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Tested Python solution for LeetCode 970 with 18 pytest cases. Generate a practice environment with lcpy.
lcpy gen -n 970 # by problem number
lcpy gen -s powerful_integers # by problem name
x, y, and bound, return a list of all the powerful integers that have a value less than or equal to bound.
An integer is powerful if it can be represented as x^i + y^j for some integers i >= 0 and j >= 0.
You may return the answer in any order. In your answer, each value should occur at most once.
Input: x = 2, y = 3, bound = 10
Output: [2,3,4,5,7,9,10]
Explanation:
2 = 2^0 + 3^0
3 = 2^1 + 3^0
4 = 2^0 + 3^1
5 = 2^1 + 3^1
7 = 2^2 + 3^1
9 = 2^3 + 3^0
10 = 2^0 + 3^2
Input: x = 3, y = 5, bound = 15
Output: [2,4,6,8,10,14]
class Solution:
# Time: O(log(x, bound) * log(y, bound))
# Space: O(log(x, bound) * log(y, bound))
def powerful_integers(self, x: int, y: int, bound: int) -> list[int]:
def powers(base: int) -> list[int]:
if base == 1:
return [1] if bound >= 1 else []
vals: list[int] = []
val = 1
while val <= bound:
vals.append(val)
val *= base
return vals
found: set[int] = set()
for xi in powers(x):
for yj in powers(y):
total = xi + yj
if total <= bound:
found.add(total)
return list(found)
| Time | Space |
|---|---|
| O(log(x, bound) * log(y, bound)) | O(log(x, bound) * log(y, bound)) |