# Find Total Power Amazon OA 2023 Solution

We have research and collected a bundle of questions which was asked in Amazon OA in the year of 2022 and 2023. Today, we are going to see another problem from amazon oa called Find Total Power which was asked in 2022, this questions might be still active in some of the Amazon OA so save all the solutions and lets see how can we solve this problem.

## Find Total Power Amazon OA 2023 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:

• 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`.

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 <= 105`
• `1 <= strength[i] <= 109`

Related: Google Online Assessment 2022 Questions List

### SOLUTION

Program: Find Total Power Amazon OA Solution in Python

``````class Solution:
def totalStrength(self, A: List[int]) -> int:
N = len(A)
Q = int(1e9)+7

# monostack
# ple[i] = previous lesser element, than the one at i
st, ple = [], [-1]*N
for i in range(N-1,-1,-1):
while st and A[st[-1]] > A[i]:
ple[st.pop()] = i
st += [i]

# preprocessing
ps = [0] * (N+1)   # suffix sum
ds = [0] * (N+1)   # suffix sum of suffix sum
dpM = [0] * (N+1)  # dpM[i] = sum( suffixMin of A[0..i] )
for z in range(N):
i, j = ~z-1, ~z
ps[i] = A[j] + ps[j]
ds[i] = ps[i] + ds[j]
k = ple[z]
dpM[z] = A[z] * (z-k)
if k != -1: dpM[z] += dpM[k]

def query(L, R):  # -> sum( sum(A[k..R]) for k in [L..R] )
if R < L: return 0
diff = ds[L] - ds[R+1]
chop = ps[R+1]
size = R-L+1
return diff - chop * size

ans = 0
dpC = [0] * (N+1)
for i in range(N):
j = ple[i]
x = A[i] * query(j+1, i) % Q
if j == -1: y = 0
else:
s = ps[j+1] - ps[i+1]
y = (dpC[j] + dpM[j] * s) % Q
dpC[i] = (x + y) % Q
ans = (ans + dpC[i]) % Q

return ans``````

Program: Find Total Power Amazon OA Solution in Java

``````    public int totalStrength(int[] A) {
int res = 0, ac = 0, mod = (int)1e9 + 7, n = A.length;
Stack<Integer> stack = new Stack<>();
int[] acc = new int[n + 2];
for (int r = 0; r <= n; ++r) {
int a = r < n ? A[r] : 0;
ac = (ac + a) % mod;
acc[r + 1] = (ac + acc[r]) % mod;
while (!stack.isEmpty() && A[stack.peek()] > a) {
int i = stack.pop();
int l = stack.isEmpty() ? -1 : stack.peek();
long lacc = l < 0 ? acc[i] : acc[i] - acc[l], racc = acc[r] - acc[i];
int ln = i - l, rn = r - i;
res = (int)(res + (racc * ln - lacc * rn) % mod * A[i] % mod) % mod;
}
stack.push(r);
}
return (res + mod) % mod;
}``````

Program: Find Total Power Amazon OA Solution in C++

``````    int totalStrength(vector<int>& A) {
int res = 0, ac = 0, mod = 1e9 + 7, n = A.size();
vector<int> stack = {}, acc(n + 2);
for (int r = 0; r <= n; ++r) {
int a = r < n ? A[r] : 0;
ac = (ac + a) % mod;
acc[r + 1] = (ac + acc[r]) % mod;
while (!stack.empty() && A[stack.back()] > a) {
int i = stack.back(); stack.pop_back();
int l = stack.empty() ? -1 : stack.back();
long lacc = l < 0 ? acc[i] : acc[i] - acc[l], racc = acc[r] - acc[i];
int ln = i - l, rn = r - i;
res = (res + (racc * ln - lacc * rn) % mod * A[i] % mod) % mod;
}
stack.push_back(r);
}
return (res + mod) % mod;
}``````
The text passage describes a problem statement for a coding challenge titled "Find Total Power" from Amazon's Online Assessment (OA). It includes a detailed explanation of the problem, examples, and solutions in Python, Java, and C++.
no_question

the passage does not contain a direct mathematical question or a word problem that requires a solution. instead, it provides a problem statement and solutions for a coding challenge. the examples given are part of the problem description and are not standalone questions.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Find Total Power Amazon OA 2023 Solution

We have research and collected a bundle of questions which was asked in Amazon OA in the year of 2022 and 2023. Today, we are going to see another problem from amazon oa called Find Total Power which was asked in 2022, this questions might be still active in some of the Amazon OA so save all the solutions and lets see how can we solve this problem.

## Find Total Power Amazon OA 2023 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:

• 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`.

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 <= 105`
• `1 <= strength[i] <= 109`

Related: Google Online Assessment 2022 Questions List

### SOLUTION

Program: Find Total Power Amazon OA Solution in Python

``````class Solution:
def totalStrength(self, A: List[int]) -> int:
N = len(A)
Q = int(1e9)+7

# monostack
# ple[i] = previous lesser element, than the one at i
st, ple = [], [-1]*N
for i in range(N-1,-1,-1):
while st and A[st[-1]] > A[i]:
ple[st.pop()] = i
st += [i]

# preprocessing
ps = [0] * (N+1)   # suffix sum
ds = [0] * (N+1)   # suffix sum of suffix sum
dpM = [0] * (N+1)  # dpM[i] = sum( suffixMin of A[0..i] )
for z in range(N):
i, j = ~z-1, ~z
ps[i] = A[j] + ps[j]
ds[i] = ps[i] + ds[j]
k = ple[z]
dpM[z] = A[z] * (z-k)
if k != -1: dpM[z] += dpM[k]

def query(L, R):  # -> sum( sum(A[k..R]) for k in [L..R] )
if R < L: return 0
diff = ds[L] - ds[R+1]
chop = ps[R+1]
size = R-L+1
return diff - chop * size

ans = 0
dpC = [0] * (N+1)
for i in range(N):
j = ple[i]
x = A[i] * query(j+1, i) % Q
if j == -1: y = 0
else:
s = ps[j+1] - ps[i+1]
y = (dpC[j] + dpM[j] * s) % Q
dpC[i] = (x + y) % Q
ans = (ans + dpC[i]) % Q

return ans``````

Program: Find Total Power Amazon OA Solution in Java

``````    public int totalStrength(int[] A) {
int res = 0, ac = 0, mod = (int)1e9 + 7, n = A.length;
Stack<Integer> stack = new Stack<>();
int[] acc = new int[n + 2];
for (int r = 0; r <= n; ++r) {
int a = r < n ? A[r] : 0;
ac = (ac + a) % mod;
acc[r + 1] = (ac + acc[r]) % mod;
while (!stack.isEmpty() && A[stack.peek()] > a) {
int i = stack.pop();
int l = stack.isEmpty() ? -1 : stack.peek();
long lacc = l < 0 ? acc[i] : acc[i] - acc[l], racc = acc[r] - acc[i];
int ln = i - l, rn = r - i;
res = (int)(res + (racc * ln - lacc * rn) % mod * A[i] % mod) % mod;
}
stack.push(r);
}
return (res + mod) % mod;
}``````

Program: Find Total Power Amazon OA Solution in C++

``````    int totalStrength(vector<int>& A) {
int res = 0, ac = 0, mod = 1e9 + 7, n = A.size();
vector<int> stack = {}, acc(n + 2);
for (int r = 0; r <= n; ++r) {
int a = r < n ? A[r] : 0;
ac = (ac + a) % mod;
acc[r + 1] = (ac + acc[r]) % mod;
while (!stack.empty() && A[stack.back()] > a) {
int i = stack.back(); stack.pop_back();
int l = stack.empty() ? -1 : stack.back();
long lacc = l < 0 ? acc[i] : acc[i] - acc[l], racc = acc[r] - acc[i];
int ln = i - l, rn = r - i;
res = (res + (racc * ln - lacc * rn) % mod * A[i] % mod) % mod;
}
stack.push_back(r);
}
return (res + mod) % mod;
}``````
user
The text passage describes a problem statement for a coding challenge titled "Find Total Power" from Amazon's Online Assessment (OA). It includes a detailed explanation of the problem, examples, and solutions in Python, Java, and C++.

TYPE: NO_QUESTION

The passage does not contain a direct mathematical question or a word problem that requires a solution. Instead, it provides a problem statement and solutions for a coding challenge. The examples given are part of the problem description and are not standalone questions.