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How can I design a custom Java data structure that combines stack and queue functionalities, and how can I find the minimum path cost in a grid using dynamic programming?

Answer:

To design a custom Java data structure combining stack and queue functionalities, use Java's LinkedList. Implement push(value) and pop() methods for stack operations, and enqueue(value) and dequeue() for queue operations. Both sets of operations are efficiently handled with O(1) time complexity using LinkedList, which supports adding and removing elements from both ends.

For finding the minimum path cost in a grid, use dynamic programming. Create a 2D array to store minimum costs. Initialize the top-left cell and fill the first row and column with cumulative sums. Then, update each cell with the minimum cost to reach it from either the cell above or the cell to the left.

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