leetcode-problemset/leetcode-cn/originData/count-all-possible-routes.json

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        "question": {
            "questionId": "1680",
            "questionFrontendId": "1575",
            "categoryTitle": "Algorithms",
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            "title": "Count All Possible Routes",
            "titleSlug": "count-all-possible-routes",
            "content": "<p>You are given an array of <strong>distinct</strong> positive integers locations where <code>locations[i]</code> represents the position of city <code>i</code>. You are also given integers <code>start</code>, <code>finish</code> and <code>fuel</code> representing the starting city, ending city, and the initial amount of fuel you have, respectively.</p>\n\n<p>At each step, if you are at city <code>i</code>, you can pick any city <code>j</code> such that <code>j != i</code> and <code>0 &lt;= j &lt; locations.length</code> and move to city <code>j</code>. Moving from city <code>i</code> to city <code>j</code> reduces the amount of fuel you have by <code>|locations[i] - locations[j]|</code>. Please notice that <code>|x|</code> denotes the absolute value of <code>x</code>.</p>\n\n<p>Notice that <code>fuel</code> <strong>cannot</strong> become negative at any point in time, and that you are <strong>allowed</strong> to visit any city more than once (including <code>start</code> and <code>finish</code>).</p>\n\n<p>Return <em>the count of all possible routes from </em><code>start</code> <em>to</em> <code>finish</code>. Since the answer may be too large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> locations = [2,3,6,8,4], start = 1, finish = 3, fuel = 5\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The following are all possible routes, each uses 5 units of fuel:\n1 -&gt; 3\n1 -&gt; 2 -&gt; 3\n1 -&gt; 4 -&gt; 3\n1 -&gt; 4 -&gt; 2 -&gt; 3\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> locations = [4,3,1], start = 1, finish = 0, fuel = 6\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The following are all possible routes:\n1 -&gt; 0, used fuel = 1\n1 -&gt; 2 -&gt; 0, used fuel = 5\n1 -&gt; 2 -&gt; 1 -&gt; 0, used fuel = 5\n1 -&gt; 0 -&gt; 1 -&gt; 0, used fuel = 3\n1 -&gt; 0 -&gt; 1 -&gt; 0 -&gt; 1 -&gt; 0, used fuel = 5\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> locations = [5,2,1], start = 0, finish = 2, fuel = 3\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> It is impossible to get from 0 to 2 using only 3 units of fuel since the shortest route needs 4 units of fuel.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= locations.length &lt;= 100</code></li>\n\t<li><code>1 &lt;= locations[i] &lt;= 10<sup>9</sup></code></li>\n\t<li>All integers in <code>locations</code> are <strong>distinct</strong>.</li>\n\t<li><code>0 &lt;= start, finish &lt; locations.length</code></li>\n\t<li><code>1 &lt;= fuel &lt;= 200</code></li>\n</ul>\n",
            "translatedTitle": "统计所有可行路径",
            "translatedContent": "<p>给你一个 <strong>互不相同</strong>&nbsp;的整数数组，其中&nbsp;<code>locations[i]</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;个城市的位置。同时给你&nbsp;<code>start</code>，<code>finish</code>&nbsp;和&nbsp;<code>fuel</code>&nbsp;分别表示出发城市、目的地城市和你初始拥有的汽油总量</p>\n\n<p>每一步中，如果你在城市 <code>i</code>&nbsp;，你可以选择任意一个城市 <code>j</code>&nbsp;，满足 &nbsp;<code>j != i</code>&nbsp;且&nbsp;<code>0 &lt;= j &lt; locations.length</code>&nbsp;，并移动到城市&nbsp;<code>j</code>&nbsp;。从城市&nbsp;<code>i</code>&nbsp;移动到&nbsp;<code>j</code>&nbsp;消耗的汽油量为&nbsp;<code>|locations[i] - locations[j]|</code>，<code>|x|</code>&nbsp;表示&nbsp;<code>x</code>&nbsp;的绝对值。</p>\n\n<p>请注意，&nbsp;<code>fuel</code>&nbsp;任何时刻都&nbsp;<strong>不能</strong>&nbsp;为负，且你&nbsp;<strong>可以</strong>&nbsp;经过任意城市超过一次（包括&nbsp;<code>start</code>&nbsp;和&nbsp;<code>finish</code>&nbsp;）。</p>\n\n<p>请你返回从<em>&nbsp;</em><code>start</code>&nbsp;到&nbsp;<code>finish</code>&nbsp;所有可能路径的数目。</p>\n\n<p>由于答案可能很大， 请将它对&nbsp;<code>10^9 + 7</code>&nbsp;取余后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>locations = [2,3,6,8,4], start = 1, finish = 3, fuel = 5\n<strong>输出：</strong>4\n<strong>解释：</strong>以下为所有可能路径，每一条都用了 5 单位的汽油：\n1 -&gt; 3\n1 -&gt; 2 -&gt; 3\n1 -&gt; 4 -&gt; 3\n1 -&gt; 4 -&gt; 2 -&gt; 3\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>locations = [4,3,1], start = 1, finish = 0, fuel = 6\n<strong>输出：</strong>5\n<strong>解释：</strong>以下为所有可能的路径：\n1 -&gt; 0，使用汽油量为 fuel = 1\n1 -&gt; 2 -&gt; 0，使用汽油量为 fuel = 5\n1 -&gt; 2 -&gt; 1 -&gt; 0，使用汽油量为 fuel = 5\n1 -&gt; 0 -&gt; 1 -&gt; 0，使用汽油量为 fuel = 3\n1 -&gt; 0 -&gt; 1 -&gt; 0 -&gt; 1 -&gt; 0，使用汽油量为 fuel = 5\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>locations = [5,2,1], start = 0, finish = 2, fuel = 3\n<strong>输出：</strong>0\n<strong>解释：</strong>没有办法只用 3 单位的汽油从 0 到达 2 。因为最短路径需要 4 单位的汽油。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= locations.length &lt;= 100</code></li>\n\t<li><code>1 &lt;= locations[i] &lt;= 10<sup>9</sup></code></li>\n\t<li>所有&nbsp;<code>locations</code>&nbsp;中的整数 <strong>互不相同</strong>&nbsp;。</li>\n\t<li><code>0 &lt;= start, finish &lt;&nbsp;locations.length</code></li>\n\t<li><code>1 &lt;= fuel &lt;= 200</code></li>\n</ul>\n",
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                    "code": "class Solution {\npublic:\n    int countRoutes(vector<int>& locations, int start, int finish, int fuel) {\n\n    }\n};",
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                    "code": "# @param {Integer[]} locations\n# @param {Integer} start\n# @param {Integer} finish\n# @param {Integer} fuel\n# @return {Integer}\ndef count_routes(locations, start, finish, fuel)\n\nend",
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                "Use dynamic programming to solve this problem with each state defined by the city index and fuel left.",
                "Since the array contains distinct integers fuel will always be spent in each move and so there can be no cycles."
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