Watch 10 video solutions for Sum of Total Strength of Wizards, a hard level problem involving Array, Stack, Monotonic Stack. This walkthrough by Ashish Pratap Singh has 1,002,241 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
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:
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.
A 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: - [1] from [1,3,1,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1 - [3] from [1,3,1,2] has a total strength of min([3]) * sum([3]) = 3 * 3 = 9 - [1] from [1,3,1,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1 - [2] from [1,3,1,2] has a total strength of min([2]) * sum([2]) = 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:
Input: strength = [5,4,6] Output: 213 Explanation: The following are all the contiguous groups of wizards: - [5] from [5,4,6] has a total strength of min([5]) * sum([5]) = 5 * 5 = 25 - [4] from [5,4,6] has a total strength of min([4]) * sum([4]) = 4 * 4 = 16 - [6] from [5,4,6] has a total strength of min([6]) * sum([6]) = 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 <= 1051 <= strength[i] <= 109