# 970. Powerful Integers

Given two positive 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`

``````class Solution {
public:
vector<int> powerfulIntegers(int x, int y, int bound) {
set<int> res;
for (int a = 1; a < bound; a *= x) {
for (int b = 1; a + b <= bound; b *= y) {
res.insert(a + b);
if (y == 1) break;
}
if (x == 1) break;
}
return vector<int>(res.begin(), res.end());
}
};
``````

Github 同步地址:

https://github.com/grandyang/leetcode/issues/970

https://leetcode.com/problems/powerful-integers/

https://leetcode.com/problems/powerful-integers/discuss/214212/JavaC%2B%2BPython-Easy-Brute-Force

https://leetcode.com/problems/powerful-integers/discuss/214197/Java-straightforward-try-all-combinations

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