1024 Video Stitching.py

#!/usr/bin/python3
"""
You are given a series of video clips from a sporting event that lasted T
seconds.  These video clips can be overlapping with each other and have varied
lengths.

Each video clip clips[i] is an interval: it starts at time clips[i][0] and ends
at time clips[i][1].  We can cut these clips into segments freely: for example,
a clip [0, 7] can be cut into segments [0, 1] + [1, 3] + [3, 7].

Return the minimum number of clips needed so that we can cut the clips into
segments that cover the entire sporting event ([0, T]).  If the task is
impossible, return -1.

Example 1:
Input: clips = [[0,2],[4,6],[8,10],[1,9],[1,5],[5,9]], T = 10
Output: 3
Explanation:
We take the clips [0,2], [8,10], [1,9]; a total of 3 clips.
Then, we can reconstruct the sporting event as follows:
We cut [1,9] into segments [1,2] + [2,8] + [8,9].
Now we have segments [0,2] + [2,8] + [8,10] which cover the sporting event [0, 10].
Example 2:

Input: clips = [[0,1],[1,2]], T = 5
Output: -1
Explanation:
We can't cover [0,5] with only [0,1] and [0,2].
Example 3:

Input: clips = [[0,1],[6,8],[0,2],[5,6],[0,4],[0,3],[6,7],[1,3],[4,7],[1,4],[2,5],[2,6],[3,4],[4,5],[5,7],[6,9]], T = 9
Output: 3
Explanation:
We can take clips [0,4], [4,7], and [6,9].
Example 4:

Input: clips = [[0,4],[2,8]], T = 5
Output: 2
Explanation:
Notice you can have extra video after the event ends.

Note:
1 <= clips.length <= 100
0 <= clips[i][0], clips[i][1] <= 100
0 <= T <= 100
"""
from typing import List


class Solution:
    def videoStitching(self, clips: List[List[int]], T: int) -> int:
        """
        Greedy is correct. The larger the coverage, the better
        """
        clips.sort()
        prev_e = 0
        ret = 0

        i = 0
        while i < len(clips):
            if clips[i][0] > prev_e:  # gap
                break

            max_e = -float("inf")
            while i < len(clips) and clips[i][0] <= prev_e:
                max_e = max(max_e, clips[i][1])
                i += 1

            prev_e = max_e  # take
            ret += 1
            if prev_e >= T:
                break

        return ret if prev_e >= T else -1

    def videoStitching_error(self, clips: List[List[int]], T: int) -> int:
        """
        gready take the max coverage?
        """
        A = [(s, -e, s, e) for s, e in clips]
        A.sort()
        ret = 1
        _, _, prev_s, prev_e = A[0]
        if prev_s > 0:
            return False

        for _, _, s, e in A[1:]:
            if s <= prev_e and e > prev_e:
                prev_e = e
                ret += 1


if __name__ == "__main__":
    assert Solution().videoStitching([[0,4],[2,8]], 5) == 2