The greedy approach involves sorting the intervals by their end times. Then, we iterate through the sorted list and count the number of overlapping intervals to remove. The idea is to always pick the interval with the earliest end time, which leaves more room for the remaining intervals.
Steps:
Time Complexity: O(n log n) due to sorting.
Space Complexity: O(1), excluding the input space for the intervals.
1def eraseOverlapIntervals(intervals):
2 intervals.sort(key=lambda x: x[1])
3 end = float('-inf')
4 count = 0
5 for interval in intervals:
6 if interval[0] >= end:
7 end = interval[1]
8 else:
9 count += 1
10 return countThe Python function first sorts intervals by their end values. It iterates over the intervals to update the 'end' and count overlapping ones. The key trick is maintaining the smallest 'end' to maximize selection of across iterations.
This approach utilizes dynamic programming to solve the problem. It is typically less efficient than the greedy method but serves as an illustrative illustration of tackling overlap problems using dp.
Time Complexity: O(n^2) due to nested loops for dp updates.
Space Complexity: O(n) required for the dp array.
1using System;
2
3public class Solution {
4 public int EraseOverlapIntervals(int[][] intervals) {
5 Array.Sort(intervals, (a, b) => a[0].CompareTo(b[0]));
6 int n = intervals.Length;
7 int[] dp = new int[n];
8 Array.Fill(dp, 1);
9 int maxCount = 1;
10 for (int i = 1; i < n; i++) {
11 for (int j = 0; j < i; j++) {
12 if (intervals[j][1] <= intervals[i][0]) {
13 dp[i] = Math.Max(dp[i], dp[j] + 1);
14 }
15 }
16 maxCount = Math.Max(maxCount, dp[i]);
17 }
18 return n - maxCount;
19 }
20}This C# snippet sorts intervals based on their starting points and applies the dynamic programming technique to figure out the longest sequence of non-overlapping intervals by maintaining and updating a dp array.