8.3 Magic Index solution from book

Author: amejiarosario

src/08-dynamic-programming/magic-index.js

@@ -23,12 +23,14 @@ function findMagicIndexSlow(array) {
  * @returns {number}
  */
 function findMagicIndex(array, offset = 0) {
+  if(!array || array.length === 0) {
+    return -1;
+  }
+
   const middle = parseInt(array.length/2);
   const index = middle + offset;
 
-  if(array.length === 0) {
-    return -1;
-  } else if(index === array[middle]) {
+  if(index === array[middle]) {
     return index;
   } else if(index > array[middle]) {
     return findMagicIndex(array.slice(middle + 1), middle + 1);
@@ -37,5 +39,62 @@ function findMagicIndex(array, offset = 0) {
   }
 }
 
+/**
+ * O(log n)
+ *
+ * breaks when elements values are repeated
+ *
+ * @param array
+ * @param start
+ * @param end
+ * @returns {*}
+ */
+function findMagicIndex2(array, start = 0, end = (Array.isArray(array) && array.length)) {
+  if(!array || end <= start) { return -1; }
+
+  const midIndex = parseInt((start + end)/2);
+  const midValue = array[midIndex];
+
+  if(midIndex === midValue) {
+    return midValue;
+  }
+
+  if(midIndex > midValue) {
+    return findMagicIndex2(array, midIndex + 1, end);
+  }
+
+  if(midIndex < midValue) {
+    return findMagicIndex2(array, 0, midIndex);
+  }
+}
+
+/**
+ * O(log n)
+ *
+ * Handles cases when elements has repeated values
+ *
+ * @param array
+ * @param start
+ * @param end
+ * @returns {*}
+ */
+function findMagicIndexFastRepeated(array, start = 0, end = (Array.isArray(array) && array.length-1)) {
+  if(!Array.isArray(array) || end < start) { return -1; }
+
+  const midIndex = parseInt((start + end)/2);
+  const midValue = array[midIndex];
+
+  if(midIndex === midValue) {
+    return midValue;
+  }
+
+  const left = findMagicIndexFastRepeated(array, start, Math.min(midIndex - 1, midValue));
+  if(left !== -1) {
+    return left;
+  }
+
+  const right = findMagicIndexFastRepeated(array, Math.max(midIndex + 1, midValue), end);
+  return right;
+}
 
-module.exports = findMagicIndex;
+module.exports = findMagicIndexFastRepeated;

src/08-dynamic-programming/magic-index.spec.js

@@ -2,45 +2,57 @@ const expect = require('chai').expect;
 const findMagicIndex = require('./magic-index');
 
 describe('findMagicIndex', function() {
-  it('all sorted', function () {
-    const array = [0, 1, 2, 3, 4, 5, 6, 7];
-    expect(findMagicIndex(array)).to.equal(0);
-  });
-
-  it('no magic index', function () {
-    const array = [10, 100, 240];
-    expect(findMagicIndex(array)).to.equal(-1);
-  });
-
-  it('values are not distinct', function () {
-    // index       0  1  2  3  4
-    const array = [1, 2, 3, 3, 5];
-    expect(findMagicIndex(array)).to.equal(3);
-  });
-
-  it('has negative values', function () {
-    // index         0    1   2  3  4  5  6  7  8   9  10
-    const array = [-40, -20, -1, 1, 2, 3, 5, 7, 9, 12, 13];
-    expect(findMagicIndex(array)).to.equal(7);
-  });
-
-  it('should work with 1 element', function () {
-    const array = [0];
-    expect(findMagicIndex(array)).to.equal(0);
-  });
-
-  it('should work with 1 element that is not a magic index', function () {
-    const array = [10];
-    expect(findMagicIndex(array)).to.equal(-1);
-  });
-
-  it('should work with 2 elements', function () {
-    const array = [1, 1];
-    expect(findMagicIndex(array)).to.equal(1);
-  });
-
-
-  it('should handle null cases', function () {
-    expect(findMagicIndex()).to.equal(-1);
+  describe('when elements are distinct', function () {
+    it('no magic index', function () {
+      const array = [10, 100, 240];
+      expect(findMagicIndex(array)).to.equal(-1);
+    });
+
+    it('has negative values', function () {
+      // index         0    1   2  3  4  5  6  7  8   9  10
+      const array = [-40, -20, -1, 1, 2, 3, 5, 7, 9, 12, 13];
+      expect(findMagicIndex(array)).to.equal(7);
+    });
+
+    it('should work with 1 element', function () {
+      const array = [0];
+      expect(findMagicIndex(array)).to.equal(0);
+    });
+
+    it('should work with 1 element that is not a magic index', function () {
+      const array = [10];
+      expect(findMagicIndex(array)).to.equal(-1);
+    });
+
+    it('should handle undefined cases', function () {
+      expect(findMagicIndex()).to.equal(-1);
+    });
+
+    it('should handle null cases', function () {
+      expect(findMagicIndex(null)).to.equal(-1);
+    });
+
+    it('should handle true cases', function () {
+      expect(findMagicIndex(true)).to.equal(-1);
+    });
+  });
+
+  describe('when some elements are repeated', function () {
+    it('should work with 2 elements', function () {
+      const array = [1, 1];
+      expect(findMagicIndex(array)).to.equal(1);
+    });
+
+    it('values are NOT distinct to the right', function () {
+      // index       0  1  2  3  4
+      const array = [1, 2, 3, 3, 5];
+      expect(findMagicIndex(array)).to.equal(3);
+    });
+
+    it('repeated values on the left', function () {
+      // index         0    1   2  3  4  5  6  7  8   9  10
+      const array = [-40, -20,  2, 2, 2, 3, 5, 8, 9, 12, 13];
+      expect(findMagicIndex(array)).to.equal(2);
+    });
   });
 });