Merge pull request #86 from jaebradley/implement-binary-search

Implement binary search

Author: jaebradley

codereview/binarySearch.md

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+## Purpose
+
+Implement a binary search algorithm that takes a sorted `int` array and some `int` target value and returns the index of the
+target value, if it exists.
+
+## Discussion
+
+The way I thought about implementing a binary search algorithm was the following
+
+1. Given an array of sorted `int` values, pick the first, last, and middle indices (round down if there is an even number of indices).
+2. If the target value equals any of the values at the first/ last / middle index, return that index.
+   Else, check to see if the target value is less / greater than the middle index value.
+   1. If it's less than the middle index value, than we can assume that the target value, if it exists,
+      is between the first index and the middle index (since the array should be sorted). Thus, we can call our search
+      function on this sub-array, specifying a start index of the first index + 1 (since we already checked this)
+      and an end index of the middle index - 1 (again, since we already checked this).
+  2. If it's greater than the middle index value, we can assume that the target value is between the middle index and the last index.
+     Thus, we can call the search function on this sub-array, specifying a start index of the middle index + 1 and an
+     end index of the last index - 1.
+3. We continue this process of analyzing the sub-arrays until our sub-array is empty, in which case a `NoSuchElementException`
+   is thrown.
+
+
+Things that I'm unsure about
+
+* Does it make sense to have the `public` `search` method immediately call the `private` `searchSubArray` method?
+  The reason I did this is to obfuscate the idea of a `leftIndex` / `rightIndex` from the API user.
+* Does the `NoSuchElementException` make sense? Would returning `-1` make more sense?
+* Any particular thoughts on my use of early returns?
+
+## Implementation
+
+    import java.util.NoSuchElementException;
+
+    public class BinarySearcher {
+        /**
+         * Executes a binary search for some target value given an input array of sorted values
+         * @param values a sorted array
+         * @param target a value to search for
+         * @return the index of the target value, if it exists. If the target value does not exist, a NoSuchElementException is thrown.
+         */
+        public static int search(int[] values, int target) {
+            return searchSubArray(values, 0, values.length - 1, target);
+        }
+
+        private static int searchSubArray(int[] values, int leftIndex, int rightIndex, int target) {
+            if (values.length == 0 || leftIndex < 0 || rightIndex < 0) {
+                throw new NoSuchElementException(String.format("Unable to find target: {} in values", target));
+            }
+
+            if (target == values[leftIndex]) {
+                return leftIndex;
+            }
+
+            if (target == values[rightIndex]) {
+                return rightIndex;
+            }
+
+            int middleIndex = Double.valueOf(Math.floor((rightIndex - leftIndex) / 2)).intValue();
+
+            int middleValue = values[middleIndex];
+
+            if (target < middleValue) {
+                return searchSubArray(values, leftIndex + 1, middleIndex - 1, target);
+            }
+
+            else if (target > middleValue) {
+                return searchSubArray(values, middleIndex + 1, rightIndex - 1, target);
+            }
+
+            else {
+                return middleIndex;
+            }
+        }
+    }

src/main/java/problems/impl/BinarySearcher.java

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+package problems.impl;
+
+import java.util.NoSuchElementException;
+
+public class BinarySearcher {
+    /**
+     * Executes a binary search for some target value given an input array of sorted values
+     * @param values a sorted array
+     * @param target a value to search for
+     * @return the index of the target value, if it exists. If the target value does not exist, a NoSuchElementException is thrown.
+     */
+    public static int search(int[] values, int target) {
+        if (values.length == 0) {
+            throw new NoSuchElementException(String.format("Unable to find target: {} in values", target));
+        }
+
+        int leftIndex = 0;
+        int rightIndex = values.length - 1;
+        while (leftIndex < rightIndex) {
+            int middleIndex = leftIndex + (rightIndex - leftIndex) / 2;
+            int middleValue = values[middleIndex];
+
+            if (target < middleValue) {
+                rightIndex = middleIndex;
+            } else if (target > middleValue) {
+                leftIndex = middleIndex + 1;
+            } else {
+                return middleIndex;
+            }
+        }
+
+        return leftIndex;
+    }
+}

src/test/java/problems/impl/BinarySearcherTest.java

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+package problems.impl;
+
+import org.junit.Test;
+
+import java.util.NoSuchElementException;
+
+import static org.junit.Assert.*;
+
+public class BinarySearcherTest {
+    private final int[] values = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
+
+    @Test
+    public void itShouldFindElements() {
+        for (int value : values) {
+            assertEquals(value - 1, BinarySearcher.search(values, value));
+        }
+    }
+
+    @Test
+    public void itShouldThrowForAnEmptyArray() {
+        try {
+            BinarySearcher.search(new int[] {}, 1);
+        } catch (NoSuchElementException e) {
+            // expected
+        }
+    }
+
+    @Test
+    public void itShouldThrowSinceItCannotFindElement() {
+        try {
+            BinarySearcher.search(values, -1);
+        } catch (NoSuchElementException e) {
+            // expected
+        }
+    }
+
+    @Test
+    public void itShouldFindElementInSingleElementArray() {
+        assertEquals(0, BinarySearcher.search(new int[] { 10 }, 10));
+    }
+}