702879. Swap and Maximize
Here is a detailed Markdown blog post for the "Swap and Maximize" problem:
Swap and Maximize
Summary
The "Swap and Maximize" problem involves given an array of integers, swapping adjacent elements to maximize the sum of the array. The goal is to find the maximum possible sum by swapping elements in the array.
This problem involves algorithms related to arrays, greedy, sorting, and data structures.
Detailed Explanation
To solve this problem, we can use a simple algorithm that iterates through the array, keeping track of the maximum sum found so far. When an adjacent pair of elements is found that would increase the total sum if swapped, the swap is performed.
Here's a step-by-step breakdown of the solution:
- Initialize a variable
max_sumto store the maximum sum found so far. - Iterate through the array, keeping track of the current sum.
- For each pair of adjacent elements, calculate the sum if they are swapped.
- If the swapped sum is greater than the current
max_sum, updatemax_sumand perform the swap. - Repeat steps 2-4 until the end of the array is reached.
The time complexity for this algorithm is O(n), where n is the length of the array, since we need to iterate through each element once. The space complexity is O(1) because we only use a constant amount of space to store max_sum and other variables.
Here's an ASCII art diagram showing the swapping process:
[5, 3, 2, 7]
swap 3 and 2: [5, 2, 3, 7]
swap 2 and 7: [5, 7, 3, 2]
max_sum = 17
Optimized Solutions
Java
public int maxSum(int[] arr) {
int max_sum = 0;
for (int i = 1; i < arr.length; i++) {
if (arr[i] > arr[i-1]) {
int temp = arr[i];
arr[i] = arr[i-1];
arr[i-1] = temp;
max_sum += arr[i] - arr[i-1];
}
}
return max_sum;
}