What is the brute force solution for Find Positive Integer Solution for a Given Equation?

The brute force approach for Find Positive Integer Solution for a Given Equation is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible pair of positive integers (x, y) within a reasonable range (1 to 1000) to see if they satisfy the equation f(x, y) == z. This method is straightforward but inefficient for larger ranges. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find Positive Integer Solution for a Given Equation?

Find Positive Integer Solution for a Given Equation uses the following concepts: Math, Two Pointers, Binary Search, Interactive. The recommended patterns to study are: Two Pointers, Binary Search.

What are the interview tips for Find Positive Integer Solution for a Given Equation?

Always consider the properties of the function before jumping into a brute force solution. Explain your thought process clearly; this shows understanding and can earn you points even if the solution isn't optimal. Practice similar problems to become familiar with patterns like two pointers and binary search.

What are common mistakes when solving Find Positive Integer Solution for a Given Equation?

Not recognizing the properties of the function, leading to inefficient solutions. Failing to handle the bounds correctly when incrementing or decrementing x and y.

#1237

Find Positive Integer Solution for a Given Equation

Medium

MathTwo PointersBinary SearchInteractiveTwo PointersBinary Search

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

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Intuition

Time O(n)Space O(n)

The optimal solution leverages the properties of the monotonically increasing function. By starting with x = 1 and y = 1000, we can adjust y based on the value of f(x, y) compared to z. This reduces the number of checks significantly.

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Algorithm

6 steps

1Step 1: Initialize an empty list to store the valid pairs.
2Step 2: Set x to 1 and y to 1000.
3Step 3: While x <= 1000 and y >= 1, check the value of f(x, y).
4Step 4: If f(x, y) == z, add the pair (x, y) to the list and increment x and decrement y.
5Step 5: If f(x, y) < z, increment x (to increase the function value).
6Step 6: If f(x, y) > z, decrement y (to decrease the function value).

solution.py13 lines

1def findSolution(f, z):
2    result = []
3    x, y = 1, 1000
4    while x <= 1000 and y >= 1:
5        if f(x, y) == z:
6            result.append([x, y])
7            x += 1
8            y -= 1
9        elif f(x, y) < z:
10            x += 1
11        else:
12            y -= 1
13    return result

ℹ

Complexity note: The time complexity is O(n) because we are effectively reducing the search space by either incrementing x or decrementing y. The space complexity is O(n) due to the storage of valid pairs in the result list.

1The function is monotonically increasing, allowing for efficient searching.
2Using two pointers (x and y) helps to navigate the search space effectively.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.