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LCS (2-D DP), .

Longest common subsequence via a 2-D table.

lcs.js
function lcs(a, b) {
  const m = a.length, n = b.length;
  const dp = [];
  for (let i = 0; i <= m; i++) dp.push(new Array(n + 1).fill(0));
  for (let i = 1; i <= m; i++) {
    for (let j = 1; j <= n; j++) {
      if (a[i - 1] === b[j - 1]) dp[i][j] = dp[i - 1][j - 1] + 1;
      else dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
    }
  }
  return dp[m][n];
}

lcs("AGCAT", "GAC");

What to watch

A grid lights up cell by cell - filled cells glow as the table is built row by row.

Reading lcs (2-d dp)on a page only gets you so far - code is a process, and the process happens at runtime where you can't normally see it. In NeonFlow, this exact program runs step by step: every call opens a frame, every branch picks a path, and every value moves through memory in front of you. That's the fastest way to actually understand how lcs (2-d dp) works.

Run lcs (2-d dp) yourself

Open NeonFlow, paste this code (or any of your own), and scrub through it one step at a time.

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