October 4, 2017

# Fraudulent Activity Notifications

**Fraudulent Activity Notifications**

Hacker Land National Bank has a simple policy for warning clients about possible fraudulent account activity. If the amount spent by a client on a particular day is

*greater than or equal to 2X*the client's median spending for the last d days, they send the client a notification about potential fraud. The bank doesn't send the client any notifications until they have at least d prior days of transaction data.Given the value of d and a client's total daily expenditures for a period of n days, find and print the number of times the client will receive a notification over all n days.

**Note**: The median of a list of numbers can be found by arranging all the numbers from smallest to greatest. If there is an odd number of numbers, the middle one is picked. If there is an even number of numbers, median is then defined to be the average of the two middle values. (Wikipedia)

**Input Format**

The first line contains two space-separated integers denoting the respective values of n (the number of days there is transaction data for) and d (the number of prior days the bank uses to calculate median spending).

The second line contains n space-separated non-negative integers where each integer i denotes expenditure (i.e., the client's total expenditure for day i).

The second line contains n space-separated non-negative integers where each integer i denotes expenditure (i.e., the client's total expenditure for day i).

**Output Format**

Print an integer denoting the total number of times the client receives a notification over a period of days.

**Sample Input 0**

```
9 5
2 3 4 2 3 6 8 4 5
```

**Sample Output 0**

```
2
```

**Explanation 0**

We must determine the total number of notifications the client receives over a period of n=9 days. For the first five days, the customer receives no notifications because the bank has insufficient transaction data and notifications=0 .

On the sixth day, the bank has d=5 days of prior transaction data 2,3,4,2,3 and median= 3 dollars. The client spends 6 dollars, which triggers a notification because 6>=2 X median. Thus notifications=1 .

On the seventh day, the bank has d=5 days of prior transaction data, 3,4,2,3,6 and median=3 dollars. The client spends 8 dollars, which triggers a notification because 8>=2 X median. Thus, notifications=1+1=2 .

On the eighth day, the bank has d=5 days of prior transaction data 4,2,3,6,8 and median = 4 dollars. The client spends 4 dollars, which does not trigger a notification because 4<2 X median.

On the ninth day, the bank has d=5 days of prior transaction data 2,3,6,8,4 and a transaction median of 4 dollars. The client spends 5 dollars, which does not trigger a notification because 5<2 X medain.

We then print the final value of notifications (which is 2) as our answer.

**Sample Input 1**

```
5 4
1 2 3 4 4
```

**Sample Output 1**

`0`

**Code:**

public class FraudulentActivityNotifications {

private static final int MAX_EXPENDITURE = 200;

private static int solve(int[] a, int n, int d) {

int ans = 0;

int[] histogram = new int[MAX_EXPENDITURE + 1];

// Carry a histogram of the last d expenditures

for (int i = 0; i < d; i++) {

histogram[a[i]] = histogram[a[i]] + 1;

}

for (int i = d; i < n; i++) {

int cursor = 0;

int currentAmount = a[i];

double median = 0;

int left = -1;

int right = -1;

for (int e = 0; e <= MAX_EXPENDITURE; e++) {

cursor += histogram[e];

if (d % 2 == 1) {

// Odd -> Pick middle one for median

if (cursor >= d / 2 + 1) {

median = e;

break;

}

} else {

// Even -> Pick average of two middle values for median

if (cursor == d / 2) {

left = e;

}

if (cursor > d / 2 && left != -1) {

right = e;