js-concepts: dynamic programming - lcs

Author: baochau.dinh

Dynamic Programming/LCS_iterative.js

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+/**
+ * Checking whether a string (B) is a sequence of another string (A)
+ */
+
+function main(A = '', B = '') {
+  if (A.length === 0 || B.length === 0) return '';
+
+  let result = 0;
+  let i = 0, j = 0;
+  while (i < A.length && j < B.length) {
+    if (A[i] === B[j]) {
+      result++
+      i++;
+      j++;
+    } else {
+      i++;
+    }
+  }
+  return result === B.length;
+} // O(A.length + B.length)
+
+console.log(main('abcdgh', 'acdga'));

Dynamic Programming/LCS_memoization.js

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+/**
+ * Longest common subsequence - LCS
+ * 
+ * memoization solution
+ */
+
+function main(a = '', b = '') {
+  const lcs = (m, n) => {
+    if (m < 0 || n < 0) return 0;
+
+    if (a[m] === b[n]) return lcs(m - 1, n - 1) + 1;
+    else return Math.max(lcs(m, n - 1), lcs(m - 1, n));
+  }
+
+  return lcs(a.length - 1, b.length - 1);
+}
+
+function mainV2(a = '', b = '') {
+  let lcs = new Array(a.length + 1).fill(0).map(x => new Array(b.length + 1).fill(0));
+
+  for (let i = 1; i <= a.length; i++) {
+    for (let j = 1; j <= b.length; j++) {
+      if (a[i - 1] === b[j - 1]) {
+        lcs[i][j] = lcs[i - 1][j - 1] + 1;
+      }
+      else {
+        lcs[i][j] = Math.max(lcs[i][j - 1], lcs[i - 1][j]);
+      }
+    }
+  }
+
+  return lcs[a.length][b.length];
+}
+
+console.log(mainV2('aab', 'ba'));

Dynamic Programming/LCS_recursive.js

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+/**
+ * Longest common subsequence - LCS
+ * 
+ * recursive solution
+ */
+
+function main(a = '', b = '') {
+  const lcs = (m, n) => {
+    if (m < 0 || n < 0) return 0;
+
+    if (a[m] === b[n]) return lcs(m - 1, n - 1) + 1;
+    else return Math.max(lcs(m, n - 1), lcs(m - 1, n));
+  }
+
+  return lcs(a.length - 1, b.length - 1);
+}
+
+console.log(main('aabb', 'ab'));

Dynamic Programming/Palindrome_Sequence.js

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+/**
+ * Given a string A, remove some characters to receive string B (sequences)
+ * Write a function to find the longest palindrome among B
+ */
+
+function main(a = '') {
+  if (a.length === 0) return 0;
+
+  let i = 0, j = a.length - 1;
+  while (i <= j) {
+    
+  }
+}