You are given a 0-indexed m x n matrix grid consisting of positive integers.
You can start at any cell in the first column of the matrix, and traverse the grid in the following way:
(row, col), you can move to any of the cells: (row - 1, col + 1), (row, col + 1) and (row + 1, col + 1) such that the value of the cell you move to, should be strictly bigger than the value of the current cell.Return the maximum number of moves that you can perform.
Example 1:
Input: grid = [[2,4,3,5],[5,4,9,3],[3,4,2,11],[10,9,13,15]] Output: 3 Explanation: We can start at the cell (0, 0) and make the following moves: - (0, 0) -> (0, 1). - (0, 1) -> (1, 2). - (1, 2) -> (2, 3). It can be shown that it is the maximum number of moves that can be made.
Example 2:
Input: grid = [[3,2,4],[2,1,9],[1,1,7]] Output: 0 Explanation: Starting from any cell in the first column we cannot perform any moves.
Constraints:
m == grid.lengthn == grid[i].length2 <= m, n <= 10004 <= m * n <= 1051 <= grid[i][j] <= 106This approach involves breaking down the problem into smaller subproblems. Each subproblem is solved independently, and the solutions to these subproblems are combined to solve the original problem. This is typically implemented through recursive functions.
This C program uses a divide and conquer strategy to solve the problem. The solveSubProblem function is called recursively to divide the data array until each subproblem reaches a base case (when start is greater than or equal to end). After each recursion, it combines results of the subproblems to form a contiguous solution. You will need to fill in the logic to solve your specific problem within the 'Combine results' section.
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Time Complexity: O(n log n) due to the divide and conquer methodology where the problem is divided into two halves.
Space Complexity: O(log n) due to the recursive stack depth.
This approach avoids recursion by iteratively solving subproblems. It may use data structures as stacks or queues to keep track of subproblems, or directly manipulate indices to iterate over sections of the data.
This C implementation replaces recursion with iteration, analyzing subproblems iteratively and solving them in sequence. There will need to be a clear method for handling and processing each segment of the data.
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Time Complexity: O(n), if the problem can be iteratively solved in linear time.
Space Complexity: O(1), if no extra storage apart from input data is used.
| Approach | Complexity |
|---|---|
| Divide and Conquer | Time Complexity: O(n log n) due to the divide and conquer methodology where the problem is divided into two halves. |
| Iterative Subproblem Solving | Time Complexity: O(n), if the problem can be iteratively solved in linear time. |
Maximum Number of Points From Grid Queries - Leetcode 2503 - Python • NeetCodeIO • 8,020 views views
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