From 9e5deb66951fc37f1ae340e1566a412598516e29 Mon Sep 17 00:00:00 2001
From: Hari Venugopalan <harivenugopalan@Haris-MacBook-Pro.local>
Date: Wed, 20 Jun 2018 18:33:22 -0700
Subject: [PATCH 1/3] Implemented Z algorithm

---
 .../string/z-algorithm/zAlgorithm.js          | 51 +++++++++++++++++++
 1 file changed, 51 insertions(+)
 create mode 100644 src/algorithms/string/z-algorithm/zAlgorithm.js

diff --git a/src/algorithms/string/z-algorithm/zAlgorithm.js b/src/algorithms/string/z-algorithm/zAlgorithm.js
new file mode 100644
index 0000000000..b0a8480325
--- /dev/null
+++ b/src/algorithms/string/z-algorithm/zAlgorithm.js
@@ -0,0 +1,51 @@
+/**
+ * @param {string} word
+ * @param {string} text
+ * @return {number[]}
+ */
+
+function buildZArray(word, text) {
+  let zString = word+"$+"text;
+  let zArray = new Array(zString.length);
+  let left = 0, right = 0, k = 0;
+
+  for (let i = 1; i < zString.length; i++) {
+    if (i > right) {
+      left = right = 0;
+      while ( right<zString.length && zString[right-left] == zString[right]) {
+        right++;
+      }
+      zArray[i] = right-left;
+      right--;
+    } else {
+      k = i-left;
+      if (zString[k] < right-i+1) {
+        zString[i] = zString[k];
+      } else {
+        left = i;
+        while (right<zString.length && zString[right-left] == zString[right]) {
+          right++;
+        }
+        zString[i] = right-left;
+        right--;
+      }
+    }
+  }
+
+  return zArray;
+}
+/**
+ * @param {string} text
+ * @param {string} word
+ * @return {number}
+ */
+export default function knuthMorrisPratt(text, word) {
+  const zArray = buildZArray(word, text);
+
+  for (let i=0; i<zArray.length; i++) {
+    if (zArray[i] == word.length) {
+      return (i-word.length-1);
+    }
+    return -1;
+  }
+}
\ No newline at end of file

From a6f72a43a3227b8f0e452662fb435acbb5df4ce8 Mon Sep 17 00:00:00 2001
From: Hari Venugopalan <harivenugopalan@Haris-MacBook-Pro.local>
Date: Wed, 20 Jun 2018 19:18:37 -0700
Subject: [PATCH 2/3] Fixed bugs in implementation and added tests

---
 .../z-algorithm/__test__/zAlgorithm.test.js   | 12 +++++
 .../string/z-algorithm/zAlgorithm.js          | 52 +++++++++++--------
 2 files changed, 41 insertions(+), 23 deletions(-)
 create mode 100644 src/algorithms/string/z-algorithm/__test__/zAlgorithm.test.js

diff --git a/src/algorithms/string/z-algorithm/__test__/zAlgorithm.test.js b/src/algorithms/string/z-algorithm/__test__/zAlgorithm.test.js
new file mode 100644
index 0000000000..d58ff75bc9
--- /dev/null
+++ b/src/algorithms/string/z-algorithm/__test__/zAlgorithm.test.js
@@ -0,0 +1,12 @@
+import zAlgorithm from '../zAlgorithm';
+
+describe('zAlgorithm', () => {
+  it('should find word position in given text', () => {
+    expect(zAlgorithm('abcbcglx', 'abca')).toBe(-1);
+    expect(zAlgorithm('abcbcglx', 'bcgl')).toBe(3);
+    expect(zAlgorithm('abcxabcdabxabcdabcdabcy', 'abcdabcy')).toBe(15);
+    expect(zAlgorithm('abcxabcdabxabcdabcdabcy', 'abcdabca')).toBe(-1);
+    expect(zAlgorithm('abcxabcdabxaabcdabcabcdabcdabcy', 'abcdabca')).toBe(12);
+    expect(zAlgorithm('abcxabcdabxaabaabaaaabcdabcdabcy', 'aabaabaaa')).toBe(11);
+  });
+});
diff --git a/src/algorithms/string/z-algorithm/zAlgorithm.js b/src/algorithms/string/z-algorithm/zAlgorithm.js
index b0a8480325..f93318ce43 100644
--- a/src/algorithms/string/z-algorithm/zAlgorithm.js
+++ b/src/algorithms/string/z-algorithm/zAlgorithm.js
@@ -5,47 +5,53 @@
  */
 
 function buildZArray(word, text) {
-  let zString = word+"$+"text;
-  let zArray = new Array(zString.length);
-  let left = 0, right = 0, k = 0;
+  const zString = `${word}$${text}`;
+  const zArray = new Array(zString.length);
+  let left = 0;
+  let right = 0;
+  let k = 0;
 
-  for (let i = 1; i < zString.length; i++) {
+  for (let i = 1; i < zString.length; i += 1) {
     if (i > right) {
-      left = right = 0;
-      while ( right<zString.length && zString[right-left] == zString[right]) {
-        right++;
+      left = i;
+      right = i;
+
+      while (right < zString.length && zString[right - left] === zString[right]) {
+        right += 1;
       }
-      zArray[i] = right-left;
-      right--;
+
+      zArray[i] = right - left;
+      right -= 1;
     } else {
-      k = i-left;
-      if (zString[k] < right-i+1) {
-        zString[i] = zString[k];
+      k = i - left;
+      if (zArray[k] < (right - i) + 1) {
+        zArray[i] = zArray[k];
       } else {
         left = i;
-        while (right<zString.length && zString[right-left] == zString[right]) {
-          right++;
+        while (right < zString.length && zString[right - left] === zString[right]) {
+          right += 1;
         }
-        zString[i] = right-left;
-        right--;
+
+        zArray[i] = right - left;
+        right -= 1;
       }
     }
   }
 
   return zArray;
 }
+
 /**
  * @param {string} text
  * @param {string} word
  * @return {number}
  */
-export default function knuthMorrisPratt(text, word) {
+export default function zAlgorithm(text, word) {
   const zArray = buildZArray(word, text);
-
-  for (let i=0; i<zArray.length; i++) {
-    if (zArray[i] == word.length) {
-      return (i-word.length-1);
+  for (let i = 1; i < zArray.length; i += 1) {
+    if (zArray[i] === word.length) {
+      return (i - word.length - 1);
     }
-    return -1;
   }
-}
\ No newline at end of file
+  return -1;
+}

From c70f380c07909a19fe0d4aa90e9d5136ecfd4fdf Mon Sep 17 00:00:00 2001
From: Hari Venugopalan <harivenugopalan@Haris-MacBook-Pro.local>
Date: Wed, 20 Jun 2018 19:36:38 -0700
Subject: [PATCH 3/3] Added README explaining z algorithm

---
 src/algorithms/string/z-algorithm/README.md | 27 +++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 src/algorithms/string/z-algorithm/README.md

diff --git a/src/algorithms/string/z-algorithm/README.md b/src/algorithms/string/z-algorithm/README.md
new file mode 100644
index 0000000000..733ebf5cd1
--- /dev/null
+++ b/src/algorithms/string/z-algorithm/README.md
@@ -0,0 +1,27 @@
+# Z-algorithm
+
+The Z-algorithm finds occurrences of a "word" `W` 
+within a main "text string" `T` in linear time.
+
+Given a string `S` of length `n`, the algorithm produces 
+an array, `Z` where `Z[i]` represents the ongest substring 
+starting from `S[i]` which is also a prefix of `S`. Finding
+`Z` for the string obtained by concatenating the word, `W` 
+with a nonce character, say `$` followed by the text, `T`,
+helps with pattern matching, for if there is some index `i`
+such that `Z[i]` equals the pattern length, then the pattern
+must be present at that point.
+
+While the `Z` array can be computed with two nested loops, the
+following strategy shows how to obtain it in linear time, based 
+on the idea that as we iterate over the letters in the string 
+(index `i` from `1` to `n - 1`), we maintain an interval `[L, R]`
+which is the interval with maximum `R` such that `1 ≤ L ≤ i ≤ R` 
+and `S[L...R]` is a prefix that is also a substring (if no such 
+interval exists, just let `L = R =  - 1`). For `i = 1`, we can 
+simply compute `L` and `R` by comparing `S[0...]` to `S[1...]`.
+
+## Complexity
+
+- **Time:** `O(|W| + |T|)`
+- **Space:** `O(|W|)`
\ No newline at end of file