[Swift]LeetCode354. 俄罗斯套娃信封问题 | Russian Doll Envelopes

★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★
➤微信公众号：山青咏芝（shanqingyongzhi）
➤博客园地址：山青咏芝（https://www.cnblogs.com/strengthen/）
➤GitHub地址：https://github.com/strengthen/LeetCode
➤原文地址：https://www.cnblogs.com/strengthen/p/10276020.html 
➤如果链接不是山青咏芝的博客园地址，则可能是爬取作者的文章。
➤原文已修改更新！强烈建议点击原文地址阅读！支持作者！支持原创！
★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★

热烈欢迎，请直接点击！！！

进入博主App Store主页，下载使用各个作品！！！

注：博主将坚持每月上线一个新app！！！

You have a number of envelopes with widths and heights given as a pair of integers (w, h). One envelope can fit into another if and only if both the width and height of one envelope is greater than the width and height of the other envelope.

What is the maximum number of envelopes can you Russian doll? (put one inside other)

Note:
Rotation is not allowed.

Example:

Input: [[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]).

---

给定一些标记了宽度和高度的信封，宽度和高度以整数对形式 (w, h) 出现。当另一个信封的宽度和高度都比这个信封大的时候，这个信封就可以放进另一个信封里，如同俄罗斯套娃一样。

请计算最多能有多少个信封能组成一组“俄罗斯套娃”信封（即可以把一个信封放到另一个信封里面）。

说明:
不允许旋转信封。

示例:

输入: envelopes = [[5,4],[6,4],[6,7],[2,3]]
输出: 3 
解释: 最多信封的个数为 3, 组合为: [2,3] => [5,4] => [6,7]。

---

356ms

class Solution {
    //二分法
    func maxEnvelopes(_ envelopes: [[Int]]) -> Int {
        var envelopes = envelopes
        var dp:[Int] = [Int]()
        envelopes.sort(by:sortArray)
        for i in 0..<envelopes.count
        {
            var left:Int = 0
            var right:Int = dp.count
            var t:Int = envelopes[i][1]
            while(left < right)
            {
                var mid:Int = left + (right - left) / 2
                if dp[mid] < t
                {
                    left = mid + 1
                }
                else
                {
                    right = mid
                }
            }
            if right >= dp.count
            {
                dp.append(t)
            }
            else
            {
                dp[right] = t
            }            
        }
        return dp.count
    }
    
    func sortArray(_ a:[Int],_ b:[Int]) -> Bool
    {
        if a[0] == b[0]
        {
            return a[1] > b[1]
        }
        return a[0] < b[0]
    }
}

---

6948ms

class Solution {
    func maxEnvelopes(_ envelopes: [[Int]]) -> Int {
        if envelopes.count == 0 { return 0 }
        let sorted = envelopes.sorted {
            return $0[0] < $1[0]
        }
        
        var dp: [Int] = [Int](repeating: 0, count: envelopes.count)
        var res = 0
        for i in 0..<sorted.count {
            dp[i] = 1
            for j in 0..<i {
                // if i is bigger than j
                if sorted[i][0] > sorted[j][0] && sorted[i][1] > sorted[j][1] {
                    dp[i] = max(dp[i], dp[j] + 1)
                }
            }
            res = max(res, dp[i])
        }
        return res
    }
}