leetcode-problemset/leetcode-cn/originData/least-operators-to-express-number.json

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            "title": "Least Operators to Express Number",
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            "content": "<p>Given a single positive integer <code>x</code>, we will write an expression of the form <code>x (op1) x (op2) x (op3) x ...</code> where each operator <code>op1</code>, <code>op2</code>, etc. is either addition, subtraction, multiplication, or division (<code>+</code>, <code>-</code>, <code>*</code>, or <code>/)</code>. For example, with <code>x = 3</code>, we might write <code>3 * 3 / 3 + 3 - 3</code> which is a value of <font face=\"monospace\">3</font>.</p>\n\n<p>When writing such an expression, we adhere to the following conventions:</p>\n\n<ul>\n\t<li>The division operator (<code>/</code>) returns rational numbers.</li>\n\t<li>There are no parentheses placed anywhere.</li>\n\t<li>We use the usual order of operations: multiplication and division happen before addition and subtraction.</li>\n\t<li>It is not allowed to use the unary negation operator (<code>-</code>). For example, &quot;<code>x - x</code>&quot; is a valid expression as it only uses subtraction, but &quot;<code>-x + x</code>&quot; is not because it uses negation.</li>\n</ul>\n\n<p>We would like to write an expression with the least number of operators such that the expression equals the given <code>target</code>. Return the least number of operators used.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> x = 3, target = 19\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> 3 * 3 + 3 * 3 + 3 / 3.\nThe expression contains 5 operations.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> x = 5, target = 501\n<strong>Output:</strong> 8\n<strong>Explanation:</strong> 5 * 5 * 5 * 5 - 5 * 5 * 5 + 5 / 5.\nThe expression contains 8 operations.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> x = 100, target = 100000000\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> 100 * 100 * 100 * 100.\nThe expression contains 3 operations.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= x &lt;= 100</code></li>\n\t<li><code>1 &lt;= target &lt;= 2 * 10<sup>8</sup></code></li>\n</ul>\n",
            "translatedTitle": "表示数字的最少运算符",
            "translatedContent": "<p>给定一个正整数 <code>x</code>，我们将会写出一个形如&nbsp;<code>x (op1) x (op2) x (op3) x ...</code>&nbsp;的表达式，其中每个运算符&nbsp;<code>op1</code>，<code>op2</code>，… 可以是加、减、乘、除（<code>+</code>，<code>-</code>，<code>*</code>，或是&nbsp;<code>/</code>）之一。例如，对于&nbsp;<code>x = 3</code>，我们可以写出表达式&nbsp;<code>3 * 3 / 3 + 3 - 3</code>，该式的值为 3 。</p>\n\n<p>在写这样的表达式时，我们需要遵守下面的惯例：</p>\n\n<ul>\n\t<li>除运算符（<code>/</code>）返回有理数。</li>\n\t<li>任何地方都没有括号。</li>\n\t<li>我们使用通常的操作顺序：乘法和除法发生在加法和减法之前。</li>\n\t<li>不允许使用一元否定运算符（<code>-</code>）。例如，“<code>x - x</code>” 是一个有效的表达式，因为它只使用减法，但是 “<code>-x + x</code>” 不是，因为它使用了否定运算符。&nbsp;</li>\n</ul>\n\n<p>我们希望编写一个能使表达式等于给定的目标值 <code>target</code> 且运算符最少的表达式。返回所用运算符的最少数量。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>x = 3, target = 19\n<strong>输出：</strong>5\n<strong>解释：</strong>3 * 3 + 3 * 3 + 3 / 3 。表达式包含 5 个运算符。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>x = 5, target = 501\n<strong>输出：</strong>8\n<strong>解释：</strong>5 * 5 * 5 * 5 - 5 * 5 * 5 + 5 / 5 。表达式包含 8 个运算符。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>x = 100, target = 100000000\n<strong>输出：</strong>3\n<strong>解释：</strong>100 * 100 * 100 * 100 。表达式包含 3 个运算符。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= x &lt;= 100</code></li>\n\t<li><code>1 &lt;= target &lt;= 2 * 10<sup>8</sup></code></li>\n</ul>\n",
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