Code Question 1

Description
Data scientists at Amazon are working on a logistics optimization tool to arrange delivery routes based on existing route patterns.

A prototype algorithm takes in two integers, size and target_sum, and generates a sequence of size whose sum of elements equals target_sum, and the absolute values of the elements form a permutation of size size. The tool outputs the lexicographically smallest such sequence.

Given two integers, size and target_sum, return the lexicographically smallest sequence of integers such that

1. The sum of its elements equals target_sum.
2. The absolute values of its elements form a permutation of size size.

Note:
A sequence of size integers is a permutation if it contains all integers from 1 to size exactly once.
For example:

• [4, 1, 2, 5, 3] is a permutation.
• But [2, 2, 3, 4, 5] is not.

Lexicographical Order Note:
Given two permutations x and y, x is lexicographically smaller than y if there exists an index i where x[i] ≠ y[i], and for this smallest index i, x[i] < y[i].
This means that when comparing x and y element by element from the start, the first position at which they differ determines their order. If the element in x is less than the corresponding element in y at this position, x is considered smaller.

Example
Suppose size = 5, target_sum = 9
Some sequences of size 5 with sum 9 are:

Function Description
Complete the function findOptimalSequence in the editor below.

findOptimalSequence has the following parameters:

• int size: the number of elements in the sequence
• long int target_sum: the sum of elements in the sequence

Returns:

• int[size]: the lexicographically smallest sequence of size integers that meets the criteria.
• If it is not possible, return an array of size size, filled with zeroes.

Constraints:

• 1 <= size <= 100000
• -6000000000 <= target_sum <= 6000000000

Sample Case 0
Input:

size = 4  
target_sum = -2

Output:

-4  
-2  
1  
3

Explanation:
Here size = 4 and target_sum = -2
Possible sequences with size = 4 and target_sum = -2 which also form a permutation, when absolute values of elements are taken, are:

• [-1, -2, -3, 4]
• [-3, 1, 2, 4]
• [-2, -4, 1, 3]
• [-4, -2, 1, 3] etc.

Code Question 2

Description
Returns:
int: the number of subsequences of c that is lexicographically greater than s, modulo 10^9 + 7.

Constraints

• 1 <= |c| <= 100000
• 1 <= |s| <= 100
• c and s consist of lowercase English letters

Function Description
Complete the function countSecurePasswordVariations in the editor below.

countSecurePasswordVariations has the following parameters:

• string c: customer's password
• string s: system-generated password

Returns:

• int: the number of subsequences of c that is lexicographically greater than s, modulo 10^9 + 7.

Sample Case 0

Input:

c = "bab"  
s = "ab"

Output:

5

Explanation:
Let's examine all possible subsequences that can be derived from c = "bab" and compare them lexicographically with s = "ab":

From all the subsequences of c, we find that:

• 1 subsequence is lexicographically smaller than s ("a")
• 1 subsequence is lexicographically equal to s ("ab")
• 5 subsequences are lexicographically greater than s
  So the answer is 5.

另一个例子：

Input:

c = "aba"  
s = "ab"

Output:

3

Explanation:
Let's look at all possible subsequences that can be obtained from c:

From all possible subsequences, 3 are lexicographically smaller, 1 is equal, and 3 are greater than s. Hence the answer is 3.

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