From a759f8418d84616d15583d869e6ef2ce2d4fbf3c Mon Sep 17 00:00:00 2001
From: xuzhiwei <jsrdxzw@163.com>
Date: Fri, 4 Mar 2022 14:45:19 +0800
Subject: [PATCH] find kth Element in an Array

---
 .../thealgorithms/maths/FindKthNumber.java    | 73 +++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/maths/FindKthNumber.java

diff --git a/src/main/java/com/thealgorithms/maths/FindKthNumber.java b/src/main/java/com/thealgorithms/maths/FindKthNumber.java
new file mode 100644
index 000000000000..0d7f05fe571a
--- /dev/null
+++ b/src/main/java/com/thealgorithms/maths/FindKthNumber.java
@@ -0,0 +1,73 @@
+package com.thealgorithms.maths;
+
+import java.util.Arrays;
+import java.util.Random;
+
+/**
+ * use quick sort algorithm to get kth largest or kth smallest element in given array
+ */
+public class FindKthNumber {
+    private static final Random random = new Random();
+
+    public static void main(String[] args) {
+        /* generate array with random size and random elements */
+        int[] nums = generateArray(100);
+
+        /* get 3th largest element */
+        int kth = 3;
+        int kthMaxIndex = nums.length - kth;
+        int targetMax = findKthMax(nums, kthMaxIndex);
+
+        /* get 3th smallest element */
+        int kthMinIndex = kth - 1;
+        int targetMin = findKthMax(nums, kthMinIndex);
+
+        Arrays.sort(nums);
+        assert nums[kthMaxIndex] == targetMax;
+        assert nums[kthMinIndex] == targetMin;
+    }
+
+    private static int[] generateArray(int capacity) {
+        int size = random.nextInt(capacity) + 1;
+        int[] array = new int[size];
+
+        for (int i = 0; i < size; i++) {
+            array[i] = random.nextInt() % 100;
+        }
+        return array;
+    }
+
+    private static int findKthMax(int[] nums, int k) {
+        int start = 0, end = nums.length;
+        while (start < end) {
+            int pivot = partition(nums, start, end);
+            if (k == pivot) {
+                return nums[pivot];
+            } else if (k > pivot) {
+                start = pivot + 1;
+            } else {
+                end = pivot;
+            }
+        }
+        return -1;
+    }
+
+    private static int partition(int[] nums, int start, int end) {
+        int pivot = nums[start];
+        int j = start;
+        for (int i = start + 1; i < end; i++) {
+            if (nums[i] < pivot) {
+                j++;
+                swap(nums, i, j);
+            }
+        }
+        swap(nums, start, j);
+        return j;
+    }
+
+    private static void swap(int[] nums, int a, int b) {
+        int tmp = nums[a];
+        nums[a] = nums[b];
+        nums[b] = tmp;
+    }
+}