🤖 leetcode 354. Russian Doll Envelopes | hard | binary-search | javascript

🗒️ Problems

Russian Doll Envelopes - LeetCode

You are given a 2D array of integers envelopes
where envelopes[i] = [wi, hi] represents the width and the height of an envelope.

One envelope can fit into another
if and only if both the width and height of one envelope are greater than the other envelope's width and height.

Return the maximum number of envelopes you can Russian doll (i.e., put one inside the other).

Note: You cannot rotate an envelope.

Input: envelopes = [[5,4],[6,4],[6,7],[2,3]]
Output: 3
Explanation: The maximum number of envelopes you can Russian doll is 3 ([2,3] => [5,4] => [6,7]).

✨ Idea

때로는 한 번 경험을 해봐야 눈이 떠지는 문제가 있다.

• [ [ width, height ], [], ...] 를 잘 sorting 한다.
  • width 오름차순으로 정렬하고
  • 같으면 height 반대방향인 내림차순으로 정렬
• 이렇게 정렬하고 나면 width는 커지는 방향이므로 이 상태에서 height 로 LIS (Longest Increasing Subsequence)를 찾아내면 그것이 답이 된다.

🍀 Intuition

다중 조건에 의한 정렬

• width 오름차순
• 같으면 height 내림차순

envelopes.sort((a, b) => a[0] - b[0] || b[1] - a[1]);

🍀 💡 LIS

• LIS 를 binary search 로 nlogn 으로 찾는 것은 library 처럼 준비해두면 좋을 듯 하다.

const piles = [];

for (const num of array) {
  const index = bisectLeft(array, num);

  if (index < piles.length) piles[index] = num;
  else piles.push(num);
}

return piles.length;

🔥 My Solution

/**
 * @param {number[][]} envelopes
 * @return {number}
 */
var maxEnvelopes = function (envelopes) {
  const bisectLeft = (array, target) => {
    const N = array.length;

    // [0, N)
    let left = 0;
    let right = N;

    while (left < right) {
      const mid = Math.floor((left + right) / 2);

      // => [left, mid)
      if (array[mid] === target) {
        right = mid;
        // select left space => [left, mid)
      } else if (array[mid] > target) {
        right = mid;
        // select right space => [mid + 1, right)
      } else if (array[mid] < target) {
        left = mid + 1;
      }
    }
    return left;
  };

  envelopes.sort((a, b) => a[0] - b[0] || b[1] - a[1]);

  const piles = [];

  for (const [first, last] of envelopes) {
    const index = bisectLeft(piles, last);

    if (index < piles.length) {
      piles[index] = last;
    } else {
      piles.push(last);
    }
  }

  return piles.length;
};