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Java-based LeetCode algorithm problem solutions, regularly updated
2681\. Power of Heroes
Hard
You are given a **0-indexed** integer array `nums` representing the strength of some heroes. The **power** of a group of heroes is defined as follows:
* Let i0, i1, ... ,ik be the indices of the heroes in a group. Then, the power of this group is max(nums[i0], nums[i1], ... ,nums[ik])2 * min(nums[i0], nums[i1], ... ,nums[ik]).
Return _the sum of the **power** of all **non-empty** groups of heroes possible._ Since the sum could be very large, return it **modulo** 109 + 7.
**Example 1:**
**Input:** nums = [2,1,4]
**Output:** 141
**Explanation:**
1st group: [2] has power = 22 \* 2 = 8.
2nd group: [1] has power = 12 \* 1 = 1.
3rd group: [4] has power = 42 \* 4 = 64.
4th group: [2,1] has power = 22 \* 1 = 4.
5th group: [2,4] has power = 42 \* 2 = 32.
6th group: [1,4] has power = 42 \* 1 = 16.
7th group: [2,1,4] has power = 42 \* 1 = 16.
The sum of powers of all groups is 8 + 1 + 64 + 4 + 32 + 16 + 16 = 141.
**Example 2:**
**Input:** nums = [1,1,1]
**Output:** 7
**Explanation:** 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.
**Constraints:**
* 1 <= nums.length <= 105
* 1 <= nums[i] <= 109