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.
1#include <vector>
2#include <algorithm>
3
4using namespace std;
5
6int maxNonOverlapIntervals(vector<vector<int>>& intervals) {
7 if (intervals.empty()) return 0;
8 sort(intervals.begin(), intervals.end());
9 vector<int> dp(intervals.size(), 1);
10 int maxCount = 1;
11 for (size_t i = 1; i < intervals.size(); ++i) {
12 for (size_t j = 0; j < i; ++j) {
13 if (intervals[j][1] <= intervals[i][0]) {
14 dp[i] = max(dp[i], dp[j] + 1);
15 }
16 }
17 maxCount = max(maxCount, dp[i]);
18 }
19 return intervals.size() - maxCount;
20}This C++ solution leverages a similar dynamic programming strategy, sorting intervals and iterating over each interval to determine possible non-overlapping extensions. It uses a vector for dp state maintenance and updates maxCount based on sequence extensions.