LeetCode 2118: Build the Equation Solution

Master LeetCode problem 2118 (Build the Equation), a hard 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.

2118. Build the Equation

Hard

Database

Problem Explanation

Explanation:

This problem asks us to build a mathematical equation based on a given target value and a set of numbers. The equation should be constructed using addition, subtraction, and multiplication operators. We need to return all possible equations that can be formed to achieve the target value.

To solve this problem, we can use backtracking to explore all possible combinations of operators and operands. At each step, we can choose either addition, subtraction, or multiplication to build the equation. We recursively explore all possibilities and backtrack when needed.

Algorithmic Idea:

Start by defining a backtracking function that takes the current value, target value, index of the next number to be considered, the current equation string, and the result list.
In the backtracking function, check if we have reached the end of the numbers array and if the current value matches the target value. If so, add the current equation to the result list.
Otherwise, for the current number, try adding, subtracting, or multiplying it with the current value and continue exploring the possibilities recursively.
Remember to backtrack by removing the last operation from the equation string before proceeding to the next step.

Time Complexity:

The time complexity of this backtracking solution is exponential, as we are exploring all possible combinations.

Space Complexity:

The space complexity is also exponential due to the recursive nature of the backtracking algorithm.

Solution Code

class Solution {
    public List<String> buildEquation(int[] nums, int target) {
        List<String> result = new ArrayList<>();
        backtrack(nums, target, 0, 0, "", result);
        return result;
    }
    
    private void backtrack(int[] nums, int target, int index, int current, String equation, List<String> result) {
        if (index == nums.length) {
            if (current == target) {
                result.add(equation);
            }
            return;
        }
        
        for (int i = index; i < nums.length; i++) {
            if (i != index && nums[index] == 0) continue; // Skip leading zeros
            int num = nums[i];
            
            backtrack(nums, target, i + 1, current + num, equation + "+" + num, result);
            backtrack(nums, target, i + 1, current - num, equation + "-" + num, result);
            backtrack(nums, target, i + 1, current * num, equation + "*" + num, result);
        }
    }
}

Try It Yourself

Loading code editor...

Frequently Asked Questions

How to solve LeetCode 2118 (Build the Equation)?

This page provides optimized solutions for LeetCode problem 2118 (Build the Equation) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.

What is the time complexity of LeetCode 2118 (Build the Equation)?

The time complexity for LeetCode 2118 (Build the Equation) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.

Can I run code for LeetCode 2118 on DevExCode?

Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 2118 in Java, C++, or Python.

Back to LeetCode Solutions