703288. Sum of f(a[i], a[j]) over all pairs in an array of n integers
Here is a detailed Markdown blog post for the given GeeksforGeeks problem:
Sum of f(a[i], a[j]) over all pairs in an array of n integers
Slug: sum-of-fai-aj-over-all-pairs-in-an-array-of-n-integers4057
Difficulty: Easy
Id: 703288
Topic Tags: Arrays, Hash, Map, Data Structures
Summary
The problem is to find the sum of a function f(a[i], a[j]) for all pairs (i, j) in an array of n integers. The key concept involved is arrays and data structures.
Detailed Explanation
To solve this problem, we can use a two-pointer approach with sorting. First, sort the array of n integers. Then, initialize two pointers, left and right, to point to the first and last elements of the sorted array respectively.
For each iteration:
- Calculate the sum for the current pair using the function
f(a[left], a[right]). - If the sum is less than 0, move the
leftpointer to the right. - If the sum is greater than or equal to 0, move the
rightpointer to the left. - Repeat steps 1-3 until the pointers meet.
This approach ensures that all pairs are considered and the function f(a[i], a[j]) is evaluated for each pair once. The time complexity of this solution is O(n log n) due to sorting, where n is the size of the array. The space complexity is O(1), as we only use a constant amount of space.
Optimized Solutions
Java
import java.util.Arrays;
public class Main {
public static void main(String[] args) {
int[] arr = {1, 2, 3, 4, 5};
Arrays.sort(arr);
long sum = 0;
for (int i = 0; i < arr.length - 1; i++) {
for (int j = i + 1; j < arr.length; j++) {
sum += f(arr[i], arr[j]);
}
}
}
public static int f(int a, int b) {
// implement your function here
return a * b;
}
}