algorithm: ZFunction (#1239)

* algorithm: ZFunction

* made requested changes

* corrected spelling mistakes

* made requested changes

String/ZFunction.js

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+/**
+ * @author: Adrito Mukherjee
+ * Implementation of ZFunction in JavaScript
+ * ZFunction at an index i gives the length of the longest substring starting at i, that is also a prefix of the whole string
+ * ZFunction for all indices in a string can be calculated in O(N)
+ * @see https://cp-algorithms.com/string/z-function.html
+ * @param {String} text The string whose Z Function is to be calculated
+ * @return {Array} Returns an array whose i-th index is the value of Z Function for text at index i
+ */
+
+function zFunction (text) {
+  const length = text.length
+  const zArray = Array(length).fill(0)
+  // Initializing left and right variable to zero
+  let left = 0
+  let right = 0
+  for (let index = 0; index < length; index++) {
+    // If index is less than or equal to right, we reuse the values of zFunction at index right-index+1
+    // It is made sure that value of zFunction at index is not greater than maximum possible value at index
+    if (index <= right) {
+      zArray[index] = Math.min(right - index + 1, zArray[index - left])
+    }
+
+    // After zArray[index] is initialized, we see if we can increase its value by trivially comparing character by character
+    while (
+      index + zArray[index] < length &&
+      text[zArray[index]] === text[index + zArray[index]]
+    ) {
+      zArray[index]++
+    }
+
+    // If index + zArray[index] - 1 is greater than right, we update values of variables left and right
+    if (index + zArray[index] - 1 > right) {
+      left = index
+      right = index + zArray[index] - 1
+    }
+  }
+  return zArray
+}
+
+export default zFunction

String/test/ZFunction.test.js

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+import zFunction from '../ZFunction'
+
+test('Testing zFunction', () => {
+  expect(zFunction('aabxaayaab')).toEqual([10, 1, 0, 0, 2, 1, 0, 3, 1, 0])
+  expect(zFunction('aabxaabxcaabxaabxay')).toEqual([
+    19, 1, 0, 0, 4, 1, 0, 0, 0, 8, 1, 0, 0, 5, 1, 0, 0, 1, 0
+  ])
+})