2019-03-26 in class

\

@@ -0,0 +1,77 @@
+#!/usr/bin/env python3
+
+import sys
+
+def heap_extract_max(A):
+    m = A[0]
+    A[0] = A.pop()
+
+    size = len(A)
+    i = 0
+    exit = not size == 0
+    while exit:
+        left = heap_left(size, i)
+        print("left =", left)
+        if left == None:
+            break
+
+        right = heap_right(size, i)
+        print("right =", right)
+        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:]]
+    print(args)
+    print(heap_extract_max(args))
+    print(args)
+

heapsort.py

@@ -1,24 +1,41 @@
 #!/usr/bin/env python3
 
 import sys
+import math
 
-def heap_extract_max(A):
+def heap_sort(A):
-    m = A[0]
+    heap_build_max_heap(A)
-    A[0] = A.pop()
 
-    size = len(A)
+    print("Initial heap:")
+    heap_print(A, len(A))
+    print()
+
+    for i in range(len(A)-1, 0, -1):
+        A[0], A[i] = A[i], A[0]
+        heap_max_heapify(A, i)
+
+        print("\nNew heap: length =", i)
+        heap_print(A, i)
+        print()
+
+def heap_max_heapify(A, size):
+    if size < 2:
+        return
+
+    print("size =", size)
     i = 0
-    exit = size == 0
-    while exit:
-        left = heap_left(i)
-        if left == None:
-            break
 
-        right = heap_right(i)
+    left = heap_left(size, i)
-        if right == None:
+    print("left =", left)
+
+    while left is not None:
+        right = heap_right(size, i)
+        print("right =", right)
+
+        if right is None:
             if A[i] < A[left]:
                 A[i], A[left] = A[left], A[i]
-                break
+            break
 
         ma = max_3(A[i], A[left], A[right])
         if ma == A[i]:
@@ -30,7 +47,38 @@ def heap_extract_max(A):
             A[i], A[right] = A[right], A[i]
             i = right
 
-    return m
+        left = heap_left(size, i)
+        print("left =", left)
+
+
+def heap_build_max_heap(A):
+    if len(A) < 2:
+        return
+    for i in range(math.ceil(len(A)/2), 1, -1):
+        heap_max_heapify(A, i)
+
+
+def heap_print(A, size):
+    i = 1
+    newline = False
+    while i <= size:
+        print(A[i-1], end='\t')
+        newline = False
+        i = i + 1
+        if is_power_2(i):
+            print()
+            newline = True
+    if not newline:
+        print()
+
+
+def is_power_2(n):
+    while n > 1:
+        if n % 2 == 1:
+            return False
+        n = n // 2
+    return True
+
 
 def max_3(a, b, c):
     if a > b:
@@ -44,29 +92,35 @@ def max_3(a, b, c):
         else:
             return c
 
+
 def heap_parent(n):
     n = n + 1
     if n == 1:
         return None
-    else
+    else:
         return (n // 2) - 1
 
+
 def heap_left(size, n):
     n = n + 1
     l = n * 2
-    if l > size
+    if l > size:
         return None
-    else
+    else:
         return l - 1
 
+
 def heap_right(size, n):
     n = n + 1
     l = n * 2 + 1
-    if l > size
+    if l > size:
         return None
-    else
+    else:
         return l - 1
 
+
 if __name__ == "__main__":
     args = [int(x) for x in sys.argv[1:]]
+    heap_sort(args)
+    print(args)
 

notes.md

@@ -143,3 +143,37 @@ def right(x):
 
 **Max heap property**: for all i > 1 A[parent(i)] >= A[i]
 
+# Data structures
+
+Way to organize information
+
+A data structure has an interface (functions to work with the DS)
+
+A data structure has data and meta-data (like size, length).
+
+## Stack (LIFO)
+
+### Operations:
+- `push(S, x)` (put one element, move TOS)
+- `pop(S)` (remove element in TOS, move TOS)
+- `stack-empty(S)` (returns TRUE if stack is empty)
+
+## Queue (FIFO)
+
+## Structure
+
+- Based on array
+- `length`
+- `head`
+- `tail`
+
+Queue has always 1 cell free to avoid confusion with full/empty
+
+## Dictionary
+
+Data structure for fast search
+
+## Direct-access table
+
+Implementation of dictionary
+