diff --git a/src/main/java/com/thealgorithms/datastructures/heaps/LeonardoHeap.java b/src/main/java/com/thealgorithms/datastructures/heaps/LeonardoHeap.java
new file mode 100644
index 000000000000..7d43c2db209a
--- /dev/null
+++ b/src/main/java/com/thealgorithms/datastructures/heaps/LeonardoHeap.java
@@ -0,0 +1,203 @@
+package com.thealgorithms.datastructures.heaps;
+
+import com.thealgorithms.bitmanipulation.SingleBitOperations;
+import com.thealgorithms.maths.LeonardoNumber;
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.List;
+
+/**
+ * Wikipedia: https://en.wikipedia.org/wiki/Smoothsort
+ */
+public class LeonardoHeap<T extends Comparable<T>> {
+
+    private int levelTracker = 0;
+    private final List<T> heap = new ArrayList<>();
+
+    public LeonardoHeap() {
+    }
+
+    private void decreaseLevelTracker() {
+        final int lastTreeLevel = getRightMostTree();
+        levelTracker = SingleBitOperations.clearBit(levelTracker, lastTreeLevel);
+        if (lastTreeLevel != 0 && lastTreeLevel != 1) {
+            levelTracker = SingleBitOperations.setBit(levelTracker, lastTreeLevel - 1);
+            levelTracker = SingleBitOperations.setBit(levelTracker, lastTreeLevel - 2);
+        }
+    }
+
+    private void increaseLevelTracker() {
+        final List<Integer> consecutiveTreeIndices = findConsecutiveTreeIndices(levelTracker);
+        if (consecutiveTreeIndices.get(0) != -1) {
+            // if 0th or 1st index is -1 that implies there are no concequtive trees
+            levelTracker = SingleBitOperations.clearBit(levelTracker, consecutiveTreeIndices.get(0));
+            levelTracker = SingleBitOperations.clearBit(levelTracker, consecutiveTreeIndices.get(1));
+            levelTracker = SingleBitOperations.setBit(levelTracker, consecutiveTreeIndices.get(1) + 1);
+        } else if ((levelTracker & 2) == 0) {
+            levelTracker = SingleBitOperations.setBit(levelTracker, 1);
+        } else {
+            levelTracker = SingleBitOperations.setBit(levelTracker, 0);
+        }
+    }
+
+    private void maxHeapifyTree(int rootNodeIndex, int currentLevel) {
+        // A leonardo tree of level n is just 1 node(the root) plus the leonardo tree of n-1 level(left child) plus leonardo tree of n-2 level(right child)
+        // To maxheapify a leonardo tree we need to compare the current root and roots of it's left and right subtree
+        // We recursively hepify the left and right subtrees using the currentLevel
+
+        // BASE CASE
+        if (currentLevel == 0 || currentLevel == 1) {
+            return; // Trees with one node are in already max-heapified.
+        }
+
+        final int currentRootNodeIndex = rootNodeIndex;
+        final int rightChildIndex = rootNodeIndex - 1;
+        final int leftChildIndex = rootNodeIndex - LeonardoNumber.leonardoNumber(currentLevel - 2) - 1;
+        final int childIndexForSwap = (heap.get(rightChildIndex).compareTo(heap.get(leftChildIndex)) >= 0) ? rightChildIndex : leftChildIndex;
+
+        if (heap.get(childIndexForSwap).compareTo(heap.get(currentRootNodeIndex)) > 0) {
+            swap(currentRootNodeIndex, childIndexForSwap);
+            if (childIndexForSwap == rightChildIndex) {
+                maxHeapifyTree(rightChildIndex, currentLevel - 2);
+            } else { // swap happened with the left child
+                maxHeapifyTree(leftChildIndex, currentLevel - 1);
+            }
+        }
+    }
+
+    private void shiftRootAndRestoreHeap() {
+
+        if (heap.isEmpty()) {
+            return;
+        }
+
+        final Integer[] currentTreeLevels = findAllTreeIndices(levelTracker);
+        ArrayList<Integer> rootNodeIndices = getRootNodeIndices(currentTreeLevels);
+
+        int rootNodeIndexForHeapify = rootNodeIndices.getLast();
+        int treeLevelforHeapify = currentTreeLevels[currentTreeLevels.length - 1];
+
+        for (int i = 1; i < rootNodeIndices.size(); i++) {
+
+            int currentRootNodeIndex = rootNodeIndices.get(i);
+            int prevRootNodeIndex = rootNodeIndices.get(i - 1);
+            int j = i;
+            while (compareRoots(currentRootNodeIndex, prevRootNodeIndex)) {
+                final int currentLevel = currentTreeLevels[j];
+                boolean swapRequired = compareChildren(currentRootNodeIndex, prevRootNodeIndex, currentLevel);
+                if (swapRequired) {
+                    // compare child and swap
+                    swap(prevRootNodeIndex, currentRootNodeIndex);
+                    rootNodeIndexForHeapify = prevRootNodeIndex;
+                    treeLevelforHeapify = currentTreeLevels[j - 1];
+                } else {
+                    maxHeapifyTree(currentRootNodeIndex, currentLevel);
+                }
+                --j;
+
+                if (j == 0) {
+                    // We arrived at the left most tree. Do a maxheapifyTree if a swap had occurred
+                    if (swapRequired) {
+                        maxHeapifyTree(rootNodeIndexForHeapify, treeLevelforHeapify);
+                    }
+                    break;
+                }
+                currentRootNodeIndex = rootNodeIndices.get(j);
+                prevRootNodeIndex = rootNodeIndices.get(j - 1);
+            }
+        }
+
+        maxHeapifyTree(rootNodeIndexForHeapify, treeLevelforHeapify); // In case of insert and no swap.
+    }
+
+    private int getRightMostTree() {
+        // Isolate the rightmost set bit
+        int isolatedBit = levelTracker & -levelTracker;
+        int position = 0;
+
+        while (isolatedBit > 1) {
+            isolatedBit >>= 1;
+            position++;
+        }
+
+        return position;
+    }
+
+    private void swap(int i, int j) {
+        Collections.swap(heap, i, j);
+    }
+
+    public void addElement(T element) {
+        increaseLevelTracker();
+        heap.add(element);
+        shiftRootAndRestoreHeap();
+    }
+
+    public T removeElement() {
+        decreaseLevelTracker();
+        final T element = heap.removeLast();
+        shiftRootAndRestoreHeap();
+
+        return element;
+    }
+
+    private static List<Integer> findConsecutiveTreeIndices(int num) {
+        int prevOneIndex = -1;
+        int currentLevel = 0;
+
+        List<Integer> answer = new ArrayList<>();
+        answer.add(-1);
+        answer.add(-1);
+
+        for (int i = 0; num > 0; i++) {
+            currentLevel = num & 1;
+            if (currentLevel == 1) {
+                if (prevOneIndex != -1) {
+                    answer.set(0, prevOneIndex);
+                    answer.set(1, i);
+                }
+                prevOneIndex = i;
+            } else {
+                prevOneIndex = -1;
+            }
+            num >>>= 1;
+        }
+        return answer;
+    }
+
+    private static Integer[] findAllTreeIndices(int num) {
+        List<Integer> setBitIndexes = new ArrayList<>();
+        for (int i = Integer.SIZE - 1; i >= 0; i--) {
+            if ((num & (1 << i)) != 0) {
+                setBitIndexes.add(i);
+            }
+        }
+        return setBitIndexes.toArray(new Integer[0]);
+    }
+
+    private boolean compareChildren(int currentRootNodeIndex, int prevRootNodeIndex, int currentLevel) {
+        if (currentLevel <= 1) {
+            // if there are no children to compare (L1 or L0 tree) return true
+            // because we already know that element at prevRootNodeIndex is greater than element at currentRootNodeIndex
+            // so a swap will be needed
+            return true;
+        }
+        final int rightChildIndex = currentRootNodeIndex - 1;
+        final int leftChildIndex = currentRootNodeIndex - 1 - LeonardoNumber.leonardoNumber(currentLevel - 2);
+        return heap.get(prevRootNodeIndex).compareTo(heap.get(rightChildIndex)) > 0 && heap.get(prevRootNodeIndex).compareTo(heap.get(leftChildIndex)) > 0;
+    }
+
+    private boolean compareRoots(int currentRootNodeIndex, int prevRootNodeIndex) {
+        return heap.get(prevRootNodeIndex).compareTo(heap.get(currentRootNodeIndex)) > 0;
+    }
+
+    private ArrayList<Integer> getRootNodeIndices(Integer[] currentTreeLevels) {
+        int previousTreeSizeCumulative = 0;
+        ArrayList<Integer> rootNodeIndices = new ArrayList<>();
+        for (int i = 0; i < currentTreeLevels.length; i++) {
+            rootNodeIndices.add(previousTreeSizeCumulative + LeonardoNumber.leonardoNumber(currentTreeLevels[i]) - 1);
+            previousTreeSizeCumulative = previousTreeSizeCumulative + LeonardoNumber.leonardoNumber(currentTreeLevels[i]);
+        }
+        return rootNodeIndices;
+    }
+}
diff --git a/src/main/java/com/thealgorithms/sorts/SmoothSort.java b/src/main/java/com/thealgorithms/sorts/SmoothSort.java
new file mode 100644
index 000000000000..244eb11ce23c
--- /dev/null
+++ b/src/main/java/com/thealgorithms/sorts/SmoothSort.java
@@ -0,0 +1,30 @@
+package com.thealgorithms.sorts;
+
+import com.thealgorithms.datastructures.heaps.LeonardoHeap;
+
+/**
+ * Wikipedia: https://en.wikipedia.org/wiki/Smoothsort
+ */
+public final class SmoothSort implements SortAlgorithm {
+
+    public SmoothSort() {
+    }
+
+    private static <T extends Comparable<T>> void smoothSort(T[] array) {
+        LeonardoHeap<T> leonardoHeap = new LeonardoHeap<T>();
+
+        for (final var element : array) {
+            leonardoHeap.addElement(element);
+        }
+
+        for (int i = 0; i < array.length; i++) {
+            array[array.length - i - 1] = leonardoHeap.removeElement();
+        }
+    }
+
+    @Override
+    public <T extends Comparable<T>> T[] sort(T[] array) {
+        smoothSort(array);
+        return array;
+    }
+}
diff --git a/src/test/java/com/thealgorithms/datastructures/heaps/LeonardoHeapTest.java b/src/test/java/com/thealgorithms/datastructures/heaps/LeonardoHeapTest.java
new file mode 100644
index 000000000000..922adfbfcb0a
--- /dev/null
+++ b/src/test/java/com/thealgorithms/datastructures/heaps/LeonardoHeapTest.java
@@ -0,0 +1,121 @@
+package com.thealgorithms.datastructures.heaps;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class LeonardoHeapTest {
+
+    @Test
+    public void testAddElement() {
+        LeonardoHeap<Integer> heap = new LeonardoHeap<>();
+        heap.addElement(5);
+        heap.addElement(3);
+        heap.addElement(8);
+
+        assertEquals(8, heap.removeElement()); // Max element should be 8
+        assertEquals(5, heap.removeElement());
+        assertEquals(3, heap.removeElement());
+    }
+
+    @Test
+    public void testRemoveElement() {
+        LeonardoHeap<Integer> heap = new LeonardoHeap<>();
+        heap.addElement(10);
+        heap.addElement(20);
+        heap.addElement(5);
+
+        assertEquals(20, heap.removeElement());
+        assertEquals(10, heap.removeElement());
+        assertEquals(5, heap.removeElement());
+    }
+
+    @Test
+    public void testAddElementStrings() {
+        LeonardoHeap<String> heap = new LeonardoHeap<>();
+        heap.addElement("z");
+        heap.addElement("a");
+        heap.addElement("x");
+        heap.addElement("b");
+        heap.addElement("y");
+
+        assertEquals("z", heap.removeElement()); // Max element should be z
+        assertEquals("y", heap.removeElement());
+        assertEquals("x", heap.removeElement());
+        assertEquals("b", heap.removeElement());
+        assertEquals("a", heap.removeElement());
+    }
+
+    @Test
+    public void testRemoveElementString() {
+        LeonardoHeap<String> heap = new LeonardoHeap<>();
+        heap.addElement("z");
+        heap.addElement("a");
+        heap.addElement("x");
+
+        assertEquals("z", heap.removeElement());
+        assertEquals("x", heap.removeElement());
+        assertEquals("a", heap.removeElement());
+    }
+
+    @Test
+    public void testAlwaysCurrentMaxElementIsRemoved() {
+        LeonardoHeap<Integer> heap = new LeonardoHeap<>();
+        heap.addElement(5);
+        heap.addElement(8);
+        heap.addElement(7);
+        heap.addElement(3);
+
+        heap.addElement(4);
+        heap.addElement(4);
+        heap.addElement(4);
+        heap.addElement(6);
+
+        heap.addElement(8);
+        heap.addElement(8);
+
+        assertEquals(8, heap.removeElement());
+        assertEquals(8, heap.removeElement());
+        assertEquals(8, heap.removeElement());
+        assertEquals(7, heap.removeElement());
+
+        assertEquals(6, heap.removeElement());
+        assertEquals(5, heap.removeElement());
+        assertEquals(4, heap.removeElement());
+        assertEquals(4, heap.removeElement());
+
+        assertEquals(4, heap.removeElement());
+        assertEquals(3, heap.removeElement());
+    }
+
+    @Test
+    public void testForCompareChildAndSwap() {
+        LeonardoHeap<Integer> heap = new LeonardoHeap<>();
+        Integer[] elements = {5, 33, 40, 28, 95, 29, 88, 94, 12, 84, 15, 33, 2, 52, 37, 62, 48, 13, 61, 59};
+
+        for (Integer element : elements) {
+            heap.addElement(element);
+        }
+
+        assertEquals(95, heap.removeElement());
+        assertEquals(94, heap.removeElement());
+        assertEquals(88, heap.removeElement());
+        assertEquals(84, heap.removeElement());
+        assertEquals(62, heap.removeElement());
+        assertEquals(61, heap.removeElement());
+        assertEquals(59, heap.removeElement());
+        assertEquals(52, heap.removeElement());
+        assertEquals(48, heap.removeElement());
+        assertEquals(40, heap.removeElement());
+        assertEquals(37, heap.removeElement());
+        assertEquals(33, heap.removeElement());
+        assertEquals(33, heap.removeElement());
+        assertEquals(29, heap.removeElement());
+        assertEquals(28, heap.removeElement());
+        assertEquals(15, heap.removeElement());
+        assertEquals(13, heap.removeElement());
+        assertEquals(12, heap.removeElement());
+        assertEquals(5, heap.removeElement());
+        assertEquals(2, heap.removeElement());
+    }
+}
diff --git a/src/test/java/com/thealgorithms/sorts/SmoothSortTest.java b/src/test/java/com/thealgorithms/sorts/SmoothSortTest.java
new file mode 100644
index 000000000000..8df0502e80e7
--- /dev/null
+++ b/src/test/java/com/thealgorithms/sorts/SmoothSortTest.java
@@ -0,0 +1,8 @@
+package com.thealgorithms.sorts;
+
+public class SmoothSortTest extends SortingAlgorithmTest {
+    @Override
+    SortAlgorithm getSortAlgorithm() {
+        return new SmoothSort();
+    }
+}