Minimum Cost to Set Cooking Time
<p>A generic microwave supports cooking times for:</p>

<ul>
	<li>at least <code>1</code> second.</li>
	<li>at most <code>99</code> minutes and <code>99</code> seconds.</li>
</ul>

<p>To set the cooking time, you push <strong>at most four digits</strong>. The microwave normalizes what you push as four digits by <strong>prepending zeroes</strong>. It interprets the <strong>first</strong> two digits as the minutes and the <strong>last</strong> two digits as the seconds. It then <strong>adds</strong> them up as the cooking time. For example,</p>

<ul>
	<li>You push <code>9</code> <code>5</code> <code>4</code> (three digits). It is normalized as <code>0954</code> and interpreted as <code>9</code> minutes and <code>54</code> seconds.</li>
	<li>You push <code>0</code> <code>0</code> <code>0</code> <code>8</code> (four digits). It is interpreted as <code>0</code> minutes and <code>8</code> seconds.</li>
	<li>You push <code>8</code> <code>0</code> <code>9</code> <code>0</code>. It is interpreted as <code>80</code> minutes and <code>90</code> seconds.</li>
	<li>You push <code>8</code> <code>1</code> <code>3</code> <code>0</code>. It is interpreted as <code>81</code> minutes and <code>30</code> seconds.</li>
</ul>

<p>You are given integers <code>startAt</code>, <code>moveCost</code>, <code>pushCost</code>, and <code>targetSeconds</code>. <strong>Initially</strong>, your finger is on the digit <code>startAt</code>. Moving the finger above <strong>any specific digit</strong> costs <code>moveCost</code> units of fatigue. Pushing the digit below the finger <strong>once</strong> costs <code>pushCost</code> units of fatigue.</p>

<p>There can be multiple ways to set the microwave to cook for <code>targetSeconds</code> seconds but you are interested in the way with the minimum cost.</p>

<p>Return <em>the <strong>minimum cost</strong> to set</em> <code>targetSeconds</code> <em>seconds of cooking time</em>.</p>

<p>Remember that one minute consists of <code>60</code> seconds.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/30/1.png" style="width: 506px; height: 210px;" />
<pre>
<strong>Input:</strong> startAt = 1, moveCost = 2, pushCost = 1, targetSeconds = 600
<strong>Output:</strong> 6
<strong>Explanation:</strong> The following are the possible ways to set the cooking time.
- 1 0 0 0, interpreted as 10 minutes and 0 seconds.
&nbsp; The finger is already on digit 1, pushes 1 (with cost 1), moves to 0 (with cost 2), pushes 0 (with cost 1), pushes 0 (with cost 1), and pushes 0 (with cost 1).
&nbsp; The cost is: 1 + 2 + 1 + 1 + 1 = 6. This is the minimum cost.
- 0 9 6 0, interpreted as 9 minutes and 60 seconds. That is also 600 seconds.
&nbsp; The finger moves to 0 (with cost 2), pushes 0 (with cost 1), moves to 9 (with cost 2), pushes 9 (with cost 1), moves to 6 (with cost 2), pushes 6 (with cost 1), moves to 0 (with cost 2), and pushes 0 (with cost 1).
&nbsp; The cost is: 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 = 12.
- 9 6 0, normalized as 0960 and interpreted as 9 minutes and 60 seconds.
&nbsp; The finger moves to 9 (with cost 2), pushes 9 (with cost 1), moves to 6 (with cost 2), pushes 6 (with cost 1), moves to 0 (with cost 2), and pushes 0 (with cost 1).
&nbsp; The cost is: 2 + 1 + 2 + 1 + 2 + 1 = 9.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/30/2.png" style="width: 505px; height: 73px;" />
<pre>
<strong>Input:</strong> startAt = 0, moveCost = 1, pushCost = 2, targetSeconds = 76
<strong>Output:</strong> 6
<strong>Explanation:</strong> The optimal way is to push two digits: 7 6, interpreted as 76 seconds.
The finger moves to 7 (with cost 1), pushes 7 (with cost 2), moves to 6 (with cost 1), and pushes 6 (with cost 2). The total cost is: 1 + 2 + 1 + 2 = 6
Note other possible ways are 0076, 076, 0116, and 116, but none of them produces the minimum cost.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= startAt &lt;= 9</code></li>
	<li><code>1 &lt;= moveCost, pushCost &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= targetSeconds &lt;= 6039</code></li>
</ul>

['minimum-time-difference']
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    int minCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public int minCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def minCostSetTime(self, startAt, moveCost, pushCost, targetSeconds):\n        \"\"\"\n        :type startAt: int\n        :type moveCost: int\n        :type pushCost: int\n        :type targetSeconds: int\n        :rtype: int\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def minCostSetTime(self, startAt: int, moveCost: int, pushCost: int, targetSeconds: int) -> int:\n        "}, {"value": "c", "text": "C", "defaultCode": "int minCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public int MinCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number} startAt\n * @param {number} moveCost\n * @param {number} pushCost\n * @param {number} targetSeconds\n * @return {number}\n */\nvar minCostSetTime = function(startAt, moveCost, pushCost, targetSeconds) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function minCostSetTime(startAt: number, moveCost: number, pushCost: number, targetSeconds: number): number {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer $startAt\n     * @param Integer $moveCost\n     * @param Integer $pushCost\n     * @param Integer $targetSeconds\n     * @return Integer\n     */\n    function minCostSetTime($startAt, $moveCost, $pushCost, $targetSeconds) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func minCostSetTime(_ startAt: Int, _ moveCost: Int, _ pushCost: Int, _ targetSeconds: Int) -> Int {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun minCostSetTime(startAt: Int, moveCost: Int, pushCost: Int, targetSeconds: Int): Int {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  int minCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func minCostSetTime(startAt int, moveCost int, pushCost int, targetSeconds int) int {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer} start_at\n# @param {Integer} move_cost\n# @param {Integer} push_cost\n# @param {Integer} target_seconds\n# @return {Integer}\ndef min_cost_set_time(start_at, move_cost, push_cost, target_seconds)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def minCostSetTime(startAt: Int, moveCost: Int, pushCost: Int, targetSeconds: Int): Int = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn min_cost_set_time(start_at: i32, move_cost: i32, push_cost: i32, target_seconds: i32) -> i32 {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (min-cost-set-time startAt moveCost pushCost targetSeconds)\n  (-> exact-integer? exact-integer? exact-integer? exact-integer? exact-integer?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec min_cost_set_time(StartAt :: integer(), MoveCost :: integer(), PushCost :: integer(), TargetSeconds :: integer()) -> integer().\nmin_cost_set_time(StartAt, MoveCost, PushCost, TargetSeconds) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec min_cost_set_time(start_at :: integer, move_cost :: integer, push_cost :: integer, target_seconds :: integer) :: integer\n  def min_cost_set_time(start_at, move_cost, push_cost, target_seconds) do\n    \n  end\nend"}]
{
  "name": "minCostSetTime",
  "params": [
    {
      "name": "startAt",
      "type": "integer"
    },
    {
      "type": "integer",
      "name": "moveCost"
    },
    {
      "type": "integer",
      "name": "pushCost"
    },
    {
      "type": "integer",
      "name": "targetSeconds"
    }
  ],
  "return": {
    "type": "integer"
  }
}
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['Math', 'Enumeration']