Day 47: Find the kth smallest element in an input array

day47/README.md

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+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
+
+## 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

day47/findKSmallestInArray.py

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+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():
+    testEfficientSortIdea()
+    testMinHeapIdea()
+    testMaxHeapIdea()
+
+if __name__ == "__main__":
+    tests()