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LeetCode 1494: Parallel Courses II Solution

Master LeetCode problem 1494 (Parallel Courses II), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

Problem Explanation

Explanation:

To solve this problem, we can use a topological sorting algorithm combined with dynamic programming. We will first construct the prerequisite graph from the given relations and then perform a topological sort to determine the order in which the courses can be taken. We will use dynamic programming to calculate the minimum number of semesters needed to take all courses.

  1. Construct the prerequisite graph from the given relations.
  2. Perform topological sorting to get the order in which courses can be taken.
  3. Use dynamic programming to calculate the minimum number of semesters needed to take all courses.

Time Complexity: O(n * 2^n) Space Complexity: O(2^n)

:

Solution Code

class Solution {
    public int minNumberOfSemesters(int n, int[][] relations, int k) {
        int[] pre = new int[n];
        for (int[] relation : relations) {
            pre[relation[1] - 1] |= 1 << (relation[0] - 1);
        }
        
        int[] dp = new int[1 << n];
        Arrays.fill(dp, n);
        dp[0] = 0;
        
        for (int mask = 0; mask < (1 << n); mask++) {
            int canTake = 0;
            for (int i = 0; i < n; i++) {
                if ((mask & pre[i]) == pre[i] && (mask & (1 << i)) == 0) {
                    canTake |= 1 << i;
                }
            }
            
            for (int sub = canTake; sub > 0; sub = (sub - 1) & canTake) {
                if (Integer.bitCount(sub) <= k) {
                    dp[mask | sub] = Math.min(dp[mask | sub], dp[mask] + 1);
                }
            }
        }
        
        return dp[(1 << n) - 1];
    }
}

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