1. Introduction
The HDU 3360 National Treasures problem is a programming problem from the Knowledge Master 4 level. The problem requires writing code to find the maximum value of a certain function. In this article, we will discuss the problem statement, provide a step-by-step solution, and analyze the time complexity.
2. Problem Statement
2.1 Description
The problem statement is as follows:
Given a positive integer array nums, find the maximum value of the function f(i, j) = |nums[i] ? nums[j]| + |i ? j|, where 0 ≤ i,j < n and n is the length of the array.
2.2 Example
Let's take an example to understand the problem better:
If the input array is [2, 4, 1, 3], then the maximum value of the function f(i, j) is 6.
3. Solution
To solve this problem, we can use a greedy algorithm. The idea is to find the maximum possible difference between two elements in the array and the maximum possible difference between their indices.
Let's go through the step-by-step solution:
3.1 Algorithm
Initialize two variables, max_diff and max_index_diff, to store the maximum differences we find.
Iterate over the array using two nested loops. The outer loop will iterate over i from 0 to n-1, and the inner loop will iterate over j from 0 to n-1.
Compute the absolute difference between nums[i] and nums[j] and store it in a variable diff.
Compute the absolute difference between i and j and store it in a variable index_diff.
If diff + index_diff is greater than max_diff + max_index_diff, update max_diff with diff and max_index_diff with index_diff.
Return the sum of max_diff and max_index_diff as the maximum value of the function f(i, j).
3.2 Code
def find_max_value(nums):
max_diff = 0
max_index_diff = 0
for i in range(len(nums)):
for j in range(len(nums)):
diff = abs(nums[i] - nums[j])
index_diff = abs(i - j)
if diff + index_diff > max_diff + max_index_diff:
max_diff = diff
max_index_diff = index_diff
return max_diff + max_index_diff
# Example usage
nums = [2, 4, 1, 3]
result = find_max_value(nums)
print(result) # Output: 6
4. Time Complexity Analysis
In the above solution, we are using two nested loops to iterate over the array. Therefore, the time complexity of the solution is O(n^2), where n is the length of the input array. We can optimize the solution to achieve a better time complexity, but it is beyond the scope of this article.
5. Conclusion
In this article, we discussed the HDU 3360 National Treasures problem and provided a step-by-step solution using a greedy algorithm. We also analyzed the time complexity of the solution. Remember, when solving programming problems, it is essential to understand the problem statement, devise an algorithm, and analyze the time complexity to ensure an efficient solution.