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| 1 | +package Searches; |
| 2 | + |
| 3 | +import static java.lang.String.format; |
| 4 | + |
| 5 | +import java.util.Random; |
| 6 | +import java.util.concurrent.ThreadLocalRandom; |
| 7 | +import java.util.stream.IntStream; |
| 8 | + |
| 9 | +/** |
| 10 | + * The LowerBound method is used to return an index pointing to the first element in the range |
| 11 | + * [first, last) which has a value not less than val, i.e. the index of the next smallest number |
| 12 | + * just greater than or equal to that number. If there are multiple values that are equal to val it |
| 13 | + * returns the index of the first such value. |
| 14 | + * |
| 15 | + * <p>This is an extension of BinarySearch. |
| 16 | + * |
| 17 | + * <p>Worst-case performance O(log n) Best-case performance O(1) Average performance O(log n) |
| 18 | + * Worst-case space complexity O(1) |
| 19 | + * |
| 20 | + * @author Pratik Padalia (https://github.com/15pratik) |
| 21 | + * @see SearchAlgorithm |
| 22 | + * @see BinarySearch |
| 23 | + */ |
| 24 | +class LowerBound implements SearchAlgorithm { |
| 25 | + |
| 26 | + // Driver Program |
| 27 | + public static void main(String[] args) { |
| 28 | + // Just generate data |
| 29 | + Random r = ThreadLocalRandom.current(); |
| 30 | + |
| 31 | + int size = 100; |
| 32 | + int maxElement = 100000; |
| 33 | + |
| 34 | + Integer[] integers = |
| 35 | + IntStream.generate(() -> r.nextInt(maxElement)) |
| 36 | + .limit(size) |
| 37 | + .sorted() |
| 38 | + .boxed() |
| 39 | + .toArray(Integer[]::new); |
| 40 | + |
| 41 | + // The element for which the lower bound is to be found |
| 42 | + int val = integers[r.nextInt(size - 1)] + 1; |
| 43 | + |
| 44 | + LowerBound search = new LowerBound(); |
| 45 | + int atIndex = search.find(integers, val); |
| 46 | + |
| 47 | + System.out.println( |
| 48 | + format( |
| 49 | + "Val: %d. Lower Bound Found %d at index %d. An array length %d", |
| 50 | + val, integers[atIndex], atIndex, size)); |
| 51 | + |
| 52 | + boolean toCheck = integers[atIndex] >= val || integers[size - 1] < val; |
| 53 | + System.out.println( |
| 54 | + format( |
| 55 | + "Lower Bound found at an index: %d. Is greater or max element: %b", atIndex, toCheck)); |
| 56 | + } |
| 57 | + |
| 58 | + /** |
| 59 | + * @param array is an array where the LowerBound value is to be found |
| 60 | + * @param key is an element for which the LowerBound is to be found |
| 61 | + * @param <T> is any comparable type |
| 62 | + * @return index of the LowerBound element |
| 63 | + */ |
| 64 | + @Override |
| 65 | + public <T extends Comparable<T>> int find(T[] array, T key) { |
| 66 | + return search(array, key, 0, array.length - 1); |
| 67 | + } |
| 68 | + |
| 69 | + /** |
| 70 | + * This method implements the Generic Binary Search |
| 71 | + * |
| 72 | + * @param array The array to make the binary search |
| 73 | + * @param key The number you are looking for |
| 74 | + * @param left The lower bound |
| 75 | + * @param right The upper bound |
| 76 | + * @return the location of the key |
| 77 | + */ |
| 78 | + private <T extends Comparable<T>> int search(T[] array, T key, int left, int right) { |
| 79 | + if (right <= left) { |
| 80 | + return left; |
| 81 | + } |
| 82 | + |
| 83 | + // find median |
| 84 | + int median = (left + right) >>> 1; |
| 85 | + int comp = key.compareTo(array[median]); |
| 86 | + |
| 87 | + if (comp == 0) { |
| 88 | + return median; |
| 89 | + } else if (comp < 0) { |
| 90 | + // median position can be a possible solution |
| 91 | + return search(array, key, left, median); |
| 92 | + } else { |
| 93 | + // key we are looking is greater, so we must look on the right of median position |
| 94 | + return search(array, key, median + 1, right); |
| 95 | + } |
| 96 | + } |
| 97 | +} |
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