Add LowerBound search algorithm (#2406)

Co-authored-by: Pratik <pratik.padalia@akridata.com>

Searches/LowerBound.java

@@ -0,0 +1,97 @@
+package Searches;
+
+import static java.lang.String.format;
+
+import java.util.Random;
+import java.util.concurrent.ThreadLocalRandom;
+import java.util.stream.IntStream;
+
+/**
+ * The LowerBound method is used to return an index pointing to the first element in the range
+ * [first, last) which has a value not less than val, i.e. the index of the next smallest number
+ * just greater than or equal to that number. If there are multiple values that are equal to val it
+ * returns the index of the first such value.
+ *
+ * <p>This is an extension of BinarySearch.
+ *
+ * <p>Worst-case performance O(log n) Best-case performance O(1) Average performance O(log n)
+ * Worst-case space complexity O(1)
+ *
+ * @author Pratik Padalia (https://github.com/15pratik)
+ * @see SearchAlgorithm
+ * @see BinarySearch
+ */
+class LowerBound implements SearchAlgorithm {
+
+  // Driver Program
+  public static void main(String[] args) {
+    // Just generate data
+    Random r = ThreadLocalRandom.current();
+
+    int size = 100;
+    int maxElement = 100000;
+
+    Integer[] integers =
+        IntStream.generate(() -> r.nextInt(maxElement))
+            .limit(size)
+            .sorted()
+            .boxed()
+            .toArray(Integer[]::new);
+
+    // The element for which the lower bound is to be found
+    int val = integers[r.nextInt(size - 1)] + 1;
+
+    LowerBound search = new LowerBound();
+    int atIndex = search.find(integers, val);
+
+    System.out.println(
+        format(
+            "Val: %d. Lower Bound Found %d at index %d. An array length %d",
+            val, integers[atIndex], atIndex, size));
+
+    boolean toCheck = integers[atIndex] >= val || integers[size - 1] < val;
+    System.out.println(
+        format(
+            "Lower Bound found at an index: %d. Is greater or max element: %b", atIndex, toCheck));
+  }
+
+  /**
+   * @param array is an array where the LowerBound value is to be found
+   * @param key   is an element for which the LowerBound is to be found
+   * @param <T>   is any comparable type
+   * @return index of the LowerBound element
+   */
+  @Override
+  public <T extends Comparable<T>> int find(T[] array, T key) {
+    return search(array, key, 0, array.length - 1);
+  }
+
+  /**
+   * This method implements the Generic Binary Search
+   *
+   * @param array The array to make the binary search
+   * @param key   The number you are looking for
+   * @param left  The lower bound
+   * @param right The upper bound
+   * @return the location of the key
+   */
+  private <T extends Comparable<T>> int search(T[] array, T key, int left, int right) {
+    if (right <= left) {
+      return left;
+    }
+
+    // find median
+    int median = (left + right) >>> 1;
+    int comp = key.compareTo(array[median]);
+
+    if (comp == 0) {
+      return median;
+    } else if (comp < 0) {
+      // median position can be a possible solution
+      return search(array, key, left, median);
+    } else {
+      // key we are looking is greater, so we must look on the right of median position
+      return search(array, key, median + 1, right);
+    }
+  }
+}