Given two non-negative integers x
and y
, an integer is powerful if it is equal to x^i + y^j
for some integers i >= 0
and j >= 0
.
Return a list of all powerful integers that have value less than or equal to bound
.
You may return the answer in any order. In your answer, each value should occur at most once.
Example 1:
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
Example 2:
Input: x = 3, y = 5, bound = 15 Output: [2,4,6,8,10,14]
Note:
1 <= x <= 100
1 <= y <= 100
0 <= bound <= 10^6
Solution: Brute Force
Time complexity: O(log(bound) / log(x) * log(bound) / log(y))
Space complexity: O(log(bound) / log(x) * log(bound) / log(y))
C++
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// Author: Huahua, running time: 4 ms class Solution { public: vector<int> powerfulIntegers(int x, int y, int bound) { unordered_set<int> ans; for (int a = 1; a < bound; a *= x) { for (int b = 1; a + b <= bound; b *= y) { ans.insert(a + b); if (y == 1) break; } if (x == 1) break; } return {begin(ans), end(ans)}; } }; |