From 2e6a8fca134bd5840756bb0f64b6e467ffbfe3c4 Mon Sep 17 00:00:00 2001
From: AnubhavSingh777 <vaishnavko273@gmail.com>
Date: Mon, 25 Sep 2023 00:33:33 +0530
Subject: [PATCH 1/2] added quickselect to select kth smallest element

---
 .../com/williamfiset/algorithms/sorting/QuickSelect.java | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/main/java/com/williamfiset/algorithms/sorting/QuickSelect.java b/src/main/java/com/williamfiset/algorithms/sorting/QuickSelect.java
index e66660e27..dd61dd578 100644
--- a/src/main/java/com/williamfiset/algorithms/sorting/QuickSelect.java
+++ b/src/main/java/com/williamfiset/algorithms/sorting/QuickSelect.java
@@ -17,7 +17,7 @@ private static Integer quickSelect(int[] ar, int k, int lo, int hi) {
       if (splitPoint == index) {
         return ar[splitPoint];
       } else if (splitPoint > index) {
-        return quickSelect(ar, k, lo, splitPoint);
+        return quickSelect(ar, k, lo, splitPoint - 1);
       }
       return quickSelect(ar, k, splitPoint + 1, hi);
     }
@@ -50,8 +50,9 @@ private static void swap(int[] ar, int i, int j) {
   public static void main(String[] args) {
     QuickSelect quickSelect = new QuickSelect();
     int[] array = {-10, 4, 6, 4, 8, -13, 1, 3};
-    int kthLargestElement = quickSelect.quickSelect(array, 3);
-    // Prints: 1
-    System.out.println(kthLargestElement);
+    int kthSmallestElement = quickSelect.quickSelect(array, 3);
+    // Prints: 3 (3rd smallest element)
+    System.out.println(kthSmallestElement);
   }
 }
+

From a67809f1515c795a011c56572c5de6f69debbc21 Mon Sep 17 00:00:00 2001
From: AnubhavSingh777 <vaishnavko273@gmail.com>
Date: Mon, 25 Sep 2023 00:54:13 +0530
Subject: [PATCH 2/2] added Btree implementation

---
 .../datastructures/balancedtree/Btree.java    | 138 ++++++++++++++++++
 1 file changed, 138 insertions(+)
 create mode 100644 src/main/java/com/williamfiset/algorithms/datastructures/balancedtree/Btree.java

diff --git a/src/main/java/com/williamfiset/algorithms/datastructures/balancedtree/Btree.java b/src/main/java/com/williamfiset/algorithms/datastructures/balancedtree/Btree.java
new file mode 100644
index 000000000..4b85a472f
--- /dev/null
+++ b/src/main/java/com/williamfiset/algorithms/datastructures/balancedtree/Btree.java
@@ -0,0 +1,138 @@
+package com.williamfiset.algorithms.datastructures.balancedtree;
+
+import java.util.LinkedList;
+import java.util.Queue;
+
+class BTreeNode {
+    int[] keys;
+    BTreeNode[] children;
+    int numKeys;
+    boolean isLeaf;
+
+    public BTreeNode(int t, boolean isLeaf) {
+        this.keys = new int[2 * t - 1];
+        this.children = new BTreeNode[2 * t];
+        this.isLeaf = isLeaf;
+        this.numKeys = 0;
+    }
+
+    public void traverse() {
+        int i;
+        for (i = 0; i < numKeys; i++) {
+            if (!isLeaf) {
+                children[i].traverse();
+            }
+            System.out.print(keys[i] + " ");
+        }
+
+        if (!isLeaf) {
+            children[i].traverse();
+        }
+    }
+}
+
+public class Btree {
+    private BTreeNode root;
+    private int t;
+
+    public Btree(int t) {
+        this.root = null;
+        this.t = t;
+    }
+
+    public void insert(int key) {
+        if (root == null) {
+            root = new BTreeNode(t, true);
+            root.keys[0] = key;
+            root.numKeys = 1;
+        } else {
+            if (root.numKeys == 2 * t - 1) {
+                BTreeNode newRoot = new BTreeNode(t, false);
+                newRoot.children[0] = root;
+                splitChild(newRoot, 0);
+                insertNonFull(newRoot, key);
+                root = newRoot;
+            } else {
+                insertNonFull(root, key);
+            }
+        }
+    }
+
+    private void insertNonFull(BTreeNode node, int key) {
+        int i = node.numKeys - 1;
+
+        if (node.isLeaf) {
+            while (i >= 0 && key < node.keys[i]) {
+                node.keys[i + 1] = node.keys[i];
+                i--;
+            }
+            node.keys[i + 1] = key;
+            node.numKeys++;
+        } else {
+            while (i >= 0 && key < node.keys[i]) {
+                i--;
+            }
+
+            i++;
+
+            if (node.children[i].numKeys == 2 * t - 1) {
+                splitChild(node, i);
+
+                if (key > node.keys[i]) {
+                    i++;
+                }
+            }
+
+            insertNonFull(node.children[i], key);
+        }
+    }
+
+    private void splitChild(BTreeNode parentNode, int childIndex) {
+        BTreeNode childNode = parentNode.children[childIndex];
+        BTreeNode newNode = new BTreeNode(t, childNode.isLeaf);
+        parentNode.numKeys++;
+
+        for (int j = parentNode.numKeys - 1; j > childIndex; j--) {
+            parentNode.keys[j] = parentNode.keys[j - 1];
+        }
+
+        parentNode.keys[childIndex] = childNode.keys[t - 1];
+
+        for (int j = parentNode.numKeys; j > childIndex + 1; j--) {
+            parentNode.children[j] = parentNode.children[j - 1];
+        }
+
+        parentNode.children[childIndex + 1] = newNode;
+
+        for (int j = 0; j < t - 1; j++) {
+            newNode.keys[j] = childNode.keys[j + t];
+        }
+
+        if (!childNode.isLeaf) {
+            for (int j = 0; j < t; j++) {
+                newNode.children[j] = childNode.children[j + t];
+            }
+        }
+
+        childNode.numKeys = t - 1;
+    }
+
+    public void traverse() {
+        if (root != null) {
+            root.traverse();
+        }
+    }
+
+    public static void main(String[] args) {
+        Btree bTree = new Btree(3);
+
+        int[] keys = {3, 7, 1, 5, 9, 2, 8, 4, 6};
+
+        for (int key : keys) {
+            bTree.insert(key);
+        }
+
+        System.out.println("B-Tree traversal:");
+        bTree.traverse();
+    }
+}