Leetcode 2769: Find the Maximum Achievable Number
Given two integers num and t, determine the maximum achievable number after performing at most t operations, where each operation allows simultaneous increments or decrements of num and the target number by 1.
Problem
Approach
Steps
Complexity
Input: The input consists of two integers num and t.
Example: Input: num = 5, t = 2
Constraints:
• 1 <= num, t <= 50
Output: Return the maximum achievable number after at most t operations.
Example: Output: 9 for num = 5, t = 2
Constraints:
• Output is a single integer representing the maximum achievable number.
Goal: Compute the maximum achievable number after at most t operations.
Steps:
• The maximum achievable number is equal to num + 2 * t.
• Each operation increases both the number and num by 1 or decreases both by 1.
Goal: Ensure the solution adheres to the problem's constraints for num and t.
Steps:
• 1 <= num, t <= 50
Assumptions:
• The values of num and t are positive integers.
• Operations are limited to increasing or decreasing both num and the number simultaneously.
• Input: Input: num = 5, t = 2
• Explanation: After two operations, the maximum achievable number is 9. Each operation increases num and the target number by 1.
• Input: Input: num = 2, t = 3
• Explanation: After three operations, the maximum achievable number is 8. Each operation increases num and the target number by 1.
Approach: The solution calculates the maximum achievable number using a direct mathematical formula based on the given constraints.
Observations:
• Each operation allows the target number to diverge from num by at most 2 units per operation.
• The problem can be solved using simple arithmetic.
• The maximum achievable number is calculated as num + 2 * t.
Steps:
• Given num and t, compute the maximum achievable number as num + 2 * t.
• No iteration is needed; use direct computation.
Empty Inputs:
• Not applicable, as num and t are always provided.
Large Inputs:
• Test for maximum values of num = 50 and t = 50 to ensure correctness.
Special Values:
• Smallest values of num = 1 and t = 1.
Constraints:
• Ensure no invalid input scenarios.
int theMaximumAchievableX(int num, int t) {
return num + 2 * t;
}
1 : Function Definition
int theMaximumAchievableX(int num, int t) {
Defines the function `theMaximumAchievableX`, which takes two integers `num` and `t` as input and calculates the maximum achievable value by adding twice `t` to `num`.
2 : Return Statement
return num + 2 * t;
Calculates the result by adding `2 * t` to `num` and returns this value as the output of the function.
Best Case: O(1)
Average Case: O(1)
Worst Case: O(1)
Description: The computation involves a single arithmetic operation.
Best Case: O(1)
Worst Case: O(1)
Description: No additional space is required beyond input storage.
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