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The softmax function turns a list of scores (logits) into probabilities. Language models use it to choose the next word:
softmax(x)_i = e^(x_i) / (e^(x_1) + e^(x_2) + … + e^(x_n))
Large scores make e^x overflow, so first subtract the largest score from every score. The result is mathematically the same.
Implement softmax(logits).
Input
logits: A list of scores.
Output
Return the list of probabilities, in the same order. They are all between 0 and 1 and add up to 1.
Constraints
1 ≤ length ≤ 1,000
-1,000 ≤ each score ≤ 1,000
Examples
Example 1
Input:
logits = [1.0, 2.0, 3.0]
Expected output:
[0.090031, 0.244728, 0.665241]Explanation
e¹ ≈ 2.718, e² ≈ 7.389 and e³ ≈ 20.086 add up to 30.193, so the probabilities are about [0.090031, 0.244728, 0.665241].
Example 2
Input:
logits = [1000.0, 1000.0]
Expected output:
[0.5, 0.5]Explanation
Computing e^1000 directly overflows. Subtracting the maximum gives [0, 0], and e⁰ / (e⁰ + e⁰) = 0.5 for both.
References
-
Example 1 Not runInput:
logits = [1.0, 2.0, 3.0]Expected output:[0.090031, 0.244728, 0.665241]Your output -
Example 2 Not runInput:
logits = [1000.0, 1000.0]Expected output:[0.5, 0.5]Your output
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💡 Swift Basics Guide for Beginners
1. Declaring Variables and Constants
Use var for variables and let for constants in Swift.
var age = 30
let pi = 3.14159
var name = "Alice"
let isActive = true
// Constants cannot be reassigned
// pi = 3.14 // ❌ Error2. Conditionals (if / switch)
Use if, else if, else for logic, and switch for multiple branches.
let number = 2
if number == 1 {
print("One")
} else if number == 2 {
print("Two")
} else {
print("Other")
}
switch number {
case 1:
print("One")
case 2:
print("Two")
default:
print("Other")
}3. Loops
Swift supports for-in, while, and repeat-while loops.
for i in 0..<3 {
print(i)
}
var n = 3
while n > 0 {
print(n)
n -= 1
}4. Arrays
Arrays store ordered collections of values.
var numbers = [10, 20, 30]
print(numbers[1])5. Array Manipulation
Use array methods like append and removeLast.
var nums = [1, 2, 3]
nums.append(4)
nums.removeLast()
for n in nums {
print(n)
}6. Console Input/Output
Use print() for output. Input requires additional work in Swift Playgrounds or Xcode.
let name = "Alice"
print("Hello, \(name)")7. Functions
Define reusable functions with parameters and return values.
func add(a: Int, b: Int) -> Int {
return a + b
}
print(add(a: 3, b: 4))8. Dictionaries
Dictionaries store key-value pairs.
var ages = ["Alice": 30]
print(ages["Alice"] ?? 0)9. Error Handling
Swift uses do-catch for error handling.
enum MyError: Error {
case runtimeError(String)
}
do {
throw MyError.runtimeError("Something went wrong")
} catch let error {
print(error)
}10. File I/O
Swift uses FileManager or String methods for file I/O.
let text = "Hello File"
try text.write(toFile: "file.txt", atomically: true, encoding: .utf8)
let content = try String(contentsOfFile: "file.txt")
print(content)11. String Manipulation
Use methods like count, contains, uppercased(), etc.
let text = "Hello World"
print(text.count)
print(text.contains("World"))
print(text.uppercased())12. Classes & Objects
Swift supports OOP using class and init.
class Person {
var name: String
init(name: String) {
self.name = name
}
func greet() {
print("Hi, I'm \(name)")
}
}
let p = Person(name: "Alice")
p.greet()13. Optionals
Swift uses ? and ! to handle optional values.
var name: String? = "Alice"
print(name ?? "Unknown")
if let unwrappedName = name {
print(unwrappedName)
}