new katas

Author: brabemi

3-binomial_expansion.py

@@ -0,0 +1,102 @@
+# https://www.codewars.com/kata/binomial-expansion/train/python
+
+import math
+
+def axb_extract(expr):
+    expr = expr[::-1]
+    parts = expr.split('+', 1)
+    if len(parts) != 2:
+        parts = expr.split('-', 1)
+        parts[0] += '-'
+
+    a_str = parts[1]
+    a_str = a_str[1:]
+    a_str = a_str[::-1]
+    if a_str == '' or a_str == '-':
+        a_str += '1'
+
+    a = int(a_str)
+    x = parts[1][0]
+    b = int(parts[0][::-1])
+
+    return a, x, b
+
+def binom_coef(n):
+    top = list(range(n, math.floor((n+1)/2), -1))
+    bot = list(range(1, math.ceil((n+1)/2), 1))
+
+    for i in range(1, len(top)):
+        top[i] *= top[i-1]
+        bot[i] *= bot[i-1]
+
+    coef = [1]
+    for i in range(len(top)):
+        coef.append(top[i]//bot[i])
+
+    coef2 = coef if n % 2 == 1 else coef[:-1]
+    coef += coef2[::-1]
+
+    return coef
+
+def expand(expr):
+    parts = expr.split('^', 1)
+    exponent = int(parts[1])
+
+    if exponent == 0:
+        return '1'
+    elif exponent == 1:
+        return parts[0][1:-1]
+
+    a, x, b = axb_extract(parts[0][1:-1])
+
+    coef = binom_coef(exponent)
+    # print(bc)
+
+    qa = 1
+    qb = 1
+    for i in range(exponent+1):
+        coef[exponent-i] *= qb
+        coef[i] *= qa
+        qb *= b
+        qa *= a
+
+    elements = []
+
+    for i in range(exponent, -1, -1):
+        sign = '+' if coef[i] > 0 else '-'
+        elem_coef = abs(coef[i]) if abs(coef[i]) > 1 else ''
+        if i > 1:
+            elements.append('{}{}{}^{}'.format(sign, elem_coef, x, i))
+        elif i == 1:
+            elements.append('{}{}{}'.format(sign, elem_coef, x))
+        else:
+            elements.append('{}{}'.format(sign, elem_coef))
+
+    if elements[0][0] == '+':
+        elements[0] = elements[0][1:]
+
+    if len(elements[-1]) == 1:
+        elements[-1] += '1'
+
+    return ''.join(elements)
+
+
+
+
+
+print(expand("(2x+1)^0"), "1")
+print(expand("(x+1)^0"), "1")
+print(expand("(x+1)^1"), "x+1")
+print(expand("(x+1)^2"), "x^2+2x+1")
+
+print(expand("(x-1)^0"), "1")
+print(expand("(x-1)^1"), "x-1")
+print(expand("(x-1)^2"), "x^2-2x+1")
+
+print(expand("(5m+3)^4"), "625m^4+1500m^3+1350m^2+540m+81")
+print(expand("(2x-3)^3"), "8x^3-36x^2+54x-27")
+print(expand("(7x-7)^0"), "1")
+
+print(expand("(-5m+3)^4"), "625m^4-1500m^3+1350m^2-540m+81")
+print(expand("(-2k-3)^3"), "-8k^3-36k^2-54k-27")
+print(expand("(-7x-7)^0"), "1")

4-middle_permutation.py

@@ -0,0 +1,19 @@
+def middle_permutation(string):
+    string = sorted(string)
+    retval = ''
+    n = len(string)
+    if n % 2 == 1:
+        retval += string[n//2]
+        string = string[:n//2] + string[n//2+1:]
+        n -= 1
+    retval += string[n//2-1]
+    string = string[:n//2-1] + string[n//2:]
+    retval += ''.join(string[::-1])
+    return retval
+
+print(middle_permutation("abc"),"bac")
+print(middle_permutation("abcd"),"bdca")
+print(middle_permutation("abcdx"),"cbxda")
+print(middle_permutation("abcdxg"),"cxgdba")
+print(middle_permutation("abcdxgz"),"dczxgba")
+print(middle_permutation("abcdefghijklmnopqrst"),"dczxgba")

5-double_cola.py

@@ -0,0 +1,14 @@
+# https://www.codewars.com/kata/double-cola
+
+def whoIsNext(names, r):
+    queue_len = len(names)
+    while r > queue_len:
+        r -= queue_len
+        queue_len *= 2
+    return names[(r-1) * len(names) // queue_len]
+
+print(whoIsNext(["Sheldon", "Leonard", "Penny", "Rajesh", "Howard"], 1)=="Sheldon")
+print(whoIsNext(["Sheldon", "Leonard", "Penny", "Rajesh", "Howard"], 6)=="Sheldon")
+print(whoIsNext(["Sheldon", "Leonard", "Penny", "Rajesh", "Howard"], 7)=="Sheldon")
+print(whoIsNext(["Sheldon", "Leonard", "Penny", "Rajesh", "Howard"], 52)=="Penny")
+print(whoIsNext(["Sheldon", "Leonard", "Penny", "Rajesh", "Howard"], 7230702951)=="Leonard")

5-is_my_friend_cheating.py

@@ -0,0 +1,16 @@
+# https://www.codewars.com/kata/is-my-friend-cheating
+import math
+
+def removNb(n):
+    retval = []
+    overall_sum = n*(n+1)//2
+    limit = math.ceil(math.sqrt(overall_sum))
+    for a in range(1, limit):
+        b = (overall_sum - a) // (a + 1)
+        if b < n and (a * b) == (overall_sum - a - b):
+            retval.append((a, b))
+            retval.append((b, a))
+    return sorted(retval)
+
+print((removNb(100), []))
+print((removNb(26), [(15, 21), (21, 15)]))