recursion

Author: chrislucas

python/PowerSum/.idea/PowerSum.iml

@@ -0,0 +1,68 @@
+'''
+https://www.hackerrank.com/challenges/the-power-sum/problem
+'''
+
+'''
+De quantas formas e possivel escrever um numero M
+na forma de soma de potencias N
+'''
+
+
+def top_down(base, exp, acc=1):
+    X = acc ** exp
+    if X > base:
+        return 0
+    elif X == base:
+        return 1
+    u = top_down(base, exp, acc + 1)
+    v = top_down(base - X, exp, acc + 1)
+    return u + v
+
+
+def another_top_down(base, exp, acc=1):
+    x = base - (acc ** exp)
+    if x < 0:  # se  acc ^ exp > que a base x < 0 portanto acc ^ exp nao faz parte da solucao
+        return 0
+    elif x == 0:  # acc ^ x == base entao base - (acc ^ x) == 0 logo acc ^ x faz parte da solucao
+        return 1
+    u = another_top_down(base, exp, acc + 1)  # sem adicionar acc ^ exp a solucao
+    v = another_top_down(x, exp, acc + 1)  # adicionando acc ^ exp a solucao
+    return u + v
+
+
+def bottom_up_approach(base, exp):
+    from math import sqrt
+    acc = 1
+    table = [0] * (base + 1)
+    for i in range(2, int(sqrt(base) + 1)):
+        x = acc ** i
+        acc += 1
+
+    return table[base - 1]
+
+
+'''
+E se eu quisesse saber de quantas formas e possivel escrever
+um numero como potencias de 1 a P
+'''
+
+
+def run():
+    n = int(input())
+    p = int(input())
+    print(another_top_down(n, p))
+
+
+def test():
+    print(top_down(10, 2), another_top_down(10, 2))
+    print(top_down(4, 2), another_top_down(4, 2))
+    print(top_down(4, 1), another_top_down(4, 1))
+    print(top_down(10, 1), another_top_down(10, 1))
+    print(top_down(100, 3), another_top_down(100, 3))
+    print(top_down(100, 2), another_top_down(100, 2))
+
+
+test()
+
+if __name__ == '__main__':
+    pass