From 71c91a10caf9bb0f142b213892c537b6c6671e8e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E3=82=81=E3=81=90=E3=81=BF=E3=82=93?=
 <59683877+AbnerHung@users.noreply.github.com>
Date: Wed, 13 Oct 2021 12:48:19 +0800
Subject: [PATCH] Add BFPRT algorithm (#2590)

---
 Others/BFPRT.java | 129 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 129 insertions(+)
 create mode 100644 Others/BFPRT.java

diff --git a/Others/BFPRT.java b/Others/BFPRT.java
new file mode 100644
index 00000000..7b2adcc7
--- /dev/null
+++ b/Others/BFPRT.java
@@ -0,0 +1,129 @@
+package Others;
+
+import java.util.Arrays;
+
+/**
+ * BFPRT algorithm.
+ */
+public class BFPRT {
+
+    public static int[] getMinKNumsByBFPRT(int[] arr, int k) {
+        if (k < 1 || k > arr.length) {
+            return null;
+        }
+        int minKth = getMinKthByBFPRT(arr, k);
+        int[] res = new int[k];
+        int index = 0;
+        for (int i = 0; i < arr.length; i++) {
+            if (arr[i] < minKth) {
+                res[index++] = arr[i];
+            }
+        }
+        for (; index != res.length; index++) {
+            res[index] = minKth;
+        }
+        return res;
+    }
+
+    public static int getMinKthByBFPRT(int[] arr, int k) {
+        int[] copyArr = copyArray(arr);
+        return bfprt(copyArr, 0, copyArr.length - 1, k - 1);
+    }
+
+    public static int[] copyArray(int[]arr) {
+        int[] copyArr = new int[arr.length];
+        for(int i = 0; i < arr.length; i++) {
+            copyArr[i] = arr[i];
+        }
+        return copyArr;
+    }
+
+    public static int bfprt(int[] arr, int begin, int end, int i) {
+        if (begin == end) {
+            return arr[begin];
+        }
+        int pivot = medianOfMedians(arr, begin, end);
+        int[] pivotRange = partition(arr, begin, end, pivot);
+        if (i >= pivotRange[0] && i <= pivotRange[1]) {
+            return arr[i];
+        } else if (i < pivotRange[0]) {
+            return bfprt(arr, begin, pivotRange[0] - 1, i);
+        } else {
+            return bfprt(arr, pivotRange[1] + 1, end, i);
+        }
+    }
+
+    /**
+     * wikipedia: https://en.wikipedia.org/wiki/Median_of_medians .
+     * @param arr an array.
+     * @param begin begin num.
+     * @param end end num.
+     * @return median of medians.
+     */
+    public static int medianOfMedians(int[] arr, int begin, int end) {
+        int num = end - begin + 1;
+        int offset = num % 5 == 0 ? 0 : 1;
+        int[] mArr = new int[num / 5 + offset];
+        for (int i = 0;i < mArr.length;i++) {
+            mArr[i] = getMedian(arr, begin + i * 5, Math.min(end, begin + i * 5 + 4));
+        }
+        return bfprt(mArr, 0, mArr.length - 1, mArr.length / 2);
+    }
+
+    public static void swap(int[]arr, int i, int j) {
+        int swap = arr[i];
+        arr[i] = arr[j];
+        arr[j] = swap;
+    }
+
+    public static int[] partition(int[] arr,int begin,int end,int num)
+    {
+        int small=begin-1;
+        int cur=begin;
+        int big=end+1;
+        while(cur!=big)
+        {
+            if (arr[cur]<num)
+            {
+                swap(arr,++small,cur++);
+            }else if (arr[cur]>num)
+            {
+                swap(arr,--big,cur);
+            } else {
+                cur++;
+            }
+        }
+        int[] pivotRange=new int[2];
+        pivotRange[0]=small+1;
+        pivotRange[1]=big-1;
+        return pivotRange;
+    }
+
+    public static int getMedian(int[] arr, int begin, int end) {
+        insertionSort(arr, begin, end);
+        int sum = begin + end;
+        int mid = sum / 2 + (sum % 2);
+        return arr[mid];
+    }
+
+    public static void insertionSort(int[] arr, int begin, int end) {
+        if (arr == null || arr.length < 2) {
+            return;
+        }
+        for (int i = begin + 1;i != end + 1;i++) {
+            for (int j = i;j != begin;j--) {
+                if (arr[j - 1] > arr[j]) {
+                    swap(arr, j - 1, j);
+                } else {
+                    break;
+                }
+            }
+        }
+    }
+
+    public static void main(String[] args) {
+        int[] arr = { 11, 9, 1, 3, 9, 2, 2, 5, 6, 5, 3, 5, 9, 7, 2, 5, 5, 1, 9 };
+        int[] minK = getMinKNumsByBFPRT(arr,5);
+        System.out.println(Arrays.toString(minK));
+    }
+}