CareerCup

Looks like a TSP, which is a O(2^n) problem.
This is why I created a greedy algorithm:

object ShortestDeliveryPath {
    val officeLocation = Location(0,0)
    val homeLocation = Location(100,100)
    val deliveryLocations = List((20,30), (50,50), (70,70)).map(Location.tupled)

    case class Location(x: Int, y: Int)


    def main (args: Array[String]) {
        val route = calculateRoute()
        println(route)
    }

    def calculateRoute() = {
        def go(location: Location, processedLocations: mutable.LinkedHashSet[Location]): mutable.LinkedHashSet[Location] = {
            val nextLocation = closestLocation(location, processedLocations)
            nextLocation.map(loc => go(loc, processedLocations + location)).getOrElse(processedLocations)
        }
        val route = (go(officeLocation, new mutable.LinkedHashSet()+officeLocation) + homeLocation).toList
        (route, routeDistance(route))
    }

    def routeDistance(route: List[Location]): Int = {
        route.sliding(2).map{case List(x, y) => distance(x, y)}.sum
    }

    def closestLocation(currentLocation: Location, processedLocations: mutable.LinkedHashSet[Location]): Option[Location] = {
        deliveryLocations
          .filterNot(processedLocations.contains)
          .map(loc => (loc, distance(loc, currentLocation)))
          .reduceOption((x, y) => if(x._2 < y._2) x else y)
          .map(_._1)
    }

    def distance(location1: Location, location2: Location) = Math.abs(location1.x - location2.x) + Math.abs(location1.y - location2.y)
}

coded using backtracking approach

int vist(vector< pair<int , int > > cust,pair<int ,int > home,vector<bool> vis,int i){
    int max=9999;
    int flag=1;
    for(int j=0;j<vis.size();j++){
        if(!vis[j]){
            flag=0;
            vis[j]=true;
            int temp = abs(cust[j].first,cust[i].first)+abs(cust[j].second,cust[i].second)+vist(cust,home,vis,j);
            vis[j]=false;
            if(temp<max) max=temp;
        }
    }
    if(flag==1){
        return abs(cust[i].first,home.first)+abs(cust[i].second,home.second);
    }
    else return max;
}


int location (pair<int ,int > off ,vector< pair<int , int > > cust ,pair<int ,int > home){
    vector<bool> vis(cust.size(),false);
    int max=9999;
    for(int j=0;j<vis.size();j++){
        if(!vis[j]){
            vis[j]=true;
            int temp = abs(cust[j].first,off.first)+abs(cust[j].second,off.second)+vist(cust,home,vis,j);
            vis[j]=false;
            if(temp<max) max=temp;
        }
    }
    return max;
}
int main(){
    pair<int ,int > off (88,81);
    pair<int ,int > home (85,80);
    vector<pair<int ,int > > cust;
    cust.push_back(make_pair(19,22));
    cust.push_back(make_pair(31,15));
    cust.push_back(make_pair(27,29));
    cust.push_back(make_pair(30,10));
    cust.push_back(make_pair(20,26));
    cust.push_back(make_pair(5,14));
    cout<<location(off,cust,home);
}

int main(){
pair<int ,int > off (88,81);
pair<int ,int > home (85,80);
vector<pair<int ,int > > cust;
cust.push_back(make_pair(19,22));
cust.push_back(make_pair(31,15));
cust.push_back(make_pair(27,29));
cust.push_back(make_pair(30,10));
cust.push_back(make_pair(20,26));
cust.push_back(make_pair(5,14));
cout<<location(off,cust,home);
}

#include<iostream>
using namespace std;

int abs(int aa)
{
	if(aa<0)
		return -1*aa;
	return aa;
}

int x[12],y[12],ox,oy,hx,hy,vis[12],ans,n,ct;

void solve(int xx,int yy,int visited,int curr_cost,int idx)
{
	int cost = 0;

	if(idx!=-1)
		vis[idx]=1;

	if(visited==n){
		//cout<<ct++<<endl;
		curr_cost += abs(xx-hx)+abs(yy-hy);
		ans = min(ans,curr_cost);
		return;
	}

	for(int i=0;i<n;i++)
	{
		if(!vis[i])
		{
			cost = curr_cost + abs(xx-x[i]) + abs(yy-y[i]);
			solve(x[i],y[i],visited+1,cost,i);
			vis[i]=0;
		}
	}

	if(idx!=-1)
		vis[idx]=0;
}

int main()
{
	ct=0;
	cin>>n;
	ans = INT_MAX;
	cin>>ox>>oy;
	cin>>hx>>hy;
	for(int i=0;i<n;i++)
	{
		vis[i]=0;
		cin>>x[i]>>y[i];
	}
	solve(ox,oy,0,0,-1);
	cout<<ans;
}

// Mr KIM by Himani ma'am on  GFG
#include<iostream>
using namespace std;

int abs(int aa)
{
	if(aa<0)
		return -1*aa;
	return aa;
}

int x[12],y[12],ox,oy,hx,hy,vis[12],ans,n,ct;

void solve(int xx,int yy,int visited,int curr_cost,int idx)
{
	int cost = 0;

	if(idx!=-1)
		vis[idx]=1;

	if(visited==n){
		//cout<<ct++<<endl;
		curr_cost += abs(xx-hx)+abs(yy-hy);
		ans = min(ans,curr_cost);
		return;
	}

	for(int i=0;i<n;i++)
	{
		if(!vis[i])
		{
			cost = curr_cost + abs(xx-x[i]) + abs(yy-y[i]);
			solve(x[i],y[i],visited+1,cost,i);
			vis[i]=0;
		}
	}

	if(idx!=-1)
		vis[idx]=0;
}

int main()
{
	ct=0;
	cin>>n;
	ans = INT_MAX;
	cin>>ox>>oy;
	cin>>hx>>hy;
	for(int i=0;i<n;i++)
	{
		vis[i]=0;
		cin>>x[i]>>y[i];
	}
	solve(ox,oy,0,0,-1);
	cout<<ans;
}