1. Code Question 1
Developers at Amazon are building a multi-process analysis tool to analyze the computational intensity of the processes. There are n processes and the i-th process needs process[i] computation resources for completion.
Two processes are considered to be computationally the same if their resource requirements differ by at most m.
Given the array process and an integer m, find the number of pairs of processes that are computationally the same.
Example
Suppose n = 4, process = [7, 10, 13, 11], and m = 3.
| Pairs | Difference | Computationally Same |
|---|---|---|
| (7, 10) | 7 - 10 | |
| (7, 13) | 7 - 13 | |
| (7, 11) | 7 - 11 | |
| (10, 13) | 10 - 13 | |
| (10, 11) | 10 - 11 | |
| (13, 11) | 13 - 11 |
The result is 4 pairs.
Function Description
Complete the function getComputationalEquivalents in the editor below.
getComputationalEquivalents has the following parameters:
- int process[n]: the computational resource requirement of the processes.
- int m: the threshold for being computationally the same.
Returns
- long int: the number of pairs of processes that are computationally the same.
Constraints
1 <= n <= 200,0001 <= process[i] <= 1,000,0000 <= m <= 1,000,000
Sample Case 0
Input
STDIN FUNCTION
----- --------
4 process[] size n = 4
100 200 300 400 process = [100, 200, 300, 400]
250 m = 250
Output
5
Explanation
The computationally-same processes are:
- (100, 200)
- (100, 300)
- (200, 300)
- (200, 400)
- (300, 400)
Thus, the result is 5.
Sample Case 1
Input
STDIN FUNCTION
----- --------
3 process[] size n = 3
10 12 11 process = [10, 12, 11]
0 m = 0
Output
0
Explanation
All the pairs of processes have differences between computational resource requirements greater than 0.
2. Code Question 2
Data analysts at Amazon are analyzing time-series data. It was concluded that the data of the n-th item was dependent on the data of some x-th day if there is a positive integer k such that floor(n / k) = x, where floor(z) represents the largest integer less than or equal to z.
Given n, find the sum of all the days' numbers on which the data of the x-th (0 ≤ x ≤ n) will be dependent.
Example
Suppose n = 5.
| x | k | floor(n / k) |
|---|---|---|
| 6 | Does not exist | - |
| 5 | floor(5 / 5) = 1 | 1 |
| 2 | floor(5 / 2) = 2 | 2 |
| 3 | Does not exist | - |
| 4 | Does not exist | - |
| 1 | floor(5 / 1) = 5 | 5 |
Hence the answer is 0 + 1 + 2 + 5 = 8.
Function Description
Complete the function getDataDependenceSum in the editor below.
getDataDependenceSum takes the following arguments:
- long int n: the day to analyze the data dependency for
Returns
- long int: the sum of all the dependent days' numbers
Constraints
1 ≤ n ≤ 10^10
Sample Case 0
Input
STDIN FUNCTION
----- --------
13 n = 13
Output
29
Explanation
The data of n = 13-th day is dependent on [0, 1, 2, 3, 4, 6, 13] obtained for k = [14, 13, 6, 4, 3, 2, 1].
Sample Case 1
Input
STDIN FUNCTION
----- --------
1 n = 1
Output
1
Explanation
The only dependency is 1.
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