Solution3.java

/// https://leetcode.com/problems/non-overlapping-intervals/description/
/// Author : liuyubobobo
/// Time   : 2017-11-19

import java.util.Arrays;
import java.util.Comparator;

/// Dynamic Programming based on ending point
/// Time Complexity:  O(n^2)
/// Space Complexity: O(n)
public class Solution3 {

    // Definition for an interval.
    public static class Interval {
        int start;
        int end;
        Interval() { start = 0; end = 0; }
        Interval(int s, int e) { start = s; end = e; }
    }

    public int eraseOverlapIntervals(Interval[] intervals) {

        if(intervals.length == 0)
            return 0;

        Arrays.sort(intervals, new Comparator<Interval>() {
            @Override
            public int compare(Interval o1, Interval o2) {
                if(o1.end != o2.end)
                    return o1.end - o2.end;
                return o1.start - o2.start;
            }
        });

        int[] memo = new int[intervals.length];
        Arrays.fill(memo, 1);
        for(int i = 1 ; i < intervals.length ; i ++)
            // memo[i]
            for(int j = 0 ; j < i ; j ++)
                if(intervals[i].start >= intervals[j].end)
                    memo[i] = Math.max(memo[i], 1 + memo[j]);

        int res = 0;
        for(int i = 0; i < memo.length ; i ++)
            res = Math.max(res, memo[i]);

        return intervals.length - res;
    }

    public static void main(String[] args) {
        Interval[] interval1 = {new Interval(1,2),
                new Interval(2,3),
                new Interval(3,4),
                new Interval(1,3)};
        System.out.println((new Solution3()).eraseOverlapIntervals(interval1));

        Interval[] interval2 = {new Interval(1,2),
                new Interval(1,2),
                new Interval(1,2)};
        System.out.println((new Solution3()).eraseOverlapIntervals(interval2));

        Interval[] interval3 = {new Interval(1,2),
                new Interval(2,3)};
        System.out.println((new Solution3()).eraseOverlapIntervals(interval3));
    }
}