DRAFT: feat: add "expand around center" approach visualization

Dynamic Programming/Expand Around Center/README.md

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+# Expand Around Center
+
+The "expand around center" approach is a common algorithmic technique used to solve problems related to palindromes or symmetric sequences. The basic idea is to consider each position in the sequence as a possible center of a palindrome and then expand outwards in both directions from that center to find the longest palindrome or the number of palindromic substrings.
+
+For example, consider the string "racecar". We can start by considering each character in the string as a possible center, and then expand around it to check if it forms a palindrome. If we start with the center at index 3 (the letter "e"), we can expand outwards in both directions to find that the longest palindrome centered at index 3 is "cec". Similarly, we can check all other centers to find the longest palindrome in the string.
+
+The "expand around center" approach is a simple and efficient way to solve many palindrome-related problems. It can be used to find the longest palindromic substring in a given string, count the number of palindromic substrings, or check if a given string is a palindrome.
+
+The "expand around center" approach is efficient, with a time complexity of O(n^2), where n is the length of the input string.
+
+## References
+
+- [@bhprtk/longest-palindromic-substring](https://medium.com/@bhprtk/longest-palindromic-substring-a8190fab03ff#:~:text=Expand%20Around%20Center%3A,the%20center%20is%20%22bb%22%20.)

Dynamic Programming/Expand Around Center/code.js

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+const { Tracer, Array1DTracer, Layout, VerticalLayout } = require('algorithm-visualizer');
+
+const tracer = new Array1DTracer('Longest Palindromic Substring');
+Layout.setRoot(new VerticalLayout([tracer]));
+
+function expandAroundCenter(s, left, right) {
+  tracer.select(left, right);
+  Tracer.delay();
+
+  while (left >= 0 && right < s.length && s[left] === s[right]) {
+    left--;
+    right++;
+    tracer.select(left, right);
+    Tracer.delay();
+  }
+
+  tracer.deselect(left, right);
+  return right - left - 1;
+}
+
+function longestPalindromicSubstring(s) {
+  if (s.length === 0 || s.length === 1) {
+    return s;
+  }
+
+  let start = 0;
+  let end = 0;
+
+  tracer.set(s);
+  Tracer.delay();
+
+  for (let i = 0; i < s.length; i++) {
+    const len1 = expandAroundCenter(s, i, i);
+    const len2 = expandAroundCenter(s, i, i + 1);
+    const maxLen = Math.max(len1, len2);
+
+    if (maxLen > end - start) {
+      start = i - Math.floor((maxLen - 1) / 2);
+      end = i + Math.floor(maxLen / 2);
+    }
+  }
+
+  tracer.select(start, end);
+  Tracer.delay();
+  tracer.deselect(start, end);
+
+  return s.slice(start, end + 1);
+}
+
+const input = 'babad';
+console.log(longestPalindromicSubstring(input));  // Output: "bab" or "aba"