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question:You are given a 2D grid of size n x m filled with integers. Your task is to answer q queries of the following forms: * 1 x y val — update the value at position (x, y) in the grid to val. * 2 x1 y1 x2 y2 — find the sum of all values in the subgrid that spans from (x1, y1) to (x2, y2), inclusive. To accommodate the queries efficiently, you will process the updates and queries using a data structure that allows dynamic modifications and range sum queries. Input The first line contains three integers n (1 ≤ n ≤ 1000), m (1 ≤ m ≤ 1000), and q (1 ≤ q ≤ 100000) — the dimensions of the grid and the number of queries, respectively. The next n lines contain m integers each, representing the initial values of the grid cells. Each of the next q lines describes one of the two types of queries: * 1 x y val (1 ≤ x ≤ n, 1 ≤ y ≤ m, -10^9 ≤ val ≤ 10^9). * 2 x1 y1 x2 y2 (1 ≤ x1 ≤ x2 ≤ n, 1 ≤ y1 ≤ y2 ≤ m). Output For each query of the second type, print a single line with the sum of the values in the specified subgrid. Example Input 3 3 5 1 2 3 4 5 6 7 8 9 2 1 1 2 2 1 2 2 10 2 1 1 2 2 2 2 2 3 3 1 3 3 -5 2 1 1 3 3 Output 12 19 27 52 Explanation - Initial grid: 1 2 3 4 5 6 7 8 9 - Query 1: Sum of subgrid (1,1) to (2,2) is 1+2+4+5 = 12. - Query 2: Update cell (2,2) to 10. - Grid after update: 1 2 3 4 10 6 7 8 9 - Query 3: Sum of subgrid (1,1) to (2,2) is 1+2+4+10 = 17. - Query 4: Sum of subgrid (2,2) to (3,3) is 10+6+8+9 = 33. - Query 5: Update cell (3,3) to -5. - Grid after update: 1 2 3 4 10 6 7 8 -5 - Query 6: Sum of subgrid (1,1) to (3,3) is 1+2+3+4+10+6+7+8-5 = 36.
answer:class Grid: def __init__(self, n, m, grid): self.n = n self.m = m self.grid = grid self.prefix_sum = [[0] * (m + 1) for _ in range(n + 1)] self._build_prefix_sum() def _build_prefix_sum(self): for i in range(1, self.n + 1): for j in range(1, self.m + 1): self.prefix_sum[i][j] = self.grid[i-1][j-1] + self.prefix_sum[i-1][j] + self.prefix_sum[i][j-1] - self.prefix_sum[i-1][j-1] def update_value(self, x, y, val): original_val = self.grid[x-1][y-1] self.grid[x-1][y-1] = val diff = val - original_val for i in range(x, self.n + 1): for j in range(y, self.m + 1): self.prefix_sum[i][j] += diff def get_subgrid_sum(self, x1, y1, x2, y2): return (self.prefix_sum[x2][y2] - self.prefix_sum[x1-1][y2] - self.prefix_sum[x2][y1-1] + self.prefix_sum[x1-1][y1-1]) # Process input, build the grid and execute the queries def process_queries(n, m, q, grid_values, queries): results = [] grid = Grid(n, m, grid_values) for query in queries: if query[0] == 1: _, x, y, val = query grid.update_value(x, y, val) elif query[0] == 2: _, x1, y1, x2, y2 = query results.append(grid.get_subgrid_sum(x1, y1, x2, y2)) return results
question:A "Brackets Balance" problem is a string problem where you need to determine if the brackets in the given string are balanced. The string contains three types of brackets: (), {}, and []. The brackets must close in the correct order, i.e., an opening bracket must be closed by the same type of bracket and in the correct order. Input The first line of the input is an integer T (1 ≤ T ≤ 100), the number of test cases. Each test case consists of a single line of input which is a non-empty string containing only the characters '(', ')', '{', '}', '[' and ']'. Output For each test case, print "YES" if the given string has balanced brackets, otherwise print "NO". Explanation for sample Input/Output For the 1st test case the string "([])" has balanced brackets. For the 2nd test case the string "([)]" has unbalanced brackets. SAMPLE INPUT 5 ([]) ([)] {{[[(())]]}} [] [{()}()] SAMPLE OUTPUT YES NO YES YES YES
answer:def is_balanced(s): Determines if the brackets in the string are balanced. stack = [] bracket_map = {")": "(", "}": "{", "]": "["} for char in s: if char in bracket_map.values(): stack.append(char) elif char in bracket_map.keys(): if stack == [] or stack.pop() != bracket_map[char]: return "NO" return "YES" if stack == [] else "NO" def bracket_balance(T, test_cases): Processes multiple test cases to determine if each has balanced brackets. results = [] for test in test_cases: results.append(is_balanced(test)) return results
question:A farmer is interested in the production of apples in his orchard. Each apple tree in the orchard produces a fixed number of apples every year. The farmer can collect apples from each tree only once a year. Given the number of trees in the orchard (N) and a list that represents the number of apples each tree produces (an array of N integers), determine the total number of apples the farmer can collect in a year. -----Constraints----- - All values in input are integers. - 1 leq N leq 100 - 1 leq Number of apples produced by each tree leq 1000 -----Input----- Input is given from Standard Input in the following format: N a_1 a_2 a_3 ... a_N -----Output----- Print the total number of apples the farmer can collect in a year. -----Sample Input----- 5 10 20 15 25 30 -----Sample Output----- 100
answer:def total_apples_collected(N, apples): Calculate the total number of apples collected from the orchard. Args: N (int): The number of trees in the orchard. apples (list of int): A list representing the number of apples each tree produces. Returns: int: The total number of apples collected. return sum(apples) # Example usage: # N = 5 # apples = [10, 20, 15, 25, 30] # print(total_apples_collected(N, apples)) # Output: 100
question:Design a function that, given a positive integer ( N ) and an array of ( N ) integers, returns the length and elements of the longest increasing subsequence within that array. An increasing subsequence is a sequence of indices such that for all ( i ) and ( j ) in the sequence, if ( i < j ) then ( text{array}[i] < text{array}[j] ). -----Input:----- The first line of the input is a positive integer ( N ) indicating the length of the array. The next line contains ( N ) integers separated by spaces representing the elements of the array. -----Output:----- The first line of the output must contain a single integer ( L ) denoting the length of the longest increasing subsequence. The second line should contain ( L ) integers separated by spaces representing the elements of the longest increasing subsequence. If there are multiple longest increasing subsequences, any one of them can be returned. -----Constraints:----- - ( 1 leq N leq 1000 ) - (-10^5 leq text{array}[i] leq 10^5) -----Sample input 1:----- 6 5 2 8 6 3 6 -----Sample output 1:----- 3 2 3 6 -----Sample input 2:----- 5 1 3 2 4 5 -----Sample output 2:----- 4 1 2 4 5 -----Sample input 3:----- 5 9 8 7 6 5 -----Sample output 3:----- 1 9
answer:def longest_increasing_subsequence(N, array): Returns the length and the elements of the longest increasing subsequence in the given array. Args: N : int : length of the array array : list of int : input array Returns: length : int : length of the longest increasing subsequence subseq : list of int : the longest increasing subsequence if N == 0: return 0, [] dp = [1] * N parent = [-1] * N for i in range(1, N): for j in range(0, i): if array[i] > array[j] and dp[i] < dp[j] + 1: dp[i] = dp[j] + 1 parent[i] = j length = max(dp) index = dp.index(length) subseq = [] while index != -1: subseq.append(array[index]) index = parent[index] subseq.reverse() return length, subseq