October 10, 2023
Problem Description
The task is to find the minimum value that can be achieved by appropriately placing parentheses in a given string s consisting of numbers and operators. s contains only numbers and ‘+’ and ‘-‘ operators.
For example, if the input is "5-3+2", it can be arranged using parentheses to achieve the minimum value.
Thus, the result can vary depending on how the parentheses are placed. Let’s explore the following examples to understand the problem more clearly.
Example Input: "5-3+2"
Possible Results:
1) (5-3)+2 = 4
2) 5-(3+2) = 0
Minimum Value: 0
Input Format and Constraints
Input: String s (1 ≤ s.length ≤ 50) consisting of numbers and ‘+’ or ‘-‘.
Output: Returns the minimum value as an integer.
Solution Process
1. Understanding and Analyzing the Problem
The first step to solve the problem is to clearly understand how parentheses can be arranged. As in the example above, each operator can be grouped within parentheses to form calculations. This grouping significantly affects the final result.
2. Greedy Approach
One method that can be used to find the minimum value is the greedy algorithm. The ‘greedy algorithm’ makes the choice that seems the best at the moment to solve the problem. However, in this case, the greedy approach might not always yield the optimal solution, so caution is required.
3. Parsing the Input String
First, we need to parse the input string based on the ‘+’ and ‘-‘ symbols to create an array of numbers and operators. For example, if s = "5-3+2", it can be separated as follows:
numbers = [5, 3, 2]
operators = ['-', '+']
4. Calculating the Minimum Value
Now we need to address each operator. If ‘-‘ exists, all subsequent numbers after that position must be subtracted. Meanwhile, all numbers except the current one should be added. This process will help us calculate the minimum value.
5. JavaScript Implementation Code
function minValue(s) {
let numbers = s.split(/[-+]/g).map(Number);
let operators = s.match(/[-+]/g) || [];
let minValue = numbers[0];
for (let i = 0; i < operators.length; i++) {
if (operators[i] === '-') {
minValue -= numbers[i + 1];
for (let j = i + 1; j < numbers.length; j++) {
minValue -= numbers[j];
}
break;
} else {
minValue += numbers[i + 1];
}
}
return minValue;
}
console.log(minValue("5-3+2")); // Output: 0
6. Time Complexity Analysis
The above algorithm parses the input string once and subsequently traverses the operators and numbers, giving it a time complexity of O(n). Here, n represents the length of the input string. This is a sufficiently efficient approach.
7. Final Summary
This problem has shown how significantly the proper placement of parentheses affects the result. Additionally, we learned how to efficiently solve the problem using greedy algorithms and arrays. Wishing you success in your coding tests!