Dynamic Programming in JavaScript - AI Conversation

Dynamic programming is an optimization technique that solves complex problems by breaking them down into simpler subproblems and storing the results to avoid redundant calculations. In JavaScript, it's particularly useful for algorithmic challenges and optimization problems.

Core Concepts

Memoization - Store results of expensive function calls and return cached results when the same inputs occur again.

Tabulation - Build up solutions bottom-up using a table (usually an array) to store intermediate results.

Common Patterns

Here are some practical examples in JavaScript:

Fibonacci with Memoization:

function fibonacci(n, memo = {}) {
  if (n in memo) return memo[n];
  if (n <= 2) return 1;
  
  memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo);
  return memo[n];
}

Fibonacci with Tabulation:

function fibonacciTab(n) {
  if (n <= 2) return 1;
  
  const dp = [0, 1, 1];
  for (let i = 3; i <= n; i++) {
    dp[i] = dp[i - 1] + dp[i - 2];
  }
  return dp[n];
}

Coin Change Problem:

function coinChange(coins, amount) {
  const dp = Array(amount + 1).fill(Infinity);
  dp[0] = 0;
  
  for (let coin of coins) {
    for (let i = coin; i <= amount; i++) {
      dp[i] = Math.min(dp[i], dp[i - coin] + 1);
    }
  }
  
  return dp[amount] === Infinity ? -1 : dp[amount];
}

Longest Common Subsequence:

function longestCommonSubsequence(text1, text2) {
  const m = text1.length, n = text2.length;
  const dp = Array(m + 1).fill().map(() => Array(n + 1).fill(0));
  
  for (let i = 1; i <= m; i++) {
    for (let j = 1; j <= n; j++) {
      if (text1[i - 1] === text2[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];
}

When to Use Dynamic Programming

Dynamic programming is ideal when a problem has:

• Overlapping subproblems - the same smaller problems are solved multiple times
• Optimal substructure - optimal solutions can be constructed from optimal solutions of subproblems

Common use cases include pathfinding algorithms, optimization problems, string matching, and many coding interview questions involving arrays or sequences.

The key insight is trading space for time complexity - using extra memory to dramatically reduce the number of calculations needed.