IIRFilter {
+
+ private final int order;
+ private final double[] coeffsA;
+ private final double[] coeffsB;
+ private final double[] historyX;
+ private final double[] historyY;
+
+ /**
+ * Construct an IIR Filter
+ *
+ * @param order the filter's order
+ * @throws IllegalArgumentException if order is zero or less
+ */
+ public IIRFilter(int order) throws IllegalArgumentException {
+ if (order < 1) {
+ throw new IllegalArgumentException("order must be greater than zero");
+ }
+
+ this.order = order;
+ coeffsA = new double[order + 1];
+ coeffsB = new double[order + 1];
+
+ // Sane defaults
+ coeffsA[0] = 1.0;
+ coeffsB[0] = 1.0;
+
+ historyX = new double[order];
+ historyY = new double[order];
+ }
+
+ /**
+ * Set coefficients
+ *
+ * @param aCoeffs Denominator coefficients
+ * @param bCoeffs Numerator coefficients
+ * @throws IllegalArgumentException if {@code aCoeffs} or {@code bCoeffs} is
+ * not of size {@code order}, or if {@code aCoeffs[0]} is 0.0
+ */
+ public void setCoeffs(double[] aCoeffs, double[] bCoeffs) throws IllegalArgumentException {
+ if (aCoeffs.length != order) {
+ throw new IllegalArgumentException("aCoeffs must be of size " + order + ", got " + aCoeffs.length);
+ }
+
+ if (aCoeffs[0] == 0.0) {
+ throw new IllegalArgumentException("aCoeffs.get(0) must not be zero");
+ }
+
+ if (bCoeffs.length != order) {
+ throw new IllegalArgumentException("bCoeffs must be of size " + order + ", got " + bCoeffs.length);
+ }
+
+ for (int i = 0; i < order; i++) {
+ coeffsA[i] = aCoeffs[i];
+ coeffsB[i] = bCoeffs[i];
+ }
+ }
+
+ /**
+ * Process a single sample
+ *
+ * @param sample the sample to process
+ * @return the processed sample
+ */
+ public double process(double sample) {
+ double result = 0.0;
+
+ // Process
+ for (int i = 1; i <= order; i++) {
+ result += (coeffsB[i] * historyX[i - 1] - coeffsA[i] * historyY[i - 1]);
+ }
+ result = (result + coeffsB[0] * sample) / coeffsA[0];
+
+ // Feedback
+ for (int i = order - 1; i > 0; i--) {
+ historyX[i] = historyX[i - 1];
+ historyY[i] = historyY[i - 1];
+ }
+
+ historyX[0] = sample;
+ historyY[0] = result;
+
+ return result;
+ }
+}
diff --git a/src/main/java/com/thealgorithms/backtracking/AllPathsFromSourceToTarget.java b/src/main/java/com/thealgorithms/backtracking/AllPathsFromSourceToTarget.java
new file mode 100644
index 000000000000..c35a36d97a57
--- /dev/null
+++ b/src/main/java/com/thealgorithms/backtracking/AllPathsFromSourceToTarget.java
@@ -0,0 +1,101 @@
+package com.thealgorithms.backtracking;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Program description - To find all possible paths from source to destination
+ * Wikipedia
+ *
+ * @author Siddhant Swarup Mallick
+ */
+@SuppressWarnings({"rawtypes", "unchecked"})
+public class AllPathsFromSourceToTarget {
+
+ // No. of vertices in graph
+ private final int v;
+
+ // To store the paths from source to destination
+ static List> nm = new ArrayList<>();
+ // adjacency list
+ private ArrayList
> allPathsFromSourceToTarget(int vertices, int[][] a, int source, int destination) {
+ // Create a sample graph
+ AllPathsFromSourceToTarget g = new AllPathsFromSourceToTarget(vertices);
+ for (int[] i : a) {
+ g.addEdge(i[0], i[1]);
+ // edges are added
+ }
+ g.storeAllPaths(source, destination);
+ // method call to store all possible paths
+ return nm;
+ // returns all possible paths from source to destination
+ }
+}
diff --git a/src/main/java/com/thealgorithms/backtracking/ArrayCombination.java b/src/main/java/com/thealgorithms/backtracking/ArrayCombination.java
new file mode 100644
index 000000000000..f8cd0c40c20e
--- /dev/null
+++ b/src/main/java/com/thealgorithms/backtracking/ArrayCombination.java
@@ -0,0 +1,54 @@
+package com.thealgorithms.backtracking;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * This class provides methods to find all combinations of integers from 0 to n-1
+ * of a specified length k using backtracking.
+ */
+public final class ArrayCombination {
+ private ArrayCombination() {
+ }
+
+ /**
+ * Generates all possible combinations of length k from the integers 0 to n-1.
+ *
+ * @param n The total number of elements (0 to n-1).
+ * @param k The desired length of each combination.
+ * @return A list containing all combinations of length k.
+ * @throws IllegalArgumentException if n or k are negative, or if k is greater than n.
+ */
+ public static List
> combination(int n, int k) {
+ if (n < 0 || k < 0 || k > n) {
+ throw new IllegalArgumentException("Invalid input: n must be non-negative, k must be non-negative and less than or equal to n.");
+ }
+
+ List
> combinations = new ArrayList<>();
+ combine(combinations, new ArrayList<>(), 0, n, k);
+ return combinations;
+ }
+
+ /**
+ * A helper method that uses backtracking to find combinations.
+ *
+ * @param combinations The list to store all valid combinations found.
+ * @param current The current combination being built.
+ * @param start The starting index for the current recursion.
+ * @param n The total number of elements (0 to n-1).
+ * @param k The desired length of each combination.
+ */
+ private static void combine(List
> combinations, List
> combinationSum(int[] candidates, int target) {
+ List
> results = new ArrayList<>();
+ if (candidates == null || candidates.length == 0) {
+ return results;
+ }
+
+ // Sort to help with pruning duplicates and early termination
+ Arrays.sort(candidates);
+ backtrack(candidates, target, 0, new ArrayList<>(), results);
+ return results;
+ }
+
+ private static void backtrack(int[] candidates, int remaining, int start, List
> results) {
+ if (remaining == 0) {
+ // Found valid combination; add a copy
+ results.add(new ArrayList<>(combination));
+ return;
+ }
+
+ for (int i = start; i < candidates.length; i++) {
+ int candidate = candidates[i];
+
+ // If candidate is greater than remaining target, further candidates (sorted) will also be too big
+ if (candidate > remaining) {
+ break;
+ }
+
+ // include candidate
+ combination.add(candidate);
+ // Because we can reuse the same element, we pass i (not i + 1)
+ backtrack(candidates, remaining - candidate, i, combination, results);
+ // backtrack: remove last
+ combination.remove(combination.size() - 1);
+ }
+ }
+}
diff --git a/src/main/java/com/thealgorithms/backtracking/CrosswordSolver.java b/src/main/java/com/thealgorithms/backtracking/CrosswordSolver.java
new file mode 100644
index 000000000000..6bfb026c7de9
--- /dev/null
+++ b/src/main/java/com/thealgorithms/backtracking/CrosswordSolver.java
@@ -0,0 +1,125 @@
+package com.thealgorithms.backtracking;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.List;
+
+/**
+ * A class to solve a crossword puzzle using backtracking.
+ * Example:
+ * Input:
+ * puzzle = {
+ * {' ', ' ', ' '},
+ * {' ', ' ', ' '},
+ * {' ', ' ', ' '}
+ * }
+ * words = List.of("cat", "dog")
+ *
+ * Output:
+ * {
+ * {'c', 'a', 't'},
+ * {' ', ' ', ' '},
+ * {'d', 'o', 'g'}
+ * }
+ */
+public final class CrosswordSolver {
+ private CrosswordSolver() {
+ }
+
+ /**
+ * Checks if a word can be placed at the specified position in the crossword.
+ *
+ * @param puzzle The crossword puzzle represented as a 2D char array.
+ * @param word The word to be placed.
+ * @param row The row index where the word might be placed.
+ * @param col The column index where the word might be placed.
+ * @param vertical If true, the word is placed vertically; otherwise, horizontally.
+ * @return true if the word can be placed, false otherwise.
+ */
+ public static boolean isValid(char[][] puzzle, String word, int row, int col, boolean vertical) {
+ for (int i = 0; i < word.length(); i++) {
+ if (vertical) {
+ if (row + i >= puzzle.length || puzzle[row + i][col] != ' ') {
+ return false;
+ }
+ } else {
+ if (col + i >= puzzle[0].length || puzzle[row][col + i] != ' ') {
+ return false;
+ }
+ }
+ }
+ return true;
+ }
+
+ /**
+ * Places a word at the specified position in the crossword.
+ *
+ * @param puzzle The crossword puzzle represented as a 2D char array.
+ * @param word The word to be placed.
+ * @param row The row index where the word will be placed.
+ * @param col The column index where the word will be placed.
+ * @param vertical If true, the word is placed vertically; otherwise, horizontally.
+ */
+ public static void placeWord(char[][] puzzle, String word, int row, int col, boolean vertical) {
+ for (int i = 0; i < word.length(); i++) {
+ if (vertical) {
+ puzzle[row + i][col] = word.charAt(i);
+ } else {
+ puzzle[row][col + i] = word.charAt(i);
+ }
+ }
+ }
+
+ /**
+ * Removes a word from the specified position in the crossword.
+ *
+ * @param puzzle The crossword puzzle represented as a 2D char array.
+ * @param word The word to be removed.
+ * @param row The row index where the word is placed.
+ * @param col The column index where the word is placed.
+ * @param vertical If true, the word was placed vertically; otherwise, horizontally.
+ */
+ public static void removeWord(char[][] puzzle, String word, int row, int col, boolean vertical) {
+ for (int i = 0; i < word.length(); i++) {
+ if (vertical) {
+ puzzle[row + i][col] = ' ';
+ } else {
+ puzzle[row][col + i] = ' ';
+ }
+ }
+ }
+
+ /**
+ * Solves the crossword puzzle using backtracking.
+ *
+ * @param puzzle The crossword puzzle represented as a 2D char array.
+ * @param words The list of words to be placed.
+ * @return true if the crossword is solved, false otherwise.
+ */
+ public static boolean solveCrossword(char[][] puzzle, Collection