How hard is LeetCode 1494. Parallel Courses II?

LeetCode 1494. Parallel Courses II is rated Hard on LeetCode.

What topics does LeetCode 1494. Parallel Courses II cover?

LeetCode 1494. Parallel Courses II is tagged Bit Manipulation, Graph, Dynamic Programming and Bitmask on LeetCode.

Parallel Courses II — LeetCode 1494 Python Solution

HardBit ManipulationGraphDynamic ProgrammingBitmask

Problem: #1494
Pattern: Bit Manipulation
Reading time: 5 min
Source: leetcode.com

The problem

You are given an integer n, which indicates that there are n courses labeled from 1 to n. You are also given an array relations where relations[i] = [prevCoursei, nextCoursei], representing a prerequisite relationship between course prevCoursei and course nextCoursei: course prevCoursei has to be taken before course nextCoursei.

Example

Input: n = 4, relations = [[2,1],[3,1],[1,4]], k = 2
Output: 3
Explanation: The figure above represents the given graph.

Python solution

Python

class Solution:
    def minNumberOfSemesters(self, n: int, relations: List[List[int]], k: int) -> int:
        d = [0] * (n + 1)
        for x, y in relations:
            d[y] |= 1 << x
        q = deque([(0, 0)])
        vis = {0}
        while q:
            cur, t = q.popleft()
            if cur == (1 << (n + 1)) - 2:
                return t
            nxt = 0
            for i in range(1, n + 1):
                if (cur & d[i]) == d[i]:
                    nxt |= 1 << i
            nxt ^= cur
            if nxt.bit_count() <= k:
                if (nxt | cur) not in vis:
                    vis.add(nxt | cur)
                    q.append((nxt | cur, t + 1))
            else:
                x = nxt
                while nxt:
                    if nxt.bit_count() == k and (nxt | cur) not in vis:
                        vis.add(nxt | cur)
                        q.append((nxt | cur, t + 1))
                    nxt = (nxt - 1) & x

Complexity

Measure	Complexity
Time	O(n·m) (typical)
Space	O(n·m) or optimized auxiliary

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1494. Parallel Courses II is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1494. Parallel Courses II?: LeetCode 1494. Parallel Courses II is rated Hard on LeetCode.
What topics does LeetCode 1494. Parallel Courses II cover?: LeetCode 1494. Parallel Courses II is tagged Bit Manipulation, Graph, Dynamic Programming and Bitmask on LeetCode.