Binary search if array contains duplicates

Question

Hi,

what is the index of the search key if we search for 24 in the following array using binary search.

array = [10,20,21,24,24,24,24,24,30,40,45]
         


        

Answer 1

For the sake of completeness here's an example in typescript, non-recursive version (binary operators are used to enforce operations on integers rather than floating-point arithmetic) Example is easily convertible to other C-like languages:

function binarySearch(array: number[], query: number): [number, number] {
    let from: number;
    let till: number;

    let mid = 0 | 0;
    let min = 0 | 0;
    let max = array.length - 1 | 0;

    while (min < max) {
        mid = (min + max) >>> 1;

        if (array[mid] < query) {
            min = mid + 1 | 0;
        } else {
            max = mid - 1 | 0;
        }
    }

    mid = min;
    min--;
    max++;

    from = array[mid] < query ? (array[max] === query ? max : mid) : (array[mid] === query ? mid : min);

    min = 0 | 0;
    max = array.length - 1 | 0;

    while (min < max) {
        mid = (min + max) >>> 1;

        if (query < array[mid]) {
            max = mid - 1 | 0;
        } else {
            min = mid + 1 | 0;
        }
    }

    mid = min;
    min--;
    max++;

    till = array[mid] > query ? (array[min] === query ? min : mid) : (array[mid] === query ? mid : max);

    return [from, till];
}

Here's how it can be used:

let array = [1, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7];

console.log(binarySearch(array, 0)); // Gives [ -1,  0 ] <= No value found, note that resulting range covers area beyond array boundaries
console.log(binarySearch(array, 1)); // Gives [  0,  0 ] <= Singular range (only one value found)
console.log(binarySearch(array, 2)); // Gives [  0,  1 ] <= Queried value not found, however the range covers argument value
console.log(binarySearch(array, 3)); // Gives [  1,  3 ] <= Multiple values found
console.log(binarySearch(array, 4)); // Gives [  3,  4 ] <= Queried value not found, however the range covers argument value
console.log(binarySearch(array, 5)); // Gives [  4,  9 ] <= Multiple values found
console.log(binarySearch(array, 6)); // Gives [  9, 10 ] <= Queried value not found, however the range covers argument value
console.log(binarySearch(array, 7)); // Gives [ 10, 10 ] <= Singular range (only one value found)
console.log(binarySearch(array, 8)); // Gives [ 10, 11 ] <= No value found, note that resulting range covers area beyond array boundaries