Add py merge sort

Author: awpala

python/main.py

@@ -18,3 +18,21 @@
 A = [5, 2, 4, 6, 1, 3] # cf. Figure 2.2, p. 18
 insertion_sort(A)
 print('\nsorted:', A)
+
+A = [31, 41, 59, 26, 41, 58] # cf. Exercise 2.1-1, p. 22
+insertion_sort(A)
+print('\nsorted:', A)
+
+# CLRS Section 2.3 - Merge Sort
+from sorting.p034_merge_sort import merge_sort
+A = []
+
+print('\nSection 2.3 - Merge Sort')
+
+A = [2, 4, 5, 7, 1, 2, 3, 6] # cf. Figure 2.3, p. 32
+merge_sort(A, 0, len(A)-1)
+print('\nsorted:', A)
+
+A = [3, 41, 52, 26, 38, 57, 9, 49] # cf. Exercise 2.3-1, p. 37
+merge_sort(A, 0, len(A)-1)
+print('\nsorted:', A)

python/sorting/p034_merge_sort.py

@@ -0,0 +1,31 @@
+'''
+    CLRS Section 2.3, p. 34
+'''
+import math
+
+def merge(A, p, q, r):
+    n1 = q - p + 1
+    n2 = r - q
+    L = [None for element in range(0, n1 + 1)]; R = [None for element in range(0, n2 + 1)]
+    for i in range(0, n1):
+        L[i] = A[p + i]
+    for j in range(0, n2):
+        R[j] = A[q + j + 1]
+    L[n1] = math.inf
+    R[n2] = math.inf
+    i = 0
+    j = 0
+    for k in range(p, r + 1):
+        if L[i] <= R[j]:
+            A[k] = L[i]
+            i += 1
+        else:
+            A[k] = R[j]
+            j += 1
+
+def merge_sort(A, p, r):
+    if p < r:
+        q = (p + r)//2
+        merge_sort(A, p, q)
+        merge_sort(A, q + 1, r)
+        merge(A, p, q, r)