# [Prefix-Sum]
# https://leetcode.com/problems/check-if-all-the-integers-in-a-range-are-covered/
# 1893. Check if All the Integers in a Range Are Covered

# History:
# 1.
# Jul 19, 2021

# You are given a 2D integer array ranges and two integers left and right.
# Each ranges[i] = [starti, endi] represents an inclusive interval between starti and endi.
#
# Return true if each integer in the inclusive range [left, right] is covered by at least one interval in ranges.
# Return false otherwise.
#
# An integer x is covered by an interval ranges[i] = [starti, endi] if starti <= x <= endi.
#
#
#
# Example 1:
#
# Input: ranges = [[1,2],[3,4],[5,6]], left = 2, right = 5
# Output: true
# Explanation: Every integer between 2 and 5 is covered:
# - 2 is covered by the first range.
# - 3 and 4 are covered by the second range.
# - 5 is covered by the third range.
# Example 2:
#
# Input: ranges = [[1,10],[10,20]], left = 21, right = 21
# Output: false
# Explanation: 21 is not covered by any range.
#
#
# Constraints:
#
# 1 <= ranges.length <= 50
# 1 <= starti <= endi <= 50
# 1 <= left <= right <= 50

class Solution(object):
    def isCovered(self, ranges, left, right):
        """
        :type ranges: List[List[int]]
        :type left: int
        :type right: int
        :rtype: bool
        """
        mem = [0] * 52

        for r in ranges:
            mem[r[0]] += 1
            mem[r[1] + 1] -= 1

        for i in range(1, 52):
            mem[i] += mem[i - 1]

        for i in range(left, right + 1):
            if mem[i] == 0:
                return False

        return True
