Given a list of numbers, find the longest subsequence such that the absolute difference between adjacent elements is 1.

Hint

Start with the foundation – the base cases, which are the simplest solutions. Then, layer by layer, use the results of the previous layers to calculate the solutions for the next level. This way, we systematically build up the entire solution, avoiding redundant calculations and ensuring efficiency. It is like building a pyramid.

The underlying calculation logic remains fundamentally identical to the original recursive approach, albeit executed in reverse order.

# Python implementation

def count(ls):
  cache = {}
  mx = 1

  for i in range(len(ls)):
    if ls[i] + 1 in cache or ls[i] - 1 in cache:
      cache[ls[i]] = 1 + max(cache.get(ls[i] + 1, 0), cache.get(ls[i] - 1, 0))
    else:
      cache[ls[i]] = 1

    mx = max(mx, cache[ls[i]])

  return mx

ls = [10, 9, 4, 5, 4, 8, 6]

print(count(ls))

// Javascript implementation

function count(list) {
  const cache = {}
  let max = 1;

  for (let i = 0; i < list.length; i++) {
    if (cache[list[i] + 1] != undefined || cache[list[i] - 1] != undefined) {
      cache[list[i]] = 1 + Math.max(cache[list[i] + 1] ? cache[list[i] + 1] : 0, cache[list[i] - 1] ? cache[list[i] - 1] : 0);
    } else {
      cache[list[i]] = 1;
    }

    max = Math.max(max, cache[list[i]])
  }

  return max;
}

const list = [10, 9, 4, 5, 4, 8, 6];

console.log(count(list, 0));

Subsequence with difference of 1 (Tabulation)

Hint