# Powerful Integers Problem

## Description

LeetCode Problem 970.

Given three integers 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.

Example 1:

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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:

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Input: x = 3, y = 5, bound = 15
Output: [2,4,6,8,10,14]
``````

Constraints:

• 1 <= x, y <= 100
• 0 <= bound <= 10^6

## Sample C++ Code

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class Solution {
public:
int getBiggestPower(int num, int bound) {
if (num == 1) return 1;
int res = 0;
while (bound) {
bound /= num;
res++;
}
return res;
}

vector<int> powerfulIntegers(int x, int y, int bound) {
int xx = getBiggestPower(x, bound);
int yy = getBiggestPower(y, bound);
unordered_set<int> powerful;

for (int i = 0; i <= xx; i++) {
for (int j = 0; j <= yy; j++) {
if (pow(x, i) + pow(y, j) <= bound)
powerful.insert(pow(x, i) + pow(y, j));
}
}

return vector<int>(powerful.begin(), powerful.end());
}
};
``````