Question

– This is my find() method using Binary Search algorithm:

• It works just as you would expect it to. No problems at all.

  public int find(long searchKey) {
  int lowerBound = 0;
  int upperBound = nElems - 1;
  int currentIndex;
  
  while(true) {
      currentIndex = (lowerBound + upperBound) / 2;
      if(a[currentIndex] == searchKey)
          return currentIndex; // found it!
      else if(lowerBound > upperBound)
          return nElems; // can't find it
      else { // so then divide range
          if(a[currentIndex] < searchKey)
              lowerBound = currentIndex + 1; // it's in upper half
          else
              upperBound = currentIndex - 1; // it's in lower half
      } // end else divide range
  } // end while loop
  } // end find() method
  

Here’s the original insert() method using linear search. Pretty straightforward, right?

public void insert(long value) { // put element into array
    int j;
    for(j=0; j<nElems; j++) // find where it goes
        if(a[j] > value) // (linear search)
            break;
    for(int k=nElems; k>j; k--) // move bigger ones up
        a[k] = a[k-1];
    a[j] = value; // insert it
    nElems++; // increment size
} // end insert()

I need to modify the insert() method to use the binary search algorithm of the find() method. Here’s what I came up with so far. Obviously there’s something wrong with it, but I can’t seem to find the problem. It doesn’t work at all, i.e. no insertions are performed:

public int insertBS(long value) {
    int lowerBound = 0;
    int upperBound = nElems - 1;
    int curIn;

    while(true) {
        curIn = (lowerBound + upperBound) / 2;
        if(a[curIn] == value)
            return curIn;
        else if(lowerBound > upperBound)
            return nElems;
        else {
            if(a[curIn] < value)
                lowerBound = curIn + 1;
            else
                upperBound = curIn - 1;
        }

        for(int k=nElems; k>curIn; k--) // move bigger one up
            a[k] = a[k-1];
        a[curIn] = value; 
        nElems++; 
    }
}

Language: Java

Using ordered array.

Answer 1

Um, why not just CALL your find function?

public int insertBS(long value) {
    int curIn = find(value); // find where it goes (binary search)
    for(int k=nElems; k>curIn; k--) // move bigger one up
        a[k] = a[k-1];
    a[j] = value; // insert it
    nElems++; // increment size

}

This way, when you optimize/change your find function, your insert function will go faster, too!

As a side note, I think your find function will not give you expected behavior, as written. If you have a list of [0,1,4,5,9] and I search for 7, I will get an index of nElems (5), which could be misinterpreted as the values at indexes 0 to 4 are all less than 7. Seems a little wonky.