From 3b2274e290244500323ae53aab6d8178cb1c89de Mon Sep 17 00:00:00 2001
From: Albert Hu <alberthu@berkeley.edu>
Date: Sun, 28 May 2017 19:49:47 -0700
Subject: [PATCH 1/2] Day 47: start

---
 day47/README.md               | 13 +++++++++++++
 day47/findKSmallestInArray.py |  5 +++++
 2 files changed, 18 insertions(+)
 create mode 100644 day47/README.md
 create mode 100644 day47/findKSmallestInArray.py

diff --git a/day47/README.md b/day47/README.md
new file mode 100644
index 0000000..e6ae8d2
--- /dev/null
+++ b/day47/README.md
@@ -0,0 +1,13 @@
+Question of the day: http://www.techiedelight.com/find-kth-smallest-element-array/
+
+Given an array and positive integer `k`, find kth smallest element
+in the array.
+
+Example:
+
+arr = [7, 4, 6, 3, 9, 1]
+k = 3
+
+Output:
+
+4
diff --git a/day47/findKSmallestInArray.py b/day47/findKSmallestInArray.py
new file mode 100644
index 0000000..40d4394
--- /dev/null
+++ b/day47/findKSmallestInArray.py
@@ -0,0 +1,5 @@
+def tests():
+    assert True
+
+if __name__ == "__main__":
+    tests()

From 5d581455b406415134926c8451aaaae2dcd3139d Mon Sep 17 00:00:00 2001
From: Albert Hu <alberthu@berkeley.edu>
Date: Mon, 29 May 2017 00:38:48 -0700
Subject: [PATCH 2/2] Day 47: solve findKSmallest in Array with three different
 methods -- sort, min heap, and max heap

---
 day47/README.md               | 22 +++++++++++++++
 day47/findKSmallestInArray.py | 50 ++++++++++++++++++++++++++++++++++-
 2 files changed, 71 insertions(+), 1 deletion(-)

diff --git a/day47/README.md b/day47/README.md
index e6ae8d2..837943e 100644
--- a/day47/README.md
+++ b/day47/README.md
@@ -11,3 +11,25 @@ k = 3
 Output:
 
 4
+
+## Ideas
+
+1) Sort the array in `O(nlogn)` time and then access the kth index of the
+   array to get the answer.
+
+2) Min-heapify the array in `O(n)` time and then pop from the min heap `k`
+   times in `O(klogn)` time. Overall runtime `O(n + klogn)`.
+
+3) Max-heapify the first `k` elements of the array in `O(k)` time and then
+   repeatedly remove the max element, replacing it with a new element from
+   the input array, until there are no more unused elements from the input
+   array in `O(nlogk)` time. Once there are no more elements, the root in
+   the max heap will be the kth smallest element of the input array.
+
+Let's implement all three.
+
+## Code
+
+[Python](./day47.py)
+
+## Follow up
diff --git a/day47/findKSmallestInArray.py b/day47/findKSmallestInArray.py
index 40d4394..f35dbc4 100644
--- a/day47/findKSmallestInArray.py
+++ b/day47/findKSmallestInArray.py
@@ -1,5 +1,53 @@
+import heapq
+
+def efficientSortIdea(arr, k):
+    return sorted(arr)[k-1]
+
+def minHeapIdea(arr, k):
+    heapq.heapify(arr)
+    last = arr[0]
+    while k > 0:
+        last = heapq.heappop(arr)
+        k -= 1
+    return last
+
+def maxHeapIdea(arr, k):
+    # negate values when adding into python's min-heap implementation
+    arr = map(lambda x: -x, arr)
+    h = arr[:k]
+    heapq.heapify(h)
+    for num in arr[k:]:
+        heapq.heappushpop(h, num)
+    return -heapq.heappop(h)
+
+def testEfficientSortIdea():
+    assert efficientSortIdea([1, 2, 3, 4, 5], 3) == 3
+    assert efficientSortIdea([3, 1, 4, 2, 5], 3) == 3
+    assert efficientSortIdea([5, 4, 3, 2, 1], 3) == 3
+    assert efficientSortIdea([4, 2], 1) == 2
+    assert efficientSortIdea([1, 9, 2, 7, 4, 6, 4, 2, 1, -1, -5, -9], 5) == 1
+    assert efficientSortIdea([-3, -6, 1, 0, 1], 4) == 1
+
+def testMinHeapIdea():
+    assert minHeapIdea([1, 2, 3, 4, 5], 3) == 3
+    assert minHeapIdea([3, 1, 4, 2, 5], 3) == 3
+    assert minHeapIdea([5, 4, 3, 2, 1], 3) == 3
+    assert minHeapIdea([4, 2], 1) == 2
+    assert minHeapIdea([1, 9, 2, 7, 4, 6, 4, 2, 1, -1, -5, -9], 5) == 1
+    assert minHeapIdea([-3, -6, 1, 0, 1], 4) == 1
+
+def testMaxHeapIdea():
+    assert maxHeapIdea([1, 2, 3, 4, 5], 3) == 3
+    assert maxHeapIdea([3, 1, 4, 2, 5], 3) == 3
+    assert maxHeapIdea([5, 4, 3, 2, 1], 3) == 3
+    assert maxHeapIdea([4, 2], 1) == 2
+    assert maxHeapIdea([1, 9, 2, 7, 4, 6, 4, 2, 1, -1, -5, -9], 5) == 1
+    assert maxHeapIdea([-3, -6, 1, 0, 1], 4) == 1
+
 def tests():
-    assert True
+    testEfficientSortIdea()
+    testMinHeapIdea()
+    testMaxHeapIdea()
 
 if __name__ == "__main__":
     tests()