# 1237. Find Positive Integer Solution for a Given Equation

Given a callable function `f(x, y)` with a hidden formula and a value `z`, reverse engineer the formula and return *all positive integer pairs  `x`  and  `y`  where *`f(x,y) == z`. You may return the pairs in any order.

While the exact formula is hidden, the function is monotonically increasing, i.e.:

• `f(x, y) < f(x + 1, y)`
• `f(x, y) < f(x, y + 1)`

The function interface is defined like this:

interface CustomFunction {
public:
// Returns some positive integer f(x, y) for two positive integers x and y based on a formula.
int f(int x, int y);
};

We will judge your solution as follows:

• The judge has a list of `9` hidden implementations of `CustomFunction`, along with a way to generate an answer key of all valid pairs for a specific `z`.
• The judge will receive two inputs: a `function_id` (to determine which implementation to test your code with), and the target `z`.
• The judge will call your `findSolution` and compare your results with the answer key.
• If your results match the answer key, your solution will be `Accepted`.

Example 1:

``````Input: function_id = 1, z = 5
Output: [[1,4],[2,3],[3,2],[4,1]]
Explanation: The hidden formula for function_id = 1 is f(x, y) = x + y.
The following positive integer values of x and y make f(x, y) equal to 5:
x=1, y=4 -> f(1, 4) = 1 + 4 = 5.
x=2, y=3 -> f(2, 3) = 2 + 3 = 5.
x=3, y=2 -> f(3, 2) = 3 + 2 = 5.
x=4, y=1 -> f(4, 1) = 4 + 1 = 5.
``````

Example 2:

``````Input: function_id = 2, z = 5
Output: [[1,5],[5,1]]
Explanation: The hidden formula for function_id = 2 is f(x, y) = x * y.
The following positive integer values of x and y make f(x, y) equal to 5:
x=1, y=5 -> f(1, 5) = 1 * 5 = 5.
x=5, y=1 -> f(5, 1) = 5 * 1 = 5.
``````

Constraints:

• `1 <= function_id <= 9`
• `1 <= z <= 100`
• It is guaranteed that the solutions of `f(x, y) == z` will be in the range `1 <= x, y <= 1000`.
• It is also guaranteed that `f(x, y)` will fit in 32 bit signed integer if `1 <= x, y <= 1000`.

``````class Solution {
public:
vector<vector<int>> findSolution(CustomFunction& customfunction, int z) {
vector<vector<int>> res;
int x = 1, y = 1000;
while (x <= 1000 && y > 0) {
int val = customfunction.f(x, y);
if (val > z) --y;
else if (val < z) ++x;
else res.push_back({x++, y--});
}
return res;
}
};
``````

``````class Solution {
public:
vector<vector<int>> findSolution(CustomFunction& customfunction, int z) {
vector<vector<int>> res;
int y = 1000;
for (int x = 1; x <= 1000; ++x) {
while (y > 1 && customfunction.f(x, y) > z) --y;
if (customfunction.f(x, y) == z) res.push_back({x, y});
}
return res;
}
};
``````

Github 同步地址:

https://github.com/grandyang/leetcode/issues/1237

https://leetcode.com/problems/find-positive-integer-solution-for-a-given-equation/

https://leetcode.com/problems/find-positive-integer-solution-for-a-given-equation/discuss/414249/JavaC%2B%2BPython-O(X%2BY)

https://leetcode.com/problems/find-positive-integer-solution-for-a-given-equation/discuss/414158/JavaPython-3-3-methods%3A-time-O(x-%2B-y)-O(xlogy)-and-O(x-%2B-logy)-w-analysis.

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