Build an Array With Stack Operations

class Solution {
public:
    vector<string> constructSequence(vector<int>& target, int n) {
        vector<string> result;
        int count = 0;
        
        for (int value : target) {
            while (count < value - 1) {
                result.push_back("Push");
                result.push_back("Pop");
                count++;
            }
            
            result.push_back("Push");
            count++;
        }
        
        return result;
    }
};

The task aims to simulate stack operations that generate a specific target array sequence using a given number of integers. In the provided C++ solution, the class Solution includes the method constructSequence, which returns a vector of strings that represent "Push" and "Pop" commands to build the array up to the last number in the target sequence.

To understand and utilize the given algorithm effectively:

• The constructSequence function accepts a vector of integers (target) and an integer (n) which specifies the upper limit of numbers you can use.
• Initiate an empty string vector named result that will store the sequence of operations and an integer count to keep track of numbers used so far.
• Iterate through each integer value in the target vector.
• For each value, ensure that all numbers less than value are manipulated correctly by:
  • Inserting "Push" followed by "Pop" into the result vector for numbers between the current count and (value - 1). This simulates adding a number to the stack and then removing it since it isn't part of the final array.
  • Update count to the correct number after accounting for the "Pop" operations.
• When reaching the actual number needed from the target array, insert only "Push" to the result list and increment the count.
• Return the result vector encompassing all operations.

This algorithm effectively provides a sequence of stack operations that can form the desired target array when interpreted accordingly. Ensure to initiatize both the result vector and the count variable appropriately to reflect the operations accurately.

class Solution {
    public List<String> createStackOperations(int[] sequence, int maxVal) {
        List<String> operations = new ArrayList();
        int current = 0;

        for (int value : sequence) {
            while (current < value - 1) {
                operations.add("Push");
                operations.add("Pop");
                current++;
            }

            operations.add("Push");
            current++;
        }

        return operations;
    }
}

This Java solution simulates building an array using stack operations. The primary goal is to generate a list of operations ("Push" and "Pop") that could reconstruct a specific target sequence given a maximum value.

The approach utilizes a single loop that iterates through each number in the provided sequence. For each number, it checks how many times it should either "Push" or "Pop" an element to keep the stack aligned with the current position in the target sequence.

• Initialize an empty list of operations.
• Set a counter to follow the last number added to the stack.
• For each value in the input array:
  • Increment the counter up to one less than the current value, adding "Push" and "Pop" to the operations list for each increment (This mimics pushing numbers onto a stack and then immediately removing them until the current value is reached).
  • Add "Push" for the current value itself (This actually keeps the value in the stack).

This solution ensures that by incrementing the counter and manipulating the stack with the specified operations, the exact sequence can be formed using the minimum possible number of stack operations. The function returns the list of operations required to achieve this.

class Solution:
    def generateOperations(self, goals: List[int], max_val: int) -> List[str]:
        output = []
        current = 0
        
        for value in goals:
            while current < value - 1:
                output.append("Push")
                output.append("Pop")
                current += 1

            output.append("Push")
            current += 1

        return output

The Python solution provided solves the problem of generating a sequence of stack operations to create an array that matches a target layout, represented by goals, only using push and pop operations and with values never exceeding max_val.

Here are the steps executed in the code:

1. Initialize an empty list output to hold the sequence of stack operations, and a variable current to zero, which tracks the number currently to be processed.
2. Iterate over each number in the goals list:
   • For the current number in goals, execute a loop that keeps running as long as current is less than the current goal number minus one. Inside the loop:
     • Append "Push" to output.
     • Append "Pop" to output. This simulates pushing in a number but immediately removing it to only increase the count.
     • Increment current by one.
   • After exiting the loop (once current is appropriately positioned), append a "Push" operation to output indicating that the current number is now part of the array. Increment the current value by one.
3. After processing all numbers in the goals, the function returns output, which contains the required sequence of stack operations.

This sequential method ensures that by the end of the function each intended value in goals is part of the resulting array simulated by stack operations without exceeding any temporary values beyond max_val.