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.
1function eraseOverlapIntervals(intervals) {
2 intervals.sort((a, b) => a[1] - b[1]);
3 let end = intervals[0][1];
4 let count = 0;
5 for (let i = 1; i < intervals.length; i++) {
6 if (intervals[i][0] < end) {
7 count++;
8 } else {
9 end = intervals[i][1];
10 }
11 }
12 return count;
13}The JavaScript solution uses the default sort function with a custom comparator for sorting based on the end times of intervals. As it iterates, it counts overlapping intervals to remove by adjusting the 'end' variable low.
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 <stdio.h>
2#include <stdlib.h>
3
4int compare(const void *a, const void *b) {
5 int *intervalA = *(int **)a;
6 int *intervalB = *(int **)b;
7 return intervalA[0] - intervalB[0];
8}
9
10int maxNonOverlapIntervals(int** intervals, int intervalsSize, int* intervalsColSize) {
11 if (intervalsSize == 0) return 0;
12 qsort(intervals, intervalsSize, sizeof(int*), compare);
13 int* dp = malloc(intervalsSize * sizeof(int));
14 int maxCount = 1;
15 for (int i = 0; i < intervalsSize; i++) {
16 dp[i] = 1;
17 for (int j = 0; j < i; j++) {
18 if (intervals[j][1] <= intervals[i][0]) {
19 dp[i] = fmax(dp[i], dp[j] + 1);
20 }
21 }
22 maxCount = fmax(maxCount, dp[i]);
23 }
24 free(dp);
25 return intervalsSize - maxCount;
26}This C solution sorts the intervals by start time and uses a dp array to store the longest non-overlapping subsequence up to each interval. It checks each interval against those before it to see if it can be appended without leading to overlap.