#1441

Medium

auto_awesomeStack-based state management

LeetCode Problem Workspace

Build an Array With Stack Operations

Simulate stack operations to match a target array while processing numbers from 1 to n.

Problem Statement

You are given an integer array target and an integer n. The array target is strictly increasing and contains numbers from the range [1, n]. You must use a stack with the operations 'Push' and 'Pop' to form this target array while reading numbers in sequence from 1 to n.

Your goal is to return a sequence of operations ('Push' and 'Pop') that results in the stack forming the target array. For numbers that must appear in the target, use 'Push'. For numbers that should not be included in the stack, use both 'Push' and 'Pop'.

Examples

Example 1

Input: target = [1,3], n = 3

Output: ["Push","Push","Pop","Push"]

Initially the stack s is empty. The last element is the top of the stack. Read 1 from the stream and push it to the stack. s = [1]. Read 2 from the stream and push it to the stack. s = [1,2]. Pop the integer on the top of the stack. s = [1]. Read 3 from the stream and push it to the stack. s = [1,3].

Example 2

Input: target = [1,2,3], n = 3

Output: ["Push","Push","Push"]

Initially the stack s is empty. The last element is the top of the stack. Read 1 from the stream and push it to the stack. s = [1]. Read 2 from the stream and push it to the stack. s = [1,2]. Read 3 from the stream and push it to the stack. s = [1,2,3].

Example 3

Input: target = [1,2], n = 4

Output: ["Push","Push"]

Initially the stack s is empty. The last element is the top of the stack. Read 1 from the stream and push it to the stack. s = [1]. Read 2 from the stream and push it to the stack. s = [1,2]. Since the stack (from the bottom to the top) is equal to target, we stop the stack operations. The answers that read integer 3 from the stream are not accepted.

Constraints

1 <= target.length <= 100
1 <= n <= 100
1 <= target[i] <= n
target is strictly increasing.

Solution Approach

Simulate the Stack Operations

Start by pushing numbers into the stack from 1 to n. If the number matches the next target value, 'Push' the number. If it doesn’t match, perform 'Push' and then 'Pop' immediately to discard it. Continue until the target array is formed.

Efficient Stack Management

The problem is solved efficiently by maintaining a running check to see whether the current number matches the next value in the target array. This avoids unnecessary operations. Only push numbers that are part of the target array, and pop those that are extraneous.

Handle Stack Overflow Concerns

Since n is small (<=100), stack overflow is not a concern. However, managing stack size within constraints is important. Always ensure the 'Push' operation does not exceed the required target, and avoid pushing numbers that will be immediately discarded.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(1)

The time complexity is O(n) because we only iterate through the sequence once, performing a constant amount of work per number. The space complexity is O(1) since the stack's state is only tracked at each step, without requiring extra space beyond the input variables.

What Interviewers Usually Probe

Can the candidate optimize the handling of stack operations for larger inputs?
Is the candidate able to clearly explain the pattern of stack operations for non-target numbers?
Does the candidate understand why a 'Push' followed by 'Pop' works to discard unnecessary numbers?

Common Pitfalls or Variants

Common pitfalls

Pushing unnecessary numbers to the stack without checking if they match the target array.
Not recognizing that 'Pop' must be used for numbers that aren't part of the target array.
Failing to handle the edge cases where the stack operation sequence must be minimized.

Follow-up variants

Change the target array to include non-consecutive integers.
Modify the range of n to exceed the length of the target array.
Alter the operations so that only 'Push' can be used, forcing different solutions.

FAQ

What is the main pattern in the "Build an Array With Stack Operations" problem?

The primary pattern involves stack-based state management, where you use 'Push' to add elements to the stack and 'Pop' to discard unnecessary elements in order to match the target array.

What is the time complexity of the solution?

The time complexity is O(n) because we only perform one pass through the stream of numbers, making a constant number of operations per number.

How can I minimize the number of stack operations in this problem?

Minimize stack operations by only pushing the numbers that are part of the target array and popping numbers immediately when they aren’t part of it.

What happens if the target array is longer than the range of numbers?

Since the target array is strictly increasing and must fit within the range of numbers from 1 to n, a mismatch in length would be invalid for this problem.

Can the stack operations exceed the size of the target array?

No, the stack operations must always match the numbers required to build the target array. Any extra operations would result in unnecessary steps.

terminal

Solution

Solution 1: Simulation

We define a variable $\textit{cur}$ to represent the current number to be read, initially set to $\textit{cur} = 1$, and use an array $\textit{ans}$ to store the answer.

1

2

3

4

5

6

7

8

9

10

11

class Solution:
    def buildArray(self, target: List[int], n: int) -> List[str]:
        ans = []
        cur = 1
        for x in target:
            while cur < x:
                ans.extend(["Push", "Pop"])
                cur += 1
            ans.append("Push")
            cur += 1
        return ans

Continue Practicing

#1700 number of students unable to eat lunch #946 validate stack sequences #735 asteroid collision