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question:File Path String Manipulation You are given a string representing a file path. Your task is to implement a function `simplifyPath` that converts this path into a simplified canonical path. The rules for simplifying the path are as follows: 1. Any `.` represents the current directory and can be ignored. 2. Any `..` moves up one directory if possible, eliminating the previous part of the path. 3. Consecutive slashes ("/") are treated as a single slash. 4. The resulting simplified path should not end with a trailing slash unless it is the root directory ("/"). # Input - A non-empty string `path` representing a Unix-style file path. # Output - A string representing the simplified canonical path. # Examples Example 1: ```python path = "/home/" print(simplifyPath(path)) # Output: "/home" ``` - Explanation: "/home/" simplifies to "/home". Example 2: ```python path = "/a/./b/../../c/" print(simplifyPath(path)) # Output: "/c" ``` - Explanation: "/a/./b/../../c/" simplifies to "/c". Example 3: ```python path = "/../" print(simplifyPath(path)) # Output: "/" ``` - Explanation: "/../" simplifies to "/", since the root cannot go up any further. Example 4: ```python path = "/home//foo/" print(simplifyPath(path)) # Output: "/home/foo" ``` - Explanation: "/home//foo/" simplifies to "/home/foo". Task: Implement the `simplifyPath` function that simplifies the given `path` string based on the rules outlined above. Your solution should have linear time and space complexity. # Function Signature ```python def simplifyPath(path: str) -> str: pass ``` # Note: - Handle edge cases where the path may be empty, or contain only special characters like `.` and `..`. - Ensure the function works efficiently for very large paths with many directory levels.

answer:def simplifyPath(path: str) -> str: Simplifies the given Unix-style file path and returns the canonical path. Args: path (str): The input Unix-style file path. Returns: str: The simplified canonical path. dirs = path.split('/') stack = [] for part in dirs: if part == '' or part == '.': continue elif part == '..': if stack: stack.pop() else: stack.append(part) return '/' + '/'.join(stack)

question:You have been given an array A consisting of N positive integers. Your task is to find an integer X such that it minimizes the maximum difference between X and any element of the array. Specifically, you need to find the minimum possible value for max(|A[1]-X|, |A[2]-X|, ..., |A[N]-X|). ------ Input Format ------ The first line of the input contains an integer T denoting the number of test cases. Each of the next T lines contains: - An integer N denoting the size of the array. - N space-separated integers representing the elements of the array A. ------ Output Format ------ For each test case, output a single line containing the minimum possible value of the maximum difference. ------ Constraints ------ 1 ≤ N ≤ 100,000 1 ≤ A[i] ≤ 10^9 The sum of N over all the test cases will be less than or equal to 200,000 ------ Sample Input 1 ------ 2 5 1 5 9 12 15 3 4 6 7 ------ Sample Output 1 ------ 6 1 ------ Explanation 1 ------ Testcase 1: Consider the array [1, 5, 9, 12, 15]. The optimal choice for X is 9. The maximum difference between 9 and elements of the array is: max(|1-9|, |5-9|, |9-9|, |12-9|, |15-9|) = max(8, 4, 0, 3, 6) = 8. Thus, the minimum possible value of the maximum difference is 6. Testcase 2: Consider the array [4, 6, 7]. The optimal choice for X is 6. The maximum difference between 6 and elements of the array is: max(|4-6|, |6-6|, |7-6|) = max(2, 0, 1) = 2. Thus, the minimum possible value of the maximum difference is 1.

answer:def minimize_maximum_difference(T, test_cases): Finds the integer X that minimizes the maximum difference between X and any element of the array. Args: - T: int, number of test cases - test_cases: list of tuples (N, arr), where N is the size of the array and arr is the list of integers Returns: - List of integers, each indicating the minimum possible value of the maximum difference for each test case results = [] for N, arr in test_cases: arr.sort() median_index = N // 2 if N % 2 == 0: # For even length arrays, choose the middle value for minimizing max difference best_X = (arr[median_index - 1] + arr[median_index]) // 2 else: best_X = arr[median_index] results.append(best_X) return results

question:Given a sequence of n positive integers, determine if the sequence can be transformed into a non-decreasing sequence by changing no more than one element. -----Input----- The first line contains an integer n (1 ≤ n ≤ 10^5) — the number of elements in the sequence. The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 10^9) — the sequence itself. -----Output----- Print "YES" (without the quotes) if the sequence can be transformed into a non-decreasing sequence by changing no more than one element. Otherwise print "NO". -----Examples----- Input 4 4 2 3 4 Output YES Input 5 3 4 2 3 5 Output NO Input 3 5 4 3 Output NO

answer:def can_be_non_decreasing(n, sequence): Determines if the sequence can be transformed into a non-decreasing sequence by changing no more than one element. Parameters: n (int): the number of elements in the sequence sequence (list of int): the sequence of integers Returns: str: "YES" if it can be transformed, otherwise "NO" modified = False for i in range(n - 1): if sequence[i] > sequence[i + 1]: if modified: return "NO" modified = True # Check if modifying current element or next element can resolve the issue if i == 0 or sequence[i - 1] <= sequence[i + 1]: sequence[i] = sequence[i + 1] # modify sequence[i] else: sequence[i + 1] = sequence[i] # otherwise modify sequence[i + 1] return "YES"

question:You are given an array of integers heights representing the heights of columns in a histogram. Each column is of uniform width 1. You need to find the area of the largest rectangle that can be formed within the histogram. The rectangle must be formed by the consecutive columns of the histogram and be the largest area such that it covers all columns between any two column heights specified in the histogram. Return the area of the largest rectangle in the histogram. Example 1: Input: heights = [2,1,5,6,2,3] Output: 10 Explanation: The largest rectangle can be formed with heights [5, 6], which has a total area of 5 * 2 = 10. Example 2: Input: heights = [2,4] Output: 4 Explanation: The largest rectangle can be formed with a single column of height 4. Example 3: Input: heights = [6,2,5,4,5,1,6] Output: 12 Explanation: The largest rectangle can be formed with heights [5,4,5], which has a total area of 4 * 3 = 12. Constraints: 1 <= heights.length <= 300 0 <= heights[i] <= 1000

answer:def largestRectangleArea(heights): Returns the area of the largest rectangle that can be formed within the histogram. stack = [] max_area = 0 index = 0 while index < len(heights): if not stack or heights[stack[-1]] <= heights[index]: stack.append(index) index += 1 else: top_of_stack = stack.pop() area = (heights[top_of_stack] * ((index - stack[-1] - 1) if stack else index)) max_area = max(max_area, area) while stack: top_of_stack = stack.pop() area = (heights[top_of_stack] * ((index - stack[-1] - 1) if stack else index)) max_area = max(max_area, area) return max_area