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question:Given n non-negative integers representing the height of bars of a histogram, find the area of the largest rectangle that can be formed within the bounds of the histogram. ------ Input Format ------ - The first line contains a single integer n, the number of bars in the histogram. - The second line contains n non-negative integers separated by spaces, representing the heights of the bars in the histogram. ------ Output Format ------ - Output a single integer, the area of the largest rectangle that can be formed within the bounds of the histogram. ------ Constraints ------ 1 ≤ n ≤ 10^{5} 0 ≤ height_of_bar ≤ 10^4 ----- Sample Input 1 ------ 6 2 1 5 6 2 3 ----- Sample Output 1 ------ 10 ----- Explanation 1 ------ The largest rectangle that can be formed in the histogram has an area of 10. It spans from the third bar to the fourth bar (height 5 and 6).
answer:def largest_rectangle_area(heights): Given n non-negative integers representing the height of bars of a histogram, find the area of the largest rectangle that can be formed within the bounds of 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
question:Your task is to determine whether a given string is a valid palindrome. A palindrome is a word, phrase, number, or other sequences of characters that reads the same forward and backward (ignoring spaces, punctuation, and capitalization). Create a function named `is_palindrome` that takes in a single string parameter and returns a boolean indicating whether the string is a valid palindrome. Examples: ``` is_palindrome("Able , was I saw eLba") => True is_palindrome("race a car") => False is_palindrome("Madam In Eden, I'm Adam") => True is_palindrome("No lemon, no melon") => True ``` The function should ignore spaces, punctuation, and capitalization while determining if the string is a palindrome. Consider the following points: - An empty string or a string with a single character is considered a valid palindrome. - You may use any standard libraries or helper functions to assist with cleaning and formatting the input string.
answer:import string def is_palindrome(s): Determines if a given string is a palindrome, ignoring spaces, punctuation, and capitalization. Parameters: s (str): The input string to check for palindrome Returns: bool: True if the string is a palindrome, False otherwise # Remove punctuation and spaces, and convert to lowercase cleaned_string = ''.join(char.lower() for char in s if char.isalnum()) # Check if the cleaned string is the same forwards and backwards return cleaned_string == cleaned_string[::-1]
question:Design a function to calculate the minimum number of operations needed to convert one string into another. You are only allowed to use the following three operations: 1. Insert a character. 2. Delete a character. 3. Replace a character with another character. Given two string inputs, find the minimum number of operations required to transform the first string into the second string. # Input - The first line of the input contains two space-separated strings. - Both strings will consist only of lowercase English letters and have lengths ranging from 1 to 1000. # Output - Output a single integer representing the minimum number of operations required. # Example Input ``` kitten sitting sunday saturday ``` Output ``` 3 3 ``` # Explanation 1. `kitten` to `sitting`: replace `k` with `s`, replace `e` with `i`, and insert `g` at the end (total 3 operations). 2. `sunday` to `saturday`: insert `a` after `s`, insert `t` after `a`, and insert `r` before `d` (total 3 operations). The function should be efficient with time complexity better than O(n^2). The recommended method to solve this problem is by using dynamic programming to store intermediate results and avoid redundant calculations.
answer:def minDistance(word1, word2): Returns the minimum number of operations required to convert word1 to word2. m, n = len(word1), len(word2) # Create a DP table with (m+1) x (n+1) dimension dp = [[0] * (n + 1) for _ in range(m + 1)] # Initialize the table for i in range(m + 1): dp[i][0] = i for j in range(n + 1): dp[0][j] = j # Fill the table based on the recurrence relation for i in range(1, m + 1): for j in range(1, n + 1): if word1[i - 1] == word2[j - 1]: dp[i][j] = dp[i - 1][j - 1] else: dp[i][j] = min(dp[i - 1][j] + 1, # Delete dp[i][j - 1] + 1, # Insert dp[i - 1][j - 1] + 1) # Replace return dp[m][n] # Example usage: # print(minDistance("kitten", "sitting")) # Output: 3 # print(minDistance("sunday", "saturday")) # Output: 3
question:Write a function named `reverse_diagonal_sum` that takes a square matrix (a list of lists) of integers and returns the sum of both the main diagonal and the anti-diagonal elements. The main diagonal consists of those elements that lie on the top-left to bottom-right diagonal, while the anti-diagonal consists of elements that lie on the top-right to bottom-left diagonal. Note: If the matrix is of odd dimensions, ensure that the middle element is not counted twice. -----Input----- - A single parameter: a square matrix (a list of lists) where each element is an integer. You can assume that the matrix will have a size between 1×1 and 50×50. -----Output----- - A single integer: the sum of the elements on the main diagonal and the anti-diagonal. -----Examples----- Sample Input 1: [[1, 2, 3], [4, 5, 6], [7, 8, 9]] Sample Output 1: 25 Sample Input 2: [[5, 1], [2, 8]] Sample Output 2: 16 Explanation: - In Sample Input 1, the main diagonal elements are 1, 5, 9 and the anti-diagonal elements are 3, 5, 7. The sum is 1 + 5 + 9 + 3 + 5 + 7 = 30. Since 5 is counted twice, we subtract it once to get 25. - In Sample Input 2, the main diagonal elements are 5, 8 and the anti-diagonal elements are 1, 2. The sum is 5 + 8 + 1 + 2 = 16.
answer:def reverse_diagonal_sum(matrix): This function takes a square matrix as input and returns the sum of the elements on both the main diagonal and the anti-diagonal, without double-counting the middle element if the matrix has odd dimensions. n = len(matrix) total_sum = 0 for i in range(n): total_sum += matrix[i][i] # main diagonal element total_sum += matrix[i][n-i-1] # anti-diagonal element if n % 2 == 1: middle_index = n // 2 total_sum -= matrix[middle_index][middle_index] return total_sum