Algorithm for maximum non overlapping bridges between cities

Question

There are equal number of cities on each side of the river. A bridge is there from city on one side to the city on other side represented by 1#y3 where city 1 on the lower side having bridge to the city 3 on upper side. We have to find maximum number of non overlapping bridges . So for input 1#y2, 2#y4, 3#y1, 4#y5, 5#y3, 6#y6 out will be 4 as 1#y2, 2#y4, 4#y5, 6#y6 are non overlapping.

This is my code -

public static int maxNonOverlappingBridges(String input1[]) {
    int result = 0;
    for (int i = 0; i < input1.length; i++) {
        int total = 1;
        int notCrossing = Integer.parseInt(input1[i].substring(input1[i].length() - 1));
        for (int j = 0; j < input1.length; j++) {
            if (j < i) {
                if (Integer.parseInt(input1[j].substring(input1[j].length() - 1)) < notCrossing) {
                    total += 1;
                    notCrossing = Integer.parseInt(input1[j].substring(input1[j].length() - 1));
                }
            } else if (j > i) {
                if (Integer.parseInt(input1[j].substring(input1[j].length() - 1)) > notCrossing) {
                    total += 1;
                    notCrossing = Integer.parseInt(input1[j].substring(input1[j].length() - 1));
                }
            } else {
                notCrossing = Integer.parseInt(input1[j].substring(input1[j].length() - 1));
            }

        }
        if (total > result) result = total;
    }
    return result;
}

Is there a more optimized algorithm for this?

Answer 1

This runs in O(nLog(n)) .

public static int maxNonOverlappingBridges(String[] bridges) {
    int overlappings1 = 0;
    int overlappings2 = 0;
    int maxIndexOfCityOnOtherSide = 0;

    /*
     * Sorting bridge connections with respect to the left index. (i.e : 2 in 2#y4)
     * O(n*log(n)) time
     */      
    Arrays.sort(bridges);

    List<Integer[]> brigesAsArray = new ArrayList<>();

    Integer[] previousBridge = null; 

    for(String b: bridges){

        if(previousBridge == null){
            String[] bridgeIndexes = b.split("#y");
            previousBridge = new Integer[]{Integer.parseInt(bridgeIndexes[0]),Integer.parseInt(bridgeIndexes[1])};
            maxIndexOfCityOnOtherSide = previousBridge[1];              
            brigesAsArray.add(previousBridge);
            continue;
        }

        String[] bridgeIndexes = b.split("#y");
        Integer[] currentBridge = new Integer[]{Integer.parseInt(bridgeIndexes[0]),Integer.parseInt(bridgeIndexes[1])};

        if(currentBridge[1] < maxIndexOfCityOnOtherSide){
            //overlapping found;
            overlappings1++;
        }else{
            maxIndexOfCityOnOtherSide = currentBridge[1];
        }

        previousBridge = currentBridge;
        brigesAsArray.add(previousBridge);
    }       

    Integer[][] bridgeIndexes = brigesAsArray.toArray(new Integer[0][0]);
    brigesAsArray.toArray(bridgeIndexes);       

    /*
     * Sorting bridge connections with respect to the right index. (i.e : 4 in 2#y4)
     * O(n*log(n)) time
     */ 

    Arrays.sort(bridgeIndexes, new Comparator<Integer[]>() {
        @Override
        public int compare(Integer[] o1, Integer[] o2) {
            return Integer.compare(o1[1], o2[1]);
        }           
    });

    previousBridge = null;

    for(Integer[] b: bridgeIndexes){

        if(previousBridge == null){
            maxIndexOfCityOnOtherSide = b[0];   
            previousBridge = b;
            continue;
        }

        if(b[0] < maxIndexOfCityOnOtherSide){
            //overlapping found;
            overlappings2++;
        }else{
            maxIndexOfCityOnOtherSide = b[0];
        }

        previousBridge = b;
        brigesAsArray.add(previousBridge);
    }   
    return (bridges.length - Math.min(overlappings1, overlappings2));
}

Hope this helps.

Answer 2

simple solution with O(nLog(n)) ...

 public static int bridge_count1(String[] input1,int input2)
      {
         int count=0;
         Map<Integer,Integer> map=new TreeMap<Integer,Integer>();
         for(int i=0;i<input1.length;i++)
         {
             String cityCon=input1[i];
             String cityArray[]=cityCon.split("#");
             int fst=Integer.parseInt(cityArray[0]);
             int sec=Integer.parseInt(cityArray[1]);
             map.put(fst, sec);
         }

         Iterator<Integer> it=map.keySet().iterator();
         int max=0;
         while(it.hasNext())
         {
             int val=map.get(it.next());
             if(max<=val)
             {
                 max=val;
                 count++;
             }
        }


         return count;

  }

Answer 3

public static int bridge_count(String[] input1,int input2)
{
    int[][] track=new int[input2][input2];
    int count=0;

    for(int i=0;i<input1.length;i++)
    {
        String cityCon=input1[i];
        String cityArray[]=cityCon.split("#");
        int fst=Integer.parseInt(cityArray[0]);
        int sec=Integer.parseInt(cityArray[1]);
        track[fst-1][sec-1]=-1;
    }

    int found=0;
    int maxCol=-1;

    for(int c=0;c<input2;c++)
    {
        found=-1;
        for(int j=0;j<input2;j++)
        {
            if(track[c][j]==-1)
            {
             found=j;
             break;
            }
        }    

        if(found!=-1 && maxCol<=found)
        {
            count++;
            maxCol=found;
        }    
    }
    return count;
}