mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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194 lines
19 KiB
JSON
194 lines
19 KiB
JSON
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"title": "Count All Possible Routes",
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"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 <= j < 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> </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 -> 3\n1 -> 2 -> 3\n1 -> 4 -> 3\n1 -> 4 -> 2 -> 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 -> 0, used fuel = 1\n1 -> 2 -> 0, used fuel = 5\n1 -> 2 -> 1 -> 0, used fuel = 5\n1 -> 0 -> 1 -> 0, used fuel = 3\n1 -> 0 -> 1 -> 0 -> 1 -> 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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= locations.length <= 100</code></li>\n\t<li><code>1 <= locations[i] <= 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 <= start, finish < locations.length</code></li>\n\t<li><code>1 <= fuel <= 200</code></li>\n</ul>\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.",
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"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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