Parallel courses ii

Dynamic Programming Bit Manipulation Graph Theory Bitmask

30.6% acceptance

Feb 25, 2026

1134

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. Also, you are given the integer k. In one semester, you can take at most k courses as long as you have taken all the prerequisites in the previous semesters for the courses you are taking. Return the minimum number of semesters needed to take all courses.

Solution

Rust

Time O(n²)

Space O(n)

LeetCode

solution.rs

impl Solution {
  pub fn min_number_of_semesters(n: i32, relations: Vec<Vec<i32>>, k: i32) -> i32 {
    let n = n as usize;
    let k = k as u32;
    let full = (1u32 << n) - 1;
    let mut prereq = vec![0u32; n]; // prereq[i] = bitmask of prerequisites for course i
    for r in &relations {
      let prev = (r[0] - 1) as usize;
      let next = (r[1] - 1) as usize;
      prereq[next] |= 1 << prev;
    }
    let mut dp = vec![i32::MAX; 1 << n];
    dp[0] = 0;
    for mask in 0..=(full as usize) {
      if dp[mask] == i32::MAX { continue; }
      // find available courses
      let mask32 = mask as u32;
      let mut avail = 0u32;
      for i in 0..n {
        if mask32 & (1 << i) == 0 && (prereq[i] & mask32) == prereq[i] {
          avail |= 1 << i;
        }
      }
      // enumerate all subsets of avail with popcount <= k
      let mut sub = avail;
      loop {
        if sub.count_ones() <= k {
          let new_mask = (mask32 | sub) as usize;
          if dp[mask] + 1 < dp[new_mask] {
            dp[new_mask] = dp[mask] + 1;
          }
        }
        if sub == 0 { break; }
        sub = (sub - 1) & avail;
      }
    }
    dp[full as usize]
  }
}