2019-03-21 in class

heapsort.py

@@ -0,0 +1,72 @@
+#!/usr/bin/env python3
+
+import sys
+
+def heap_extract_max(A):
+    m = A[0]
+    A[0] = A.pop()
+
+    size = len(A)
+    i = 0
+    exit = size == 0
+    while exit:
+        left = heap_left(i)
+        if left == None:
+            break
+
+        right = heap_right(i)
+        if right == None:
+            if A[i] < A[left]:
+                A[i], A[left] = A[left], A[i]
+                break
+
+        ma = max_3(A[i], A[left], A[right])
+        if ma == A[i]:
+            break
+        elif ma == A[left]:
+            A[i], A[left] = A[left], A[i]
+            i = left
+        else:
+            A[i], A[right] = A[right], A[i]
+            i = right
+
+    return m
+
+def max_3(a, b, c):
+    if a > b:
+        if a > c:
+            return a
+        else:
+            return c
+    else:
+        if b > c:
+            return b
+        else:
+            return c
+
+def heap_parent(n):
+    n = n + 1
+    if n == 1:
+        return None
+    else
+        return (n // 2) - 1
+
+def heap_left(size, n):
+    n = n + 1
+    l = n * 2
+    if l > size
+        return None
+    else
+        return l - 1
+
+def heap_right(size, n):
+    n = n + 1
+    l = n * 2 + 1
+    if l > size
+        return None
+    else
+        return l - 1
+
+if __name__ == "__main__":
+    args = [int(x) for x in sys.argv[1:]]
+

notes.md

@@ -99,3 +99,47 @@ stated. The algorithm must terminate.
 
 Invariant condition able to make a loop equivalent to a straight path in an
 execution graph.
+
+# Heaps and Heapsort
+
+A data structure is a way to structure data.
+A binary heap is like an array and can be of two types: max heap and min heap.
+
+## Interface of an heap
+- `Build_max_heap(A)` and rearranges a into a max-heap;
+- `Heap_insert(H, key)` inserts `key` in the heap;
+- `Heap_extract_max(H)` extracts the maximum `key`;
+- `H.heap_size` returns the size of the heap.
+
+A binary heap is like a binary tree mapped on an array:
+
+```
+    1
+   / \
+  /   \
+ 2     3
+/ \   / \
+4 5   6 7
+
+=> [1234567]
+```
+
+The parent position of `n` is the integer division of n by 2:
+
+```python
+def parent(x):
+  return x // 2
+```
+
+The left of `n` is `n` times 2, and the right is `n` times 2 plus 1:
+
+```python
+def left(x):
+  return x * 2
+
+def right(x):
+  return x * 2 + 1
+```
+
+**Max heap property**: for all i > 1 A[parent(i)] >= A[i]
+

partition.py

@@ -0,0 +1,37 @@
+#!/usr/bin/env python3
+
+import sys
+import random
+
+def partition(A, begin, end):
+    v_i = random.randrange(begin, end)
+    v = A[v_i]
+    A[v_i], A[end-1] = A[end-1], A[v_i]
+    i = begin
+    j = end - 2
+    while j >= i:
+        if A[j] > v:
+            j = j - 1
+        elif A[i] <= v:
+            i = i + 1
+        else:
+            A[i], A[j] = A[j], A[i]
+            j = j - 1
+            i = i + 1
+    A[i], A[end-1] = A[end-1], A[i]
+    return i
+
+def quicksort(A, begin, end):
+    if begin < end - 1:
+        i = partition(A, begin, end)
+        print(A[begin:i], A[i], A[i+1:end])
+        quicksort(A, begin, i)
+        quicksort(A, i+1, end)
+        print(A[begin:i], A[i], A[i+1:end])
+
+if __name__ == "__main__":
+    args = [int(x) for x in sys.argv[1:]]
+    print(args)
+    quicksort(args, 0, len(args))
+    print(args)
+