ALGORITHMUS-LESENOTIZ

Longest Common Subsequence

LCS finds the longest sequence of values that appears in both inputs in the same relative order, but not necessarily contiguously.

TYPAlgorithmusKATEGORIESets & Dynamic ProgrammingTIEFEFortgeschrittenTYPISCHE KOMPLEXITÄTO(mn)

KURZE INTERVIEWANTWORT

Beginne mit diesem mentalen Modell

LCS finds the longest sequence of values that appears in both inputs in the same relative order, but not necessarily contiguously.

EINFACHE ERKLÄRUNG

So funktioniert es – ohne unnötigen Jargon

dp[i][j] usually means LCS length for prefixes ending before i and j.

Matching characters extend the diagonal state; otherwise take the best of dropping one side.

AUSFÜHRUNG

Lies den Algorithmus als Folge von Entscheidungen

Define the state precisely.

Write the transition/choice from smaller states.

Set base cases, then decide memoization, tabulation or backtracking.

Ein kleines Beispiel als Orientierung

Read a tiny input by hand and write down the state after every important operation. For Longest Common Subsequence, the goal is to make the invariant visible rather than to memorize code.

LESBARE JAVASCRIPT-IMPLEMENTIERUNGJavaScript

function lcs(a, b) {
  const dp = Array.from({ length: a.length + 1 }, () => Array(b.length + 1).fill(0));
  for (let i = 1; i <= a.length; i++) {
    for (let j = 1; j <= b.length; j++) {
      dp[i][j] = a[i - 1] === b[j - 1]
        ? dp[i - 1][j - 1] + 1
        : Math.max(dp[i - 1][j], dp[i][j - 1]);
    }
  }
  return dp[a.length][b.length];
}

So liest du diesen Code

Lerne die Syntax nicht auswendig. Folge dem Zustand, der sich in jeder Zeile ändert, und verbinde ihn mit der oben beschriebenen Invariante.

KOMPLEXITÄT

O(mn)

Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.

WANN EINSETZEN

Gut geeignet

Use DP when subproblems overlap and optimal solutions can be composed from smaller optimal states.

HÄUFIGE FEHLER

Was typischerweise schiefgeht

Writing recurrence before defining state.
Using DP when state space is larger than the original problem.

SO ERKLÄRST DU ES IM INTERVIEW

Struktur einer professionellen Antwort

Explicitly distinguish subsequence from substring. This is one of the most common interview confusions.

Problem→Kernidee→Invariante / Zustand→Big-O→Trade-off

SCHNELLER INTERVIEW-CHECK

What problem does Longest Common Subsequence solve?

LCS finds the longest sequence of values that appears in both inputs in the same relative order, but not necessarily contiguously.

Was sollte ich zur Komplexität erwähnen?

Its typical cost here is O(mn), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

Was ist der häufigste Fehler?

Writing recurrence before defining state.

WeiterlesenMemoizationTabulationBacktracking

function lcs(a, b) { const dp = Array.from({ length: a.length + 1 }, () => Array(b.length + 1).fill(0)); for (let i = 1; i <= a.length; i++) { for (let j = 1; j <= b.length; j++) { dp[i][j] = a[i - 1] === b[j - 1] ? dp[i - 1][j - 1] + 1 : Math.max(dp[i - 1][j], dp[i][j - 1]); } } return dp[a.length][b.length]; }