#2375

Medium

auto_awesomeStack-based state management

LeetCode Problem Workspace

Construct Smallest Number From DI String

Construct the lexicographically smallest string that fits the increasing and decreasing conditions of a given pattern.

Problem Statement

You are given a string pattern of length n consisting of the characters 'I' meaning increasing and 'D' meaning decreasing. You need to construct a string num of length n + 1 with the smallest lexicographical order that satisfies the conditions described by the pattern.

At each position i in num, if the pattern has 'I', then num[i] should be smaller than num[i+1], and if the pattern has 'D', then num[i] should be greater than num[i+1]. Your task is to return the lexicographically smallest string num that meets these conditions.

Examples

Example 1

Input: pattern = "IIIDIDDD"

Output: "123549876"

At indices 0, 1, 2, and 4 we must have that num[i] num[i+1]. Some possible values of num are "245639871", "135749862", and "123849765". It can be proven that "123549876" is the smallest possible num that meets the conditions. Note that "123414321" is not possible because the digit '1' is used more than once.

Example 2

Input: pattern = "DDD"

Output: "4321"

Some possible values of num are "9876", "7321", and "8742". It can be proven that "4321" is the smallest possible num that meets the conditions.

Constraints

1 <= pattern.length <= 8
pattern consists of only the letters 'I' and 'D'.

Solution Approach

Use a Stack for State Management

To ensure the lexicographically smallest order, use a stack to temporarily store digits when a 'D' pattern is encountered. Push digits in sequence and pop them when an 'I' pattern is found to maintain the correct order.

Greedy Approach for Lexicographical Minimization

A greedy strategy ensures that we always pick the smallest possible number for each position. By iterating over the pattern and adjusting the stack accordingly, we ensure that the digits are chosen in the most lexicographically favorable order.

Efficient Time and Space Management

The algorithm runs in O(n) time complexity, as each character in the pattern is processed once. The space complexity is also O(n) due to the stack used to manage state during the construction of the result.

Complexity Analysis

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

The algorithm works in linear time, O(n), because it processes each character of the input pattern once. The space complexity is also O(n) as we use a stack to store the digits temporarily for rearranging them as needed based on the pattern.

What Interviewers Usually Probe

The candidate should demonstrate an understanding of stack-based algorithms and how they can be used for state management in this context.
Look for a clear explanation of the greedy approach, ensuring that the candidate can justify how it minimizes the lexicographical order.
The candidate should efficiently explain the time and space complexity of their solution, ensuring that they are aware of the optimal performance for this problem.

Common Pitfalls or Variants

Common pitfalls

Forgetting to pop the stack when encountering an 'I' pattern may result in an incorrect number sequence.
Incorrect handling of 'I' and 'D' patterns could lead to not achieving the smallest lexicographical number.
Not managing the stack properly may lead to inefficient space or time complexity, making the solution suboptimal.

Follow-up variants

Handling larger inputs with longer patterns can add complexity, though the algorithm remains O(n) in time and space.
If the pattern is all 'I' or all 'D', the stack's behavior changes, but the approach still applies with minimal modification.
The pattern length could affect the stack usage and result in different behavior, so optimizing space usage in the stack could be a potential focus.

FAQ

What is the best approach for solving the "Construct Smallest Number From DI String" problem?

The best approach is using a stack for state management combined with a greedy technique to construct the lexicographically smallest number.

How can stack-based algorithms help in solving string pattern problems like "Construct Smallest Number From DI String"?

Stack-based algorithms allow for efficient state management, ensuring correct order by pushing and popping elements based on pattern conditions ('I' and 'D').

What is the time and space complexity for "Construct Smallest Number From DI String"?

The time complexity is O(n) because each character in the pattern is processed once. The space complexity is O(n) due to the stack used for state management.

Can I solve the "Construct Smallest Number From DI String" problem using recursion?

While recursion can be used, an iterative stack-based approach is more efficient and easier to manage, especially for handling the lexicographical minimization.

How does GhostInterview help with the "Construct Smallest Number From DI String" problem?

GhostInterview helps by guiding candidates through the stack-based approach and providing immediate feedback on common mistakes and algorithmic efficiency.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def smallestNumber(self, pattern: str) -> str:
        def dfs(u):
            nonlocal ans
            if ans:
                return
            if u == len(pattern) + 1:
                ans = ''.join(t)
                return
            for i in range(1, 10):
                if not vis[i]:
                    if u and pattern[u - 1] == 'I' and int(t[-1]) >= i:
                        continue
                    if u and pattern[u - 1] == 'D' and int(t[-1]) <= i:
                        continue
                    vis[i] = True
                    t.append(str(i))
                    dfs(u + 1)
                    vis[i] = False
                    t.pop()

        vis = [False] * 10
        t = []
        ans = None
        dfs(0)
        return ans

Continue Practicing

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