Z algorithm implementation (trekhleb#77)

* Implemented Z algorithm

* Fixed bugs in implementation and added tests

* Added README explaining z algorithm

Author: hariv

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|)`

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);
+  });
+});

src/algorithms/string/z-algorithm/zAlgorithm.js

@@ -0,0 +1,57 @@
+/**
+ * @param {string} word
+ * @param {string} text
+ * @return {number[]}
+ */
+
+function buildZArray(word, text) {
+  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 += 1) {
+    if (i > right) {
+      left = i;
+      right = i;
+
+      while (right < zString.length && zString[right - left] === zString[right]) {
+        right += 1;
+      }
+
+      zArray[i] = right - left;
+      right -= 1;
+    } else {
+      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 += 1;
+        }
+
+        zArray[i] = right - left;
+        right -= 1;
+      }
+    }
+  }
+
+  return zArray;
+}
+
+/**
+ * @param {string} text
+ * @param {string} word
+ * @return {number}
+ */
+export default function zAlgorithm(text, word) {
+  const zArray = buildZArray(word, text);
+  for (let i = 1; i < zArray.length; i += 1) {
+    if (zArray[i] === word.length) {
+      return (i - word.length - 1);
+    }
+  }
+  return -1;
+}