Explain Dynamic Programming and Other Techniques with Examples

function longestIncreasingSubsequence(nums) {
  const n = nums.length;
  if (n === 0) return 0;
  
  // Initialize an array of length n, filled with 1s, as the minimum length of any LIS is 1
  const dp = Array(n).fill(1);
  
  // Iterate through the elements in the nums array
  for (let i = 1; i < n; i++) {
    for (let j = 0; j < i; j++) {
      // Check if the current element is greater than the previous one
      if (nums[i] > nums[j]) {
        // If it is, update the dp array with the maximum length found so far
        dp[i] = Math.max(dp[i], dp[j] + 1);
      }
    }
  }
  
  // Find the maximum length of the LIS by iterating through the dp array
  let maxLIS = dp[0];
  for (let i = 1; i < n; i++) {
    maxLIS = Math.max(maxLIS, dp[i]);
  }
  
  // Return the maximum length of the LIS
  return maxLIS;
}