Find number of Employees Under every Manager

An employee and his boss are mapped in a dictionary as a number of (employee, manager) pairs, as shown 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.

Create a function to return the total number of employees, not just their direct reports, that each manager in the hierarchy has. One boss may be presumed to be the only one to whom an employee directly reports. The root node/ceo is listed as reporting to himself in the aforementioned vocabulary.

An output dictionary with the following words should be produced.

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

There may be more ways to answer this, but I found it fascinating and thought I'd share:

1. With the combination of Manager->DirectReportingEmployee, create a reverse map. Employees will, of course, be numerous, thus the value in the map is a list of strings.
       "C" --> "A", "B",
       "E" --> "D" 
       "F" --> "C", "E", "F"
2. Utilize the provided employee-manager map to iterate now, and use the newly created reverse map to determine the number of employees under the management.

	Let's call the map produced in step 2 "mngrEmpMap." Do this for each employee, abbreviated "emp."
   • Count under "emp" is 0 if "emp" is absent from "mngrEmpMap" [No one reports to "emp"]
   • b) When "emp" appears in "mngrEmpMap" Calculate the total number of employees under "emp" recursively using the list of direct reports from the map "mngrEmpMap."

Utilizing memory (Dynamic programming) to determine the number of employees under a management in step 2.b saves us from having to repeat the process for for individual employee. In the code below, the recursive function populateResultUtil() makes use of memoization to prevent re-computation of the same results.

Code in C++

#include <bits/stdc++.h>
using namespace std;

// This is a recursive function to fill count for 'mngr'
// using mngrEmpMap. This function uses memoization to
// avoid re- computations of subproblems.
int populateResultUtil(
	string mngr,
	unordered_map<string, vector<string> > mngrEmpMap,
	map<string, int>& result)
{
	int count = 0;

	// means employee is not a manager of any other employee
	if (mngrEmpMap.find(mngr) == mngrEmpMap.end()) {
		result.insert({ mngr, 0 });
		return 0;
	}

	// this employee count has already been done by this
	// method, so avoid re-computation
	else if (result.find(mngr) != result.end()) {
		count = result[mngr];
	}
	else {
		vector<string> directReportEmpList
			= mngrEmpMap[mngr];
		count = directReportEmpList.size();
		for (int i = 0; i < directReportEmpList.size();
			i++) {
			count += populateResultUtil(
				directReportEmpList[i], mngrEmpMap, result);
		}
		result.insert({ mngr, count });
	}
	return count;
}

// This function populates 'result' for given input
// 'dataset'
void populateResult(unordered_map<string, string> dataset)
{

	// A hashmap to store result. It stores count of
	// employees under every employee, the count may by 0
	// also
	map<string, int> result;

	// To store reverse of original map, each key will have
	// 0 to multiple values
	unordered_map<string, vector<string> > mngrEmpMap;

	// To fill mngrEmpMap, iterate through the given map
	for (auto d : dataset) {
		string emp = d.first;
		string mngr = d.second;
		if (emp != mngr) // excluding emp-emp entry
		{
			// If 'emp' is the first employee under 'mngr'
			if (mngrEmpMap.find(mngr) == mngrEmpMap.end()) {
				vector<string> directReportList;
				directReportList.push_back(emp);
				// add a new entry for the mngr with empty
				// directReportList
				mngrEmpMap[mngr] = directReportList;
			}
			else {
				// Get the previous list of direct reports
				// under current 'mngr' and add the current
				// 'emp' to the list
				mngrEmpMap[mngr].push_back(emp);
			}
		}
	}

	// 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 (auto d : dataset) {
		populateResultUtil(d.first, mngrEmpMap, result);
	}

	map<string, int>::iterator itr;
	auto end = result.end();
	end--; // end to second last;

	cout << "result = {";
	for (itr = result.begin(); itr != end; itr++) {
		cout << itr->first << "=" << itr->second << ", ";
	}
	cout << itr->first << "=" << itr->second;
	cout << "}";
}

int main()
{
	unordered_map<string, string> dataset;
	dataset["A"] = "C";
	dataset["B"] = "C";
	dataset["C"] = "F";
	dataset["D"] = "E";
	dataset["E"] = "F";
	dataset["F"] = "F";

	populateResult(dataset);

	return 0;
}

Output:

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

Next TopicUnion and Intersection of two Linked Lists

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