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Author: KumarJayanti

AlgoQuestion.java

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+package com.mycompany;
+
+/*
+  Algo question:
+  N people, M restaurants, on a one-dimensional street.  All the people are to meet at one restaurant,
+  find the restaurant, where total travel distance from all people to that restaurant is the shortest among all restaurants.
+
+  The problem can be solved with brutal force with O(n*m) complexity.  Question is how to solve it faster than brutal force.
+  Describe the algorithm, and why it is better than brutal force.  Coding is not required
+
+  [zc] this is one dimensional street.
+
+  A list of people can be represented with their coordinates (p1, p2, ... pn).
+
+  A list of restaurant can be represented with their coordinates (r1, r2, ... rm)
+
+  The distance between i-th people and j-th restaurant can be calculated as ABS(pi - rj)
+
+  Time Complexity of BruteForce Algorithm 1:  O(M * N)
+
+  Time Complexity of Proposed Algorithm 2 : O(M+N)
+  This Algorithm tries to compute the distance in two passes of the Combined Sorted List
+      Once from Left to Right and Another time from Right to Left
+      Time Complexity of the Algorithm :
+      O(M+N) : counting sort
+      O(M+N) : Left to Right Traversal
+      O(M+N) : Right to Left Traversal
+      O(M) : traversal over the restautart list to find the minimal cost
+      Overall Complexity =  O(3 * (M+N) + M), removing constant multiplier and lower order terms it is  O(M+N)
+
+      Space Complexity :  Needs O(M+N) extra storage for the combine list and O(M) addtional space to store
+      two lists of Restaurant objects for Left to Right and Right to Left Traversal respectively.
+
+ */
+
+import java.util.*;
+
+public class AlgoQuestion {
+
+    public static void main(String[] args) {
+
+        int[] people = new int[]{1,2,4,6,7};
+        int[] restaurants = new int[]{1,3,5};
+        int restaurantWithShortedDist = getShortestDistanceBruteForce(people, restaurants);
+        System.out.println("Nearest Restaurant for all people is: " + (restaurantWithShortedDist));
+
+        restaurantWithShortedDist = getShortestTotalDistanceOptimal(people, restaurants);
+        System.out.println("Nearest Restaurant for all people is: " + (restaurantWithShortedDist));
+
+        people = new int[]{3,4,2,5,9};
+        restaurants = new int[]{4,6,7};
+        restaurantWithShortedDist = getShortestDistanceBruteForce(people, restaurants);
+        System.out.println("Nearest Restaurant for all people is: " + (restaurantWithShortedDist));
+
+        restaurantWithShortedDist = getShortestTotalDistanceOptimal(people, restaurants);
+        System.out.println("Nearest Restaurant for all people is: " + (restaurantWithShortedDist));
+
+        people = new int[]{2,6,8,10,11};
+        restaurants = new int[]{7,9};
+        restaurantWithShortedDist = getShortestDistanceBruteForce(people, restaurants);
+        System.out.println("Nearest Restaurant for all people is: " + (restaurantWithShortedDist));
+
+        restaurantWithShortedDist = getShortestTotalDistanceOptimal(people, restaurants);
+        System.out.println("Nearest Restaurant for all people is: " + (restaurantWithShortedDist));
+
+    }
+
+    public static int getShortestDistanceBruteForce(int[] people, int[]  restaurants) {
+        int resultRestaurant= -1;
+        int globalMin = Integer.MAX_VALUE;
+        int totalOperations = 0;
+        for (int r=0; r < restaurants.length; r++) {
+            int currentRSum = 0;
+            for (int p=0; p < people.length; p++) {
+                currentRSum += Math.abs(people[p] - restaurants[r]);
+                totalOperations++;
+                if (currentRSum > globalMin) {
+                    break;
+                }
+            }
+            if (currentRSum < globalMin) {
+                globalMin = currentRSum;
+                resultRestaurant = r;
+            }
+        }
+        System.out.println("Minimum Distance for all people: " + globalMin);
+        return resultRestaurant;
+    }
+
+    public static  class Triple {
+        //distance
+        int d;
+        //r == true indicates restaurant
+        //otherwise person
+        boolean r;
+        int index;
+
+        public Triple(Integer d, Integer indx, boolean r) {
+            this.d = d;
+            this.r = r;
+            this.index = indx;
+        }
+        public int getDistance() {
+            return d;
+        }
+    }
+
+    public static class Restaurant {
+       int currentCost;
+       int cumCost;
+       int cumPeopleCount;
+       int peopleCount;
+       int currentCostRight;
+
+       Triple r;
+
+       public Restaurant(Triple r) {
+           this.r = r;
+       }
+
+       //assumes setCostAndCount method already called.
+        public void setCumCost(Restaurant prev) {
+           //if prev is null, it means i am the first restaurant in the list
+            if(prev == null) {
+                cumCost = 0;
+                cumPeopleCount = peopleCount;
+                return;
+            }
+            //the cumulative cost in any direction is the cost of moving the people from a previous restaurant
+            //to the current restaurant.
+            //For example if we have P1, P2, R3, P4, R5
+            //The algorithm assigns P1 and P2 to the next Restaurant R3.
+            //P4 is assigned to R5.
+            //Then the  cumulative cost at R5 is the cost of moving P1 and P2 from R3 to R5 plus the
+            //cost of P4 at R5.
+            //A single pass from Left to Right cannot compute the cumulative costs of all Restaurants
+            //against each of the people.  So we perform a second pass in the opposite direction
+            //to complete the cumulative cost computations.
+            //Please see below for how the total cost is computed.
+            cumCost = prev.cumCost+ prev.currentCost + Math.abs(r.d - prev.r.d) * prev.cumPeopleCount;
+            cumPeopleCount = peopleCount + prev.cumPeopleCount;
+        }
+
+        public void setCostAndCount(int c, int count) {
+           currentCost = c;
+           peopleCount = count;
+        }
+
+        public void updateCostAndCount(int costUpdate, int countUpdate) {
+            currentCost += costUpdate;
+            peopleCount += countUpdate;
+            currentCostRight = costUpdate;
+        }
+    }
+
+    //Linear implementation.
+    public static int getShortestTotalDistanceOptimal(int[] people, int[]  restaurants) {
+
+        int[] restaurantDistance = new int[restaurants.length];
+        List<Restaurant> restaurantsListLR = new ArrayList<>();
+        List<Restaurant> restaurantsListRL = new ArrayList<>();
+        List<Triple> combined = new ArrayList<>();
+        for (int i=0; i< people.length; i++) {
+            combined.add(new Triple(people[i], i, false));
+        }
+        for (int i=0; i< restaurants.length; i++) {
+            Triple t = new Triple(restaurants[i], i, true);
+            combined.add(t);
+            restaurantsListLR.add(new Restaurant(t));
+            restaurantsListRL.add(new Restaurant(t));
+        }
+
+        //TODO: do a Counting sort for people with restaurants
+        //based on the distance from origin.
+        //This will be O(M+N) when changed to Counting Sort
+        combined.sort(Comparator.comparing(Triple::getDistance));
+
+        int runningCost = 0;
+        int runningCount = 0;
+
+        Restaurant prev = null;
+        Restaurant current = null;
+        for (int i=0; i < combined.size(); i++) {
+            Triple t = combined.get(i);
+            if (t.r) {
+                //restaurant handling
+                current = restaurantsListLR.get(t.index);
+                current.setCostAndCount(Math.abs((runningCount * t.d) - runningCost), runningCount);
+                runningCost = 0;
+                runningCount = 0;
+                current.setCumCost(prev);
+                prev = current;
+
+            } else {
+               //people handling
+                runningCost += t.d;
+                runningCount++;
+            }
+        }
+
+        //if at the end of this loop we have runningCost it needs to be attributed
+        //to current restaurant
+        if (runningCount > 0) {
+            current.updateCostAndCount(Math.abs((runningCount * current.r.d) - runningCost), runningCount);
+        }
+
+        runningCost = 0;
+        runningCount = 0;
+        prev = null;
+        current = null;
+
+        for (int i= combined.size() -1; i >=0; i--) {
+            Triple t = combined.get(i);
+            if (t.r) {
+                //restaurant handling
+                current = restaurantsListRL.get(t.index);
+                current.setCostAndCount(Math.abs((runningCount * t.d) - runningCost), runningCount);
+                runningCost = 0;
+                runningCount = 0;
+                current.setCumCost(prev);
+                prev = current;
+
+            } else {
+                //people handling
+                runningCost += t.d;
+                runningCount++;
+            }
+        }
+
+        //if at the end of this loop we have runningCost it needs to be attributed
+        //to current restaurant
+        if (runningCount > 0) {
+            current.updateCostAndCount(Math.abs((runningCount * current.r.d) - runningCost), runningCount);
+        }
+
+        int minCost = Integer.MAX_VALUE;
+        int minIndex = -1;
+        for (int i=0; i < restaurantsListLR.size(); i++) {
+            Restaurant rL = restaurantsListLR.get(i);
+            Restaurant rR = restaurantsListRL.get(i);
+            int totalCost = 0;
+            //if the restaurant is a corner restaurant we compute the total cost and try to
+            //eliminate duplicate attribution for people who are on either sides of the first
+            //and last restaurants
+            //Otherwise the cost for any Middle restaurant is the cumulative cost from Left to Right
+            //Plus the cumulative cost from Right to Left, Plus the cost of people assigned to the
+            //Restaurant itself.
+
+            if (i==0) {
+                totalCost = rL.currentCost + rR.cumCost + (rR.currentCost - rR.currentCostRight);
+            } else if (i==restaurantsListLR.size() -1) {
+                totalCost = (rL.currentCost - rL.currentCostRight) + rL.cumCost + rR.currentCost;
+            } else {
+                totalCost = rL.currentCost + rR.currentCost + rL.cumCost + rR.cumCost;
+            }
+            if (totalCost < minCost) {
+                minCost = totalCost;
+                minIndex = i;
+            }
+            //System.out.println("Total Cost at Restaurant:" + i + "=" + totalCost);
+        }
+
+        System.out.println("Minimum Distance for all people: " + minCost);
+        return minIndex;
+    }
+
+}