Find number of Employees Under every Employee

Given a dictionary that contains mapping of employee and his manager as a number of (employee, manager) pairs like below.

```{ "A", "C" },
{ "B", "C" },
{ "C", "F" },
{ "D", "E" },
{ "E", "F" },
{ "F", "F" }

In this example C is manager of A,
C is also manager of B, F is manager
of C and so on.
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Write a function to get no of employees under each manager in the hierarchy not just their direct reports. It may be assumed that an employee directly reports to only one manager. In the above dictionary the root node/ceo is listed as reporting to himself.

Output should be a Dictionary that contains following.

```A - 0
B - 0
C - 2
D - 0
E - 1
F - 5 ```

Source: Microsoft Interview

This question might be solved differently but i followed this and found interesting, so sharing:

``` 1. Create a reverse map with Manager->DirectReportingEmployee
combination. Off-course employee will be multiple so Value
in Map is List of Strings.
"C" --> "A", "B",
"E" --> "D"
"F" --> "C", "E", "F"

2. Now use the given employee-manager map to iterate  and at
the same time use newly reverse map to find the count of
employees under manager.

Let the map created in step 2 be 'mngrEmpMap'
Do following for every employee 'emp'.
a) If 'emp' is not present in 'mngrEmpMap'
Count under 'emp' is 0 [Nobody reports to 'emp']
b) If 'emp' is present in 'mngrEmpMap'
Use the list of direct reports from map 'mngrEmpMap'
and recursively calculate number of total employees
under 'emp'. ```

A trick in step 2.b is to use memorization(Dynamic programming) while finding number of employees under a manager so that we don’t need to find number of employees again for any of the employees. In the below code populateResultUtil() is the recursive function that uses memoization to avoid re-computation of same results.

Below is Java implementation of above ides

```// Java program to find number of persons under every employee
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class NumberEmployeeUnderManager
{
// A hashmap to store result. It stores count of employees
// under every employee, the count may by 0 also
static Map<String,Integer> result =
new HashMap<String, Integer>();

// Driver function
public static void main(String[] args)
{
Map<String, String> dataSet = new HashMap<String, String>();
dataSet.put("A", "C");
dataSet.put("B", "C");
dataSet.put("C", "F");
dataSet.put("D", "E");
dataSet.put("E", "F");
dataSet.put("F", "F");

populateResult(dataSet);
System.out.println("result = " + result);
}

// This function populates 'result' for given input 'dataset'
private static void populateResult(Map<String, String> dataSet)
{
// To store reverse of original map, each key will have 0
// to multiple values
Map<String, List<String>> mngrEmpMap =
new HashMap<String, List<String>>();

// To fill mngrEmpMap, iterate through the given map
for (Map.Entry<String,String> entry: dataSet.entrySet())
{
String emp = entry.getKey();
String mngr = entry.getValue();
if (!emp.equals(mngr)) // excluding emp-emp entry
{
// Get the previous list of direct reports under
// current 'mgr' and add the current 'emp' to the list
List<String> directReportList = mngrEmpMap.get(mngr);

// If 'emp' is the first employee under 'mgr'
if (directReportList == null)
directReportList = new ArrayList<String>();

// Replace old value for 'mgr' with new
// directReportList
mngrEmpMap.put(mngr, directReportList);
}
}

// Now use manager-Emp map built above to populate result
// with use of populateResultUtil()

// note- we are iterating over original emp-manager map and
// will use mngr-emp map in helper to get the count
for (String mngr: dataSet.keySet())
populateResultUtil(mngr, mngrEmpMap);
}

// This is a recursive function to fill count for 'mgr' using
// mngrEmpMap.  This function uses memoization to avoid re-
// computations of subproblems.
private static int populateResultUtil(String mngr,
Map<String, List<String>> mngrEmpMap)
{
int count = 0;

// means employee is not a manager of any other employee
if (!mngrEmpMap.containsKey(mngr))
{
result.put(mngr, 0);
return 0;
}

// this employee count has already been done by this
// method, so avoid re-computation
else if (result.containsKey(mngr))
count = result.get(mngr);

else
{
List<String> directReportEmpList = mngrEmpMap.get(mngr);
count = directReportEmpList.size();
for (String directReportEmp: directReportEmpList)
count +=  populateResultUtil(directReportEmp, mngrEmpMap);

result.put(mngr, count);
}
return count;
}
}
```

Output:

`result = {D=0, E=1, F=5, A=0, B=0, C=2}`

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