Alice and Bob are playing a turn-based game on a circular field surrounded by flowers. The circle represents the field, and there are x flowers in the clockwise direction between Alice and Bob, and y flowers in the anti-clockwise direction between them.
The game proceeds as follows:
Given two integers, n and m, the task is to compute the number of possible pairs (x, y) that satisfy the conditions:
x in the clockwise direction must be in the range [1,n].y in the anti-clockwise direction must be in the range [1,m].Return the number of possible pairs (x, y) that satisfy the conditions mentioned in the statement.
Example 1:
Input: n = 3, m = 2 Output: 3 Explanation: The following pairs satisfy conditions described in the statement: (1,2), (3,2), (2,1).
Example 2:
Input: n = 1, m = 1 Output: 0 Explanation: No pairs satisfy the conditions described in the statement.
Constraints:
1 <= n, m <= 105This approach uses a stack to efficiently manage and keep track of the states required to solve the problem. The stack data structure is ideal here due to its LIFO (Last In, First Out) nature, which allows for easy reversal and state management. This is useful in scenarios like parsing nested structures or evaluating expressions.
This C code implements a stack using an array. The push function adds an element to the top of the stack, and the pop function removes and returns the top element. Array-based stacks are straightforward but require a predefined maximum size.
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Time Complexity: O(1) for both push and pop operations.
Space Complexity: O(n) where n is the maximum stack size.
This approach leverages recursion to handle the inherent hierarchical or nested nature of the problem. Recursive solutions are elegant and allow the function call stack to manage state, thus abstracting it away from the programmer.
This C code uses a recursive function to print numbers from n down to 1. Recursive calls decrement the counter n until the base case is reached, demonstrating a simple recursive pattern.
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Time Complexity: O(n) where n is the value passed to the function.
Space Complexity: O(n) due to the recursion call stack.
| Approach | Complexity |
|---|---|
| Approach 1: Using a Stack to Manage State | Time Complexity: O(1) for both push and pop operations. |
| Approach 2: Using Recursion to Simplify State Management | Time Complexity: O(n) where n is the value passed to the function. |
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