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Author: trekhleb

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

@@ -6,39 +6,95 @@ const SEPARATOR = '$';
  * @return {number[]}
  */
 function buildZArray(zString) {
-  const zArray = new Array(zString.length);
+  // Initiate zArray and fill it with zeros.
+  const zArray = new Array(zString.length).fill(null).map(() => 0);
 
-  let left = 0;
-  let right = 0;
-  let k = 0;
+  // Z box boundaries.
+  let zBoxLeftIndex = 0;
+  let zBoxRightIndex = 0;
 
-  for (let i = 1; i < zString.length; i += 1) {
-    if (i > right) {
-      left = i;
-      right = i;
+  // Position of current zBox character that is also a position of
+  // the same character in prefix.
+  // For example:
+  // Z string: ab$xxabxx
+  // Indices:  012345678
+  // Prefix:   ab.......
+  // Z box:    .....ab..
+  // Z box shift for 'a' would be 0 (0-position in prefix and 0-position in Z box)
+  // Z box shift for 'b' would be 1 (1-position in prefix and 1-position in Z box)
+  let zBoxShift = 0;
 
-      while (right < zString.length && zString[right - left] === zString[right]) {
-        right += 1;
+  // Go through all characters of the zString.
+  for (let charIndex = 1; charIndex < zString.length; charIndex += 1) {
+    if (charIndex > zBoxRightIndex) {
+      // We're OUTSIDE of Z box. In other words this is a case when we're
+      // starting from Z box of size 1.
+
+      // In this case let's make current character to be a Z box of length 1.
+      zBoxLeftIndex = charIndex;
+      zBoxRightIndex = charIndex;
+
+      // Now let's go and check current and the following characters to see if
+      // they are the same as a prefix. By doing this we will also expand our
+      // Z box. For example if starting from current position we will find 3
+      // more characters that are equal to the ones in the prefix we will expand
+      // right Z box boundary by 3.
+      while (
+        zBoxRightIndex < zString.length &&
+        zString[zBoxRightIndex - zBoxLeftIndex] === zString[zBoxRightIndex]
+      ) {
+        // Expanding Z box right boundary.
+        zBoxRightIndex += 1;
       }
 
-      zArray[i] = right - left;
-      right -= 1;
+      // Now we may calculate how many characters starting from current position
+      // are are the same as the prefix. We may calculate it by difference between
+      // right and left Z box boundaries.
+      zArray[charIndex] = zBoxRightIndex - zBoxLeftIndex;
+
+      // Move right Z box boundary left by one position just because we've used
+      // [zBoxRightIndex - zBoxLeftIndex] index calculation above.
+      zBoxRightIndex -= 1;
     } else {
-      k = i - left;
-      if (zArray[k] < (right - i) + 1) {
-        zArray[i] = zArray[k];
+      // We're INSIDE of Z box.
+
+      // Calculate corresponding Z box shift. Because we want to copy the values
+      // from zArray that have been calculated before.
+      zBoxShift = charIndex - zBoxLeftIndex;
+
+      // Check if the value that has been already calculated before
+      // leaves us inside of Z box or it goes beyond the checkbox
+      // right boundary.
+      if (zArray[zBoxShift] < (zBoxRightIndex - charIndex) + 1) {
+        // If calculated value don't force us to go outside Z box
+        // then we're safe and we may simply use previously calculated value.
+        zArray[charIndex] = zArray[zBoxShift];
       } else {
-        left = i;
-        while (right < zString.length && zString[right - left] === zString[right]) {
-          right += 1;
+        // In case if previously calculated values forces us to go outside of Z box
+        // we can't safely copy previously calculated zArray value. It is because
+        // we are sure that there is no further prefix matches outside of Z box.
+        // Thus such values must be re-calculated and reduced to certain point.
+
+        // To do so we need to shift left boundary of Z box to current position.
+        zBoxLeftIndex = charIndex;
+
+        // And start comparing characters one by one as we normally do for the case
+        // when we are outside of checkbox.
+        while (
+          zBoxRightIndex < zString.length &&
+          zString[zBoxRightIndex - zBoxLeftIndex] === zString[zBoxRightIndex]
+        ) {
+          zBoxRightIndex += 1;
         }
 
-        zArray[i] = right - left;
-        right -= 1;
+        zArray[charIndex] = zBoxRightIndex - zBoxLeftIndex;
+
+        zBoxRightIndex -= 1;
       }
     }
   }
 
+  // Return generated zArray.
   return zArray;
 }