mergesort added (#1313)

* mergesort added

* added doctest

divide_and_conquer/mergesort.py

@@ -0,0 +1,45 @@
+def merge(a,b,m,e):
+    l=a[b:m+1]
+    r=a[m+1:e+1]
+    k=b
+    i=0
+    j=0
+    while i<len(l) and j<len(r):
+        #change sign for Descending order
+        if l[i]<r[j]: 
+            a[k]=l[i]
+            i+=1
+        else:
+            a[k]=r[j]
+            j+=1
+        k+=1
+    while i<len(l):
+        a[k]=l[i]
+        i+=1
+        k+=1
+    while j<len(r):
+        a[k]=r[j]
+        j+=1
+        k+=1
+    return a
+    
+def mergesort(a,b,e):
+    """
+    >>> mergesort([3,2,1],0,2)
+    [1, 2, 3]
+    >>> mergesort([3,2,1,0,1,2,3,5,4],0,8)
+    [0, 1, 1, 2, 2, 3, 3, 4, 5]
+    """
+    if b<e:
+        m = (b+e)//2
+        #print("ms1",a,b,m)
+        mergesort(a,b,m)
+        #print("ms2",a,m+1,e)
+        mergesort(a,m+1,e)
+        #print("m",a,b,m,e)
+        merge(a,b,m,e)
+        return a
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()