import java.util.List;
import java.util.Arrays;
/**
Goal:
-----
Find the minimal value of (a[i] + a[j]) for any two distinct elements in a list.
Efficient Strategy (O(n)):
--------------------------
The smallest possible sum of two distinct elements is obtained by:
- finding the smallest element
- finding the second smallest element
Because any other pair must be >= one of these two.
We scan the list once, keeping track of:
- min1 = smallest element seen so far
- min2 = second smallest element seen so far
*/
// A function that computes the minimal sum of two distinct elements.
public class MinimalTwoSum {
public static int minimal_two_sum(List<Integer> lst) {
// Handle edge case: need at least two elements
if (lst.size() < 2) {
throw new IllegalArgumentException("List must contain at least two elements.");
}
// Initialize min1 and min2 to very large values
int min1 = Integer.MAX_VALUE;
int min2 = Integer.MAX_VALUE;
// Single pass through the list
for (int x : lst) {
if (x < min1) {
// x becomes the new smallest; old min1 becomes min2
min2 = min1;
min1 = x;
} else if (x < min2) {
// x is not the smallest, but smaller than the second smallest
min2 = x;
}
}
// The minimal sum of two distinct elements
return min1 + min2;
}
public static void main(String[] args) {
List<Integer> lst = Arrays.asList(7, -3, 10, 1, 5, 2, 4);
try {
int result = minimal_two_sum(lst);
System.out.println("Minimal sum of two elements: " + result);
} catch (Exception e) {
System.err.println("Error: " + e.getMessage());
}
}
}
/*
run:
Minimal sum of two elements: -2
*/
