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g2601_2700.s2681_power_of_heroes.readme.md Maven / Gradle / Ivy

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