mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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163 lines
16 KiB
JSON
163 lines
16 KiB
JSON
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"title": "Power of Heroes",
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"content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> representing the strength of some heroes. The<b> power</b> of a group of heroes is defined as follows:</p>\n\n<ul>\n\t<li>Let <code>i<sub>0</sub></code>, <code>i<sub>1</sub></code>, ... ,<code>i<sub>k</sub></code> be the indices of the heroes in a group. Then, the power of this group is <code>max(nums[i<sub>0</sub>], nums[i<sub>1</sub>], ... ,nums[i<sub>k</sub>])<sup>2</sup> * min(nums[i<sub>0</sub>], nums[i<sub>1</sub>], ... ,nums[i<sub>k</sub>])</code>.</li>\n</ul>\n\n<p>Return <em>the sum of the <strong>power</strong> of all <strong>non-empty</strong> groups of heroes possible.</em> Since the sum could be very large, return it <strong>modulo</strong> <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> nums = [2,1,4]\n<strong>Output:</strong> 141\n<strong>Explanation:</strong> \n1<sup>st</sup> group: [2] has power = 2<sup>2</sup> * 2 = 8.\n2<sup>nd</sup> group: [1] has power = 1<sup>2</sup> * 1 = 1. \n3<sup>rd</sup> group: [4] has power = 4<sup>2</sup> * 4 = 64. \n4<sup>th</sup> group: [2,1] has power = 2<sup>2</sup> * 1 = 4. \n5<sup>th</sup> group: [2,4] has power = 4<sup>2</sup> * 2 = 32. \n6<sup>th</sup> group: [1,4] has power = 4<sup>2</sup> * 1 = 16. \n7<sup>th</sup> group: [2,1,4] has power = 4<sup>2</sup> * 1 = 16. \nThe sum of powers of all groups is 8 + 1 + 64 + 4 + 32 + 16 + 16 = 141.\n\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1,1]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> A total of 7 groups are possible, and the power of each group will be 1. Therefore, the sum of the powers of all groups is 7.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"Try something with sorting the array.",
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"For a pair of array elements nums[i] and nums[j] (i < j), the power would be nums[i]*nums[j]^2 regardless of how many elements in between are included.",
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"The number of subsets with the above as power will correspond to 2^(j-i-1).",
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"Try collecting the terms for nums[0], nums[1], …, nums[j-1] when computing the power of heroes ending at index j to get the power in a single pass."
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