LeetCode 1237: Find Positive Integer Solution for a Given Equation Solution

Master LeetCode problem 1237 (Find Positive Integer Solution for a Given Equation), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1237. Find Positive Integer Solution for a Given Equation

Medium

Math Two Pointers Binary Search Interactive

Problem Explanation

Explanation:

To solve this problem, we need to find all positive integer pairs (x, y) where f(x, y) equals a given value z. We can achieve this by iteratively trying out different values of x and y within the given constraints and checking if f(x, y) equals z.

We can start with x = 1 and y = 1000, and iteratively decrease y while increasing x. At each step, we calculate f(x, y) and compare it with z:

If f(x, y) is less than z, we need to increase the value of f, so we increment x.
If f(x, y) is greater than z, we need to decrease the value of f, so we decrement y.
If f(x, y) equals z, we have found a valid pair, so we add it to our result.

This process ensures that we cover all possible valid pairs of x and y that satisfy the given equation.

Time Complexity:

The time complexity of this approach is O(x + y), where x and y are the maximum values of x and y within the given constraints.

Space Complexity:

The space complexity is O(1) as we are only storing the result pairs and not using any extra space.

Solution Code

class Solution {
    public List<List<Integer>> findSolution(CustomFunction customfunction, int z) {
        List<List<Integer>> result = new ArrayList<>();
        
        int x = 1, y = 1000;
        
        while(x <= 1000 && y >= 1) {
            int val = customfunction.f(x, y);
            if(val < z) {
                x++;
            } else if(val > z) {
                y--;
            } else {
                result.add(Arrays.asList(x, y));
                x++;
                y--;
            }
        }
        
        return result;
    }
}

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