[Swift]LeetCode964. 表示數字的最少運算符 | Least Operators to Express Number

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Given a single positive integer x, we will write an expression of the form x (op1) x (op2) x (op3) x ... where each operator op1, op2, etc. is either addition, subtraction, multiplication, or division (+, -, *, or /).  For example, with x = 3, we might write 3 * 3 / 3 + 3 - 3 which is a value of 3.

When writing such an expression, we adhere to the following conventions:

1. The division operator (/) returns rational numbers.
2. There are no parentheses placed anywhere.
3. We use the usual order of operations: multiplication and division happens before addition and subtraction.
4. It's not allowed to use the unary negation operator (-).  For example, "x - x" is a valid expression as it only uses subtraction, but "-x + x" is not because it uses negation.

We would like to write an expression with the least number of operators such that the expression equals the given target.  Return the least number of expressions used.

Example 1:

Input: x = 3, target = 19 Output: 5 Explanation: 3 * 3 + 3 * 3 + 3 / 3. The expression contains 5 operations. 

Example 2:

Input: x = 5, target = 501 Output: 8 Explanation: 5 * 5 * 5 * 5 - 5 * 5 * 5 + 5 / 5. The expression contains 8 operations. 

Example 3:

Input: x = 100, target = 100000000 Output: 3 Explanation: 100 * 100 * 100 * 100. The expression contains 3 operations.

Note:

• 2 <= x <= 100
• 1 <= target <= 2 * 10^8

---

給定一個正整數 x，咱們將會寫出一個形如 x (op1) x (op2) x (op3) x ... 的表達式，其中每一個運算符 op1，op2，… 能夠是加、減、乘、除（+，-，*，或是 /）之一。例如，對於 x = 3，咱們能夠寫出表達式 3 * 3 / 3 + 3 - 3，該式的值爲 3 。

在寫這樣的表達式時，咱們須要遵照下面的慣例：

1. 除運算符（/）返回有理數。
2. 任何地方都沒有括號。
3. 咱們使用一般的操做順序：乘法和除法發生在加法和減法以前。
4. 不容許使用一元否認運算符（-）。例如，「x - x」 是一個有效的表達式，由於它只使用減法，可是 「-x + x」 不是，由於它使用了否認運算符。 

咱們但願編寫一個能使表達式等於給定的目標值 target 且運算符最少的表達式。返回所用運算符的最少數量。

示例 1：

輸入：x = 3, target = 19
輸出：5
解釋：3 * 3 + 3 * 3 + 3 / 3 。表達式包含 5 個運算符。

示例 2：

輸入：x = 5, target = 501
輸出：8
解釋：5 * 5 * 5 * 5 - 5 * 5 * 5 + 5 / 5 。表達式包含 8 個運算符。

示例 3：

輸入：x = 100, target = 100000000
輸出：3
解釋：100 * 100 * 100 * 100 。表達式包含 3 個運算符。

提示：

• 2 <= x <= 100
• 1 <= target <= 2 * 10^8

---

100ms

 1 class Solution {
 2     var x:Int = 0
 3     var best:Int = 0
 4     func leastOpsExpressTarget(_ x: Int, _ target: Int) -> Int {
 5         var target  = target
 6         self.x = x
 7         var list:[Int] = [Int]()
 8         while(target != 0)
 9         {
10             list.append(target % x)
11             target /= x
12         }
13         self.best = Int.max
14         dfs(list, 0, 0, 0)
15         return best - 1
16     }
17     
18     func dfs(_ list:[Int],_ k:Int,_ add:Int,_ count:Int)
19     {
20         var add = add
21         if count >= best
22         {
23             return
24         }
25         if add == 0 && k >= list.count
26         {
27             best = min(best, count)
28             return
29         }
30         
31         if k < list.count
32         {
33             add += list[k]
34         }
35         var cost:Int = k == 0 ? 2 : k
36         var cur:Int = add % x
37         add /= x
38         dfs(list, k + 1, add, count + cost * cur)
39         if cur != 0 && k <= list.count + 2
40         {
41             dfs(list, k + 1, 1, count + cost * (x - cur))
42         }
43     }
44 }