354. Russian Doll Envelopes

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)

Example:
Given envelopes = [[5,4],[6,4],[6,7],[2,3]], the maximum number of envelopes you can Russian doll is 3 ([2,3] => [5,4] => [6,7]).

使用DP去做，但是这种问题与一般的接龙型动态规划的题目最主要的一个区别是需要首先对数据进行排序

java

class Solution {
    public int maxEnvelopes(int[][] envelopes) {
        if (envelopes == null || envelopes.length == 0) {
            return 0;
        }
        if (envelopes[0] == null || envelopes[0].length == 0) {
            return 0;
        }
        Comparator<int[]> cmp = new Comparator<int[]>() {
            public int compare(int[] a1, int[] a2) {
                if (a1[0] == a2[0]) {
                    return a1[1] - a2[1];
                } else {
                    return a1[0] - a2[0];
                }
            }  
        };
        Arrays.sort(envelopes, cmp);
        int[] f = new int[envelopes.length];
        for (int i = 0; i < f.length; i++) {
            f[i] = 1;
        }
        for (int i = 1; i < f.length; i++) {
            for (int j = 0; j < i; j++) {
                if (envelopes[i][0] > envelopes[j][0] && 
                    envelopes[i][1] > envelopes[j][1]) {
                    f[i] = Math.max(f[i], f[j] + 1);
                }
            }
        }
        int sum = 0;
        for (int i : f) {
            sum = Math.max(sum, i);
        }
        return sum;
    }
}