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question:Given an array of integers representing the heights of hills on a hiking trail, you need to find the minimum stamina required to complete the hike without the stamina dropping below 1 at any point. Each element in the array represents the change in height between two consecutive hills. Positive numbers indicate an uphill climb (which decreases stamina), and negative numbers indicate a downhill descent (which increases stamina). The stamina decreases by the height difference when going uphill and increases by the height difference when going downhill. Example 1: Input N = 5 H[] = {2, -1, 4, -3, 2} Output 6 Explanation With an initial stamina of 6, the hiker's stamina will be as follows: - Start with 6 - 6 - 2 (first uphill) = 4 - 4 + 1 (first downhill) = 5 - 5 - 4 (second uphill) = 1 - 1 + 3 (second downhill) = 4 - 4 - 2 (third uphill) = 2 The stamina never drops below 1. Example 2: Input N = 4 H[] = {1, -2, 1, -1} Output 2 Explanation With an initial stamina of 2, the hiker's stamina will be as follows: - Start with 2 - 2 - 1 (first uphill) = 1 - 1 + 2 (first downhill) = 3 - 3 - 1 (second uphill) = 2 - 2 + 1 (second downhill) = 3 The stamina never drops below 1. Your Task: You don't need to print anything, printing is done by the driver code itself. You need to complete the function minStamina() which takes the array H[] and its size N as inputs and returns the minimum initial stamina required to complete the hike. Expected Time Complexity: O(N) Expected Auxiliary Space: O(1) Constraints: 1 ≤ N ≤ 10^5 -10^3 ≤ H[i] ≤ 10^3
answer:def min_stamina(N, H): current_stamina = 1 minimum_stamina = 1 for change in H: current_stamina -= change if current_stamina < 1: minimum_stamina += (1 - current_stamina) current_stamina = 1 return minimum_stamina
question:You are given an array of integers and a list of queries. Each query consists of a starting index and an ending index. For each query, determine the sum of the integers within that range, inclusive. Input: First line contains two integers N and Q, where N is the number of integers in the array and Q is the number of queries. Second line contains N space-separated integers representing the array. Following Q lines each contain two integers L and R representing the starting and ending indices for the query (0-based indexing). Output: For each query, output the sum of the integers from index L to index R, inclusive. Constraints: 1 ≤ N ≤ 10^5 1 ≤ Q ≤ 10^4 -10^4 ≤ Array[i] ≤ 10^4 0 ≤ L ≤ R < N Sample Input: 5 3 1 2 3 4 5 0 2 1 3 2 4 Sample Output: 6 9 12
answer:def range_sum_queries(n, arr, queries): Returns a list of sums for each query. :param n: int - The number of integers in the array :param arr: list - The array of integers :param queries: list of tuples - Each tuple contains starting and ending indices (L, R) for the query :return: list - Sums for each query # Calculate prefix sums prefix_sums = [0] * (n + 1) for i in range(n): prefix_sums[i + 1] = prefix_sums[i] + arr[i] # Calculate sum for each query results = [] for l, r in queries: results.append(prefix_sums[r + 1] - prefix_sums[l]) return results def parse_input(input_str): data = input_str.strip().split('n') n, q = map(int, data[0].split()) arr = list(map(int, data[1].split())) queries = [] for i in range(2, 2 + q): l, r = map(int, data[i].split()) queries.append((l, r)) return n, arr, queries def solve(input_str): n, arr, queries = parse_input(input_str) results = range_sum_queries(n, arr, queries) return 'n'.join(map(str, results))
question:A hiking trail is represented as a sequence of coordinates (x_1, y_1), (x_2, y_2), ..., (x_n, y_n). You need to determine whether this trail ever crosses itself. Crossing is defined as two line segments (x_i, y_i) to (x_{i+1}, y_{i+1}) and (x_j, y_j) to (x_{j+1}, y_{j+1}) having an intersection point, where j neq i and j neq i-1. -----Input----- The input consists of several lines. The first line contains a single integer n (2 leq n leq 1000), the number of coordinates. Each of the next n lines contains two space-separated integers, representing the coordinates x and y (-10000 leq x, y leq 10000). -----Output----- Print "Yes" if the trail crosses itself, otherwise print "No". -----Examples----- Sample Input 1: 4 1 1 2 3 3 1 1 2 Sample Output 1: Yes Sample Input 2: 5 0 0 1 1 2 2 1 3 0 2 Sample Output 2: No
answer:def does_trail_cross(n, coordinates): def ccw(A, B, C): return (C[1] - A[1]) * (B[0] - A[0]) > (B[1] - A[1]) * (C[0] - A[0]) def intersect(A, B, C, D): return ccw(A, C, D) != ccw(B, C, D) and ccw(A, B, C) != ccw(A, B, D) for i in range(n - 1): for j in range(i - 1): if intersect(coordinates[i], coordinates[i + 1], coordinates[j], coordinates[j + 1]): return "Yes" return "No" # Example Usage: # n = 4 # coordinates = [(1, 1), (2, 3), (3, 1), (1, 2)] # print(does_trail_cross(n, coordinates)) # Output: "Yes"
question:Leila loves playing games that involve manipulating arrays. Recently, she came across an interesting problem, and now she is challenging you to solve it. Leila has an array of integers `a` of size `n`. She wants to make all the elements of the array equal. In one operation, she can choose two consecutive elements of the array and increase or decrease both of them by 1. Your task is to determine whether it is possible to make all the elements equal using the described operations, and if so, find the minimum number of operations required. A key observation here is that it is only possible if the difference between any two elements of the array is even. -----Input----- - The first line contains a single integer `n` (1 ≤ n ≤ 1000) — the size of the array. - The second line contains `n` integers `a[i]` (1 ≤ a[i] ≤ 1000) — the elements of the array. -----Output----- - If it is not possible to make all the elements of the array equal, print `-1`. - Otherwise, print a single integer representing the minimum number of operations required. -----Examples----- Input 3 4 6 8 Output 2 Input 4 3 7 5 9 Output 4 Input 3 1 2 3 Output -1
answer:def min_operations_to_equalize(n, a): Returns the minimum number of operations required to make all elements of the array equal, or -1 if it is not possible to make all the elements equal. Parameters: n (int): Size of the array. a (list): The elements of the array. Returns: int: Minimum number of operations required or -1 if it is not possible. # Check if there are any two elements with difference not even initial_parity = a[0] % 2 for num in a: if num % 2 != initial_parity: return -1 # Calculate the number of operations required to make all elements equal to the median a_sorted = sorted(a) median = a_sorted[n // 2] operations = sum(abs(x - median) // 2 for x in a) return operations