LeetCode 970. Powerful Integers

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题目

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

分析

x^i + y^j <= bound; (1<=x<=100, 1<=y<=100, 0<=bound<=10^6)

注意i，j的范围未知，不可以i，j循环。

简单来说翻译为 a + b <= bound （a=x^i, b=y^j）;

那么a，b的范围是什么呢？1<= a，b <= bound; a+b <= bound.

代码

class Solution {
    public List<Integer> powerfulIntegers(int x, int y, int bound) {
        Set<Integer> result = new HashSet<>();

        for (int a = 1; a < bound; a *= x) {
            for (int b=1; a + b <= bound; b *= y) {
                result.add(a + b);

                if(y == 1) {
                    break;
                }
            }

            if(x == 1) {
                break;
            }
        }

        return new ArrayList<>(result);
    }
}