# Sum of Total Strength of Wizards solution leetcode

## Sum of Total Strength of Wizards solution leetcode

As the ruler of a kingdom, you have an army of wizards at your command.

You are given a 0-indexed integer array `strength`, where `strength[i]` denotes the strength of the `ith` wizard. For a contiguous group of wizards (i.e. the wizards’ strengths form a subarray of `strength`), the total strength is defined as the product of the following two values:

• The strength of the weakest wizard in the group.
• The total of all the individual strengths of the wizards in the group.

Return the sum of the total strengths of all contiguous groups of wizards. Since the answer may be very large, return it modulo `109 + 7`.

## Sum of Total Strength of Wizards solution leetcode

subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

```Input: strength = [1,3,1,2]
Output: 44
Explanation: The following are all the contiguous groups of wizards:
-  from [1,3,1,2] has a total strength of min() * sum() = 1 * 1 = 1
-  from [1,3,1,2] has a total strength of min() * sum() = 3 * 3 = 9
-  from [1,3,1,2] has a total strength of min() * sum() = 1 * 1 = 1
-  from [1,3,1,2] has a total strength of min() * sum() = 2 * 2 = 4
- [1,3] from [1,3,1,2] has a total strength of min([1,3]) * sum([1,3]) = 1 * 4 = 4
- [3,1] from [1,3,1,2] has a total strength of min([3,1]) * sum([3,1]) = 1 * 4 = 4
- [1,2] from [1,3,1,2] has a total strength of min([1,2]) * sum([1,2]) = 1 * 3 = 3
- [1,3,1] from [1,3,1,2] has a total strength of min([1,3,1]) * sum([1,3,1]) = 1 * 5 = 5
- [3,1,2] from [1,3,1,2] has a total strength of min([3,1,2]) * sum([3,1,2]) = 1 * 6 = 6
- [1,3,1,2] from [1,3,1,2] has a total strength of min([1,3,1,2]) * sum([1,3,1,2]) = 1 * 7 = 7
The sum of all the total strengths is 1 + 9 + 1 + 4 + 4 + 4 + 3 + 5 + 6 + 7 = 44.
```

Example 2:

• Contestants ranked 1st will win a Apple HomePod mini
• Contestants ranked 2nd will win a Logitech G903 LIGHTSPEED Gaming Mouse
• Contestants ranked 3rd ~ 5th will win a LeetCode Backpack
• Contestants ranked 6th ~ 10th will win a LeetCode water bottle
• Contestants ranked 11th ~ 20th will win a LeetCode Big O Notebook

## Sum of Total Strength of Wizards solution leetcode

```Input: strength = [5,4,6]
Output: 213
Explanation: The following are all the contiguous groups of wizards:
-  from [5,4,6] has a total strength of min() * sum() = 5 * 5 = 25
-  from [5,4,6] has a total strength of min() * sum() = 4 * 4 = 16
-  from [5,4,6] has a total strength of min() * sum() = 6 * 6 = 36
- [5,4] from [5,4,6] has a total strength of min([5,4]) * sum([5,4]) = 4 * 9 = 36
- [4,6] from [5,4,6] has a total strength of min([4,6]) * sum([4,6]) = 4 * 10 = 40
- [5,4,6] from [5,4,6] has a total strength of min([5,4,6]) * sum([5,4,6]) = 4 * 15 = 60
The sum of all the total strengths is 25 + 16 + 36 + 36 + 40 + 60 = 213.
```

Constraints:

• `1 <= strength.length <= 105`
• `1 <= strength[i] <= 109`