import Foundation
/*
Goal:
-----
Find the minimal value of (a[i] + a[j]) for any two distinct elements in an array.
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 array 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.
func minimalTwoSum(_ arr: [Int]) throws -> Int {
// Handle edge case: need at least two elements
if arr.count < 2 {
throw NSError(domain: "MinimalTwoSumError",
code: 1,
userInfo: [NSLocalizedDescriptionKey: "Array must contain at least two elements."])
}
// Initialize min1 and min2 to very large values
var min1: Int = Int.max
var min2: Int = Int.max
// Single pass through the array
for x in arr {
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
}
let arr: [Int] = [7, -3, 10, 1, 5, 2, 4]
do {
let result = try minimalTwoSum(arr)
print("Minimal sum of two elements: \(result)")
} catch {
print("Error: \(error.localizedDescription)")
}
/*
run:
Minimal sum of two elements: -2
*/
