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leetcode-problemset/leetcode/originData/maximum-absolute-sum-of-any-subarray.json
2022-05-02 23:44:12 +08:00

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{
"data": {
"question": {
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"title": "Maximum Absolute Sum of Any Subarray",
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"content": "<p>You are given an integer array <code>nums</code>. The <strong>absolute sum</strong> of a subarray <code>[nums<sub>l</sub>, nums<sub>l+1</sub>, ..., nums<sub>r-1</sub>, nums<sub>r</sub>]</code> is <code>abs(nums<sub>l</sub> + nums<sub>l+1</sub> + ... + nums<sub>r-1</sub> + nums<sub>r</sub>)</code>.</p>\n\n<p>Return <em>the <strong>maximum</strong> absolute sum of any <strong>(possibly empty)</strong> subarray of </em><code>nums</code>.</p>\n\n<p>Note that <code>abs(x)</code> is defined as follows:</p>\n\n<ul>\n\t<li>If <code>x</code> is a negative integer, then <code>abs(x) = -x</code>.</li>\n\t<li>If <code>x</code> is a non-negative integer, then <code>abs(x) = x</code>.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,-3,2,3,-4]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The subarray [2,3] has absolute sum = abs(2+3) = abs(5) = 5.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,-5,1,-4,3,-2]\n<strong>Output:</strong> 8\n<strong>Explanation:</strong> The subarray [-5,1,-4] has absolute sum = abs(-5+1-4) = abs(-8) = 8.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
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"code": "(define/contract (max-absolute-sum nums)\n (-> (listof exact-integer?) exact-integer?)\n\n )",
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"hints": [
"What if we asked for maximum sum, not absolute sum?",
"It's a standard problem that can be solved by Kadane's algorithm.",
"The key idea is the max absolute sum will be either the max sum or the min sum.",
"So just run kadane twice, once calculating the max sum and once calculating the min sum."
],
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