2979-MostExpensiveItemThatCanNotBeBought.go

package main

// 2979. Most Expensive Item That Can Not Be Bought
// You are given two distinct prime numbers primeOne and primeTwo.

// Alice and Bob are visiting a market. 
// The market has an infinite number of items, for any positive integer x there exists an item whose price is x. 
// Alice wants to buy some items from the market to gift to Bob. 
// She has an infinite number of coins in the denomination primeOne and primeTwo. 
// She wants to know the most expensive item she can not buy to gift to Bob.

// Return the price of the most expensive item which Alice can not gift to Bob.

// Example 1:
// Input: primeOne = 2, primeTwo = 5
// Output: 3
// Explanation: The prices of items which cannot be bought are [1,3]. 
// It can be shown that all items with a price greater than 3 can be bought using a combination of coins of denominations 2 and 5.

// Example 2:
// Input: primeOne = 5, primeTwo = 7
// Output: 23
// Explanation: The prices of items which cannot be bought are [1,2,3,4,6,8,9,11,13,16,18,23]. 
// It can be shown that all items with a price greater than 23 can be bought.

// Constraints:
//     1 < primeOne, primeTwo < 10^4
//     primeOne, primeTwo are prime numbers.
//     primeOne * primeTwo < 10^5

import "fmt"

func mostExpensiveItem(primeOne int, primeTwo int) int {
    return primeOne * primeTwo - primeOne - primeTwo
}

func main() {
    // Example 1:
    // Input: primeOne = 2, primeTwo = 5
    // Output: 3
    // Explanation: The prices of items which cannot be bought are [1,3]. 
    // It can be shown that all items with a price greater than 3 can be bought using a combination of coins of denominations 2 and 5.
    fmt.Println(mostExpensiveItem(2, 5)) // 3
    // Example 2:
    // Input: primeOne = 5, primeTwo = 7
    // Output: 23
    // Explanation: The prices of items which cannot be bought are [1,2,3,4,6,8,9,11,13,16,18,23]. 
    // It can be shown that all items with a price greater than 23 can be bought.
    fmt.Println(mostExpensiveItem(5, 7)) // 23

    fmt.Println(mostExpensiveItem(2, 2)) // 0
    fmt.Println(mostExpensiveItem(3967, 3967)) // 15729155
    fmt.Println(mostExpensiveItem(2, 3967)) // 3965
    fmt.Println(mostExpensiveItem(3967, 2)) // 3965
}