From f4af3e14e071da2c22d50fe364c3fe460e8edc39 Mon Sep 17 00:00:00 2001
From: fengzw <zhiwei.feng1995@gmail.com>
Date: Fri, 25 Jun 2021 00:02:44 +0800
Subject: [PATCH] add: median of medians algorithm solution for Miscellaneous

---
 Miscellaneous/median-of-medians.go      | 71 +++++++++++++++++++++++++
 Miscellaneous/median-of-medians_test.go | 27 ++++++++++
 2 files changed, 98 insertions(+)
 create mode 100644 Miscellaneous/median-of-medians.go
 create mode 100644 Miscellaneous/median-of-medians_test.go

diff --git a/Miscellaneous/median-of-medians.go b/Miscellaneous/median-of-medians.go
new file mode 100644
index 0000000..a87e2b8
--- /dev/null
+++ b/Miscellaneous/median-of-medians.go
@@ -0,0 +1,71 @@
+package Miscellaneous
+
+import (
+	"sort"
+)
+
+//
+// coverage time complexity: O(n), worst O(n)
+// space complexity: O(n)
+//
+func findKthSmallestNumberUsingMedianOfMedians(nums []int, k int) int {
+	if k > len(nums) {
+		return -1
+	}
+	return findPivotRecursive(nums, k, 0, len(nums)-1)
+}
+
+func findPivotRecursive(nums []int, k, start, end int) int {
+	p := partitionMom(nums, start, end)
+	if p == k-1 {
+		return nums[p]
+	}
+	if p > k-1 {
+		return findPivotRecursive(nums, k, start, p-1)
+	}
+	return findPivotRecursive(nums, k, p+1, end)
+}
+
+func partitionMom(nums []int, low, high int) int {
+	if low == high {
+		return low
+	}
+
+	median := medianOfMedians(nums, low, high)
+	// median as pivot
+	// swap high and median
+	for i := low; i < high; i++ {
+		if nums[i] == median {
+			nums[i], nums[high] = nums[high], nums[i]
+			break
+		}
+	}
+
+	pivot := nums[high]
+	i := low - 1
+	for j := low; j < high; j++ {
+		if nums[j] < pivot {
+			i++
+			nums[i], nums[j] = nums[j], nums[i]
+		}
+	}
+	nums[i+1], nums[high] = nums[high], nums[i+1]
+	return i + 1
+}
+
+func medianOfMedians(nums []int, low, high int) int {
+	n := high - low + 1
+	if n < 5 {
+		return nums[low]
+	}
+
+	numOfPartitions := n / 5
+	medians := make([]int, numOfPartitions)
+	for i := 0; i < numOfPartitions; i++ {
+		partStart := low + i*5
+		sort.Ints(nums[partStart : partStart+5])
+		medians[i] = nums[partStart+2]
+	}
+
+	return partitionMom(medians, 0, numOfPartitions-1)
+}
diff --git a/Miscellaneous/median-of-medians_test.go b/Miscellaneous/median-of-medians_test.go
new file mode 100644
index 0000000..e589f92
--- /dev/null
+++ b/Miscellaneous/median-of-medians_test.go
@@ -0,0 +1,27 @@
+package Miscellaneous
+
+import "testing"
+
+func Test_findKthSmallestNumberUsingMedianOfMedians(t *testing.T) {
+	type args struct {
+		nums []int
+		k    int
+	}
+	tests := []struct {
+		name string
+		args args
+		want int
+	}{
+		{"case1", args{[]int{1, 5, 12, 2, 11, 5}, 3}, 5},
+		{"case2", args{[]int{1, 5, 12, 2, 11, 5}, 4}, 5},
+		{"case3", args{[]int{5, 12, 11, -1, 12}, 3}, 11},
+		{"case4", args{[]int{5, 12, 11, -1, 12}, 6}, -1},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := findKthSmallestNumberUsingMedianOfMedians(tt.args.nums, tt.args.k); got != tt.want {
+				t.Errorf("findKthSmallestNumberUsingMedianOfMedians() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}