leetcode-problemset/leetcode/originData/minimum-number-of-coins-to-be-added.json

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            "title": "Minimum Number of Coins to be Added",
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            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>coins</code>, representing the values of the coins available, and an integer <code>target</code>.</p>\n\n<p>An integer <code>x</code> is <strong>obtainable</strong> if there exists a subsequence of <code>coins</code> that sums to <code>x</code>.</p>\n\n<p>Return <em>the<strong> minimum</strong> number of coins <strong>of any value</strong> that need to be added to the array so that every integer in the range</em> <code>[1, target]</code><em> is <strong>obtainable</strong></em>.</p>\n\n<p>A <strong>subsequence</strong> of an array is a new <strong>non-empty</strong> array that is formed from the original array by deleting some (<strong>possibly none</strong>) of the elements without disturbing the relative positions of the remaining elements.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> coins = [1,4,10], target = 19\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We need to add coins 2 and 8. The resulting array will be [1,2,4,8,10].\nIt can be shown that all integers from 1 to 19 are obtainable from the resulting array, and that 2 is the minimum number of coins that need to be added to the array. \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> coins = [1,4,10,5,7,19], target = 19\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We only need to add the coin 2. The resulting array will be [1,2,4,5,7,10,19].\nIt can be shown that all integers from 1 to 19 are obtainable from the resulting array, and that 1 is the minimum number of coins that need to be added to the array. \n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> coins = [1,1,1], target = 20\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We need to add coins 4, 8, and 16. The resulting array will be [1,1,1,4,8,16].\nIt can be shown that all integers from 1 to 20 are obtainable from the resulting array, and that 3 is the minimum number of coins that need to be added to the array.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= target &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= coins.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= coins[i] &lt;= target</code></li>\n</ul>\n",
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                    "code": "class Solution(object):\n    def minimumAddedCoins(self, coins, target):\n        \"\"\"\n        :type coins: List[int]\n        :type target: int\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "public class Solution {\n    public int MinimumAddedCoins(int[] coins, int target) {\n        \n    }\n}",
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                    "code": "/**\n * @param {number[]} coins\n * @param {number} target\n * @return {number}\n */\nvar minimumAddedCoins = function(coins, target) {\n    \n};",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer[] $coins\n     * @param Integer $target\n     * @return Integer\n     */\n    function minimumAddedCoins($coins, $target) {\n        \n    }\n}",
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                    "code": "class Solution {\n    func minimumAddedCoins(_ coins: [Int], _ target: Int) -> Int {\n        \n    }\n}",
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                    "lang": "Kotlin",
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                    "code": "class Solution {\n    fun minimumAddedCoins(coins: IntArray, target: Int): Int {\n        \n    }\n}",
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                    "lang": "Dart",
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                    "code": "class Solution {\n  int minimumAddedCoins(List<int> coins, int target) {\n    \n  }\n}",
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                    "lang": "Go",
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                    "code": "func minimumAddedCoins(coins []int, target int) int {\n    \n}",
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                    "code": "# @param {Integer[]} coins\n# @param {Integer} target\n# @return {Integer}\ndef minimum_added_coins(coins, target)\n    \nend",
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                    "code": "impl Solution {\n    pub fn minimum_added_coins(coins: Vec<i32>, target: i32) -> i32 {\n        \n    }\n}",
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                    "lang": "Racket",
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                    "code": "(define/contract (minimum-added-coins coins target)\n  (-> (listof exact-integer?) exact-integer? exact-integer?)\n  )",
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                    "code": "defmodule Solution do\n  @spec minimum_added_coins(coins :: [integer], target :: integer) :: integer\n  def minimum_added_coins(coins, target) do\n    \n  end\nend",
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                "Sort the coins array and maintain the smallest sum that is unobtainable by induction.",
                "If we don’t use any coins, the smallest integer that we cannot obtain by sum is <code>1</code>. Suppose currently, for a fixed set of the first several coins the smallest integer that we cannot obtain is <code>x + 1</code>, namely we can form all integers in the range <code>[1, x]</code> but not <code>x + 1</code>.",
                "If the next unused coin’s value is NOT <code>x + 1</code> (note the array is sorted), we have to add <code>x + 1</code> to the array. After this addition, we can form all values from <code>x + 1</code> to <code>2 * x + 1</code> by adding <code>x + 1</code> in <code>[1, x]</code>'s formations. So now we can form all the numbers of <code>[1, 2 * x + 1]</code>. After this iteration the new value of <code>x</code> becomes <code>2 * x + 1</code>."
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