HDU 3360 National Treasures(KM,4级)

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.

免责声明:本文来自互联网,本站所有信息(包括但不限于文字、视频、音频、数据及图表),不保证该信息的准确性、真实性、完整性、有效性、及时性、原创性等,版权归属于原作者,如无意侵犯媒体或个人知识产权,请来电或致函告之,本站将在第一时间处理。猿码集站发布此文目的在于促进信息交流,此文观点与本站立场无关,不承担任何责任。

后端开发标签