Given an array arr[] of N integers and Q queries of the form {X, Y} of the following two types:
- If X = 1, rotate the given array to the left by Y positions.
- If X = 2, print the maximum sum subarray of length Y in the current state of the array.
Examples:
Input: N = 5, arr[] = {1, 2, 3, 4, 5}, Q = 2, Query[][] = {{1, 2}, {2, 3}}
Output:
Query 1: 3 4 5 1 2
Query 2: 12
Explanation:
Query 1: Shift array to the left 2 times: {1, 2, 3, 4, 5} -> {2, 3, 4, 5, 1} -> {3, 4, 5, 1, 2}
Query 2: Maximum sum subarray of length 3 is {3, 4, 5} and the sum is 12Input: N = 5, arr[] = {3, 4, 5, 1, 2}, Q = 3, Query[][] = {{1, 3}, {1, 1}, {2, 4}}
Output:
Query 1: 1 2 3 4 5
Query 2: 2 3 4 5 1
Query 3: 14
Explanation:
Query 1: Shift array to the left 3 times: {3, 4, 5, 1, 2} -> {4, 5, 1, 2, 3} -> {5, 1, 2, 3, 4} -> {1, 2, 3, 4, 5}
Query 2: Shift array to the left 1 time: {1, 2, 3, 4, 5} -> {2, 3, 4, 5, 1}
Query 3: Maximum sum subarray of length 4 is {2, 3, 4, 5} and sum is 14
Naive Approach: The simplest approach is to rotate the array by shifting elements one by one up to distance Y for queries is of type 1 and generating the sum of all the subarrays of length Y and print the maximum sum if the query is of type 2.
Time Complexity: O(Q*N*Y)
Auxiliary Space: O(N)
Efficient Approach: To optimize the above approach, the idea is to use the Juggling Algorithm for array rotation and for finding the maximum sum subarray of length Y, use the Sliding Window Technique. Follow the steps below to solve the problem:
- If X = 1, rotate the array by Y, using the Juggling Algorithm.
- Otherwise, if X = 2, find the maximum sum subarray of length Y using the Sliding Window Technique.
- Print the array if query X is 1.
- Otherwise, print the maximum sum subarray of size Y.
Below is the implementation of the above approach:
Python3
# Python3 program for the above approach # Function to calculate the maximum # sum of length k def MaxSum(arr, n, k): i, max_sum = 0, 0 sum = 0 # Calculating the max sum for # the first k elements while i < k: sum += arr[i] i += 1 max_sum = sum # Find subarray with maximum sum while (i < n): # Update the sum sum = sum - arr[i - k] + arr[i] if (max_sum < sum): max_sum = sum i += 1 # Return maximum sum return max_sum # Function to calculate gcd of the # two numbers n1 and n2 def gcd(n1, n2): # Base Case if (n2 == 0): return n1 # Recursively find the GCD else: return gcd(n2, n1 % n2) # Function to rotate the array by Y def RotateArr(arr, n, d): # For handling k >= N i = 0 j = 0 d = d % n # Dividing the array into # number of sets no_of_sets = gcd(d, n) for i in range(no_of_sets): temp = arr[i] j = i # Rotate the array by Y while (True): k = j + d if (k >= n): k = k - n if (k == i): break arr[j] = arr[k] j = k # Update arr[j] arr[j] = temp # Return the rotated array return arr # Function that performs the queries # on the given array def performQuery(arr, Q, q): N = len(arr) # Traverse each query for i in range(q): # If query of type X = 1 if (Q[i][0] == 1): arr = RotateArr(arr, N, Q[i][1]) # Print the array for t in arr: print(t, end = " ") print() # If query of type X = 2 else: print(MaxSum(arr, N, Q[i][1])) # Driver Code if __name__ == '__main__': # Given array arr[] arr = [ 1, 2, 3, 4, 5 ] q = 5 # Given Queries Q = [ [ 1, 2 ], [ 2, 3 ], [ 1, 3 ], [ 1, 1 ], [ 2, 4 ] ] # Function call performQuery(arr, Q, q) # This code is contributed by mohit kumar 29 |
3 4 5 1 2 12 1 2 3 4 5 2 3 4 5 1 14
Time Complexity: O(Q*N), where Q is the number of queries, and N is the size of the given array.
Auxiliary Space: O(N)
Please refer complete article on Queries to find maximum sum contiguous subarrays of given length in a rotating array for more details!
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