Question

1462. Course Schedule IV

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Description

There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course ai first if you want to take course bi.

• For example, the pair [0, 1] indicates that you have to take course 0 before you can take course 1.

Prerequisites can also be indirect. If course a is a prerequisite of course b, and course b is a prerequisite of course c, then course a is a prerequisite of course c.

You are also given an array queries where queries[j] = [uj, vj]. For the jth query, you should answer whether course uj is a prerequisite of course vj or not.

Return a boolean array answer, where answer[j] is the answer to the jth query.

 

Example 1:

Input: numCourses = 2, prerequisites = [[1,0]], queries = [[0,1],[1,0]]
Output: [false,true]
Explanation: The pair [1, 0] indicates that you have to take course 1 before you can take course 0.
Course 0 is not a prerequisite of course 1, but the opposite is true.

Example 2:

Input: numCourses = 2, prerequisites = [], queries = [[1,0],[0,1]]
Output: [false,false]
Explanation: There are no prerequisites, and each course is independent.

Example 3:

Input: numCourses = 3, prerequisites = [[1,2],[1,0],[2,0]], queries = [[1,0],[1,2]]
Output: [true,true]

 

Constraints:

• 2 <= numCourses <= 100
• 0 <= prerequisites.length <= (numCourses * (numCourses - 1) / 2)
• prerequisites[i].length == 2
• 0 <= ai, bi <= n - 1
• ai != bi
• All the pairs [ai, bi] are unique.
• The prerequisites graph has no cycles.
• 1 <= queries.length <= 104
• 0 <= ui, vi <= n - 1
• ui != vi

Solutions

Solution 1

class Solution:
  def checkIfPrerequisite(
    self, n: int, prerequisites: List[List[int]], queries: List[List[int]]
  ) -> List[bool]:
    f = [[False] * n for _ in range(n)]
    for a, b in prerequisites:
      f[a][b] = True
    for k in range(n):
      for i in range(n):
        for j in range(n):
          if f[i][k] and f[k][j]:
            f[i][j] = True
    return [f[a][b] for a, b in queries]

class Solution {
  public List<Boolean> checkIfPrerequisite(int n, int[][] prerequisites, int[][] queries) {
    boolean[][] f = new boolean[n][n];
    for (var p : prerequisites) {
      f[p[0]][p[1]] = true;
    }
    for (int k = 0; k < n; ++k) {
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
          f[i][j] |= f[i][k] && f[k][j];
        }
      }
    }
    List<Boolean> ans = new ArrayList<>();
    for (var q : queries) {
      ans.add(f[q[0]][q[1]]);
    }
    return ans;
  }
}

class Solution {
public:
  vector<bool> checkIfPrerequisite(int n, vector<vector<int>>& prerequisites, vector<vector<int>>& queries) {
    bool f[n][n];
    memset(f, false, sizeof(f));
    for (auto& p : prerequisites) {
      f[p[0]][p[1]] = true;
    }
    for (int k = 0; k < n; ++k) {
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
          f[i][j] |= (f[i][k] && f[k][j]);
        }
      }
    }
    vector<bool> ans;
    for (auto& q : queries) {
      ans.push_back(f[q[0]][q[1]]);
    }
    return ans;
  }
};

func checkIfPrerequisite(n int, prerequisites [][]int, queries [][]int) (ans []bool) {
  f := make([][]bool, n)
  for i := range f {
    f[i] = make([]bool, n)
  }
  for _, p := range prerequisites {
    f[p[0]][p[1]] = true
  }
  for k := 0; k < n; k++ {
    for i := 0; i < n; i++ {
      for j := 0; j < n; j++ {
        f[i][j] = f[i][j] || (f[i][k] && f[k][j])
      }
    }
  }
  for _, q := range queries {
    ans = append(ans, f[q[0]][q[1]])
  }
  return
}

function checkIfPrerequisite(n: number, prerequisites: number[][], queries: number[][]): boolean[] {
  const f = Array.from({ length: n }, () => Array(n).fill(false));
  prerequisites.forEach(([a, b]) => (f[a][b] = true));
  for (let k = 0; k < n; ++k) {
    for (let i = 0; i < n; ++i) {
      for (let j = 0; j < n; ++j) {
        f[i][j] ||= f[i][k] && f[k][j];
      }
    }
  }
  return queries.map(([a, b]) => f[a][b]);
}

Solution 2

class Solution:
  def checkIfPrerequisite(
    self, n: int, prerequisites: List[List[int]], queries: List[List[int]]
  ) -> List[bool]:
    f = [[False] * n for _ in range(n)]
    g = [[] for _ in range(n)]
    indeg = [0] * n
    for a, b in prerequisites:
      g[a].append(b)
      indeg[b] += 1
    q = deque(i for i, x in enumerate(indeg) if x == 0)
    while q:
      i = q.popleft()
      for j in g[i]:
        f[i][j] = True
        for h in range(n):
          f[h][j] = f[h][j] or f[h][i]
        indeg[j] -= 1
        if indeg[j] == 0:
          q.append(j)
    return [f[a][b] for a, b in queries]

class Solution {
  public List<Boolean> checkIfPrerequisite(int n, int[][] prerequisites, int[][] queries) {
    boolean[][] f = new boolean[n][n];
    List<Integer>[] g = new List[n];
    int[] indeg = new int[n];
    Arrays.setAll(g, i -> new ArrayList<>());
    for (var p : prerequisites) {
      g[p[0]].add(p[1]);
      ++indeg[p[1]];
    }
    Deque<Integer> q = new ArrayDeque<>();
    for (int i = 0; i < n; ++i) {
      if (indeg[i] == 0) {
        q.offer(i);
      }
    }
    while (!q.isEmpty()) {
      int i = q.poll();
      for (int j : g[i]) {
        f[i][j] = true;
        for (int h = 0; h < n; ++h) {
          f[h][j] |= f[h][i];
        }
        if (--indeg[j] == 0) {
          q.offer(j);
        }
      }
    }
    List<Boolean> ans = new ArrayList<>();
    for (var qry : queries) {
      ans.add(f[qry[0]][qry[1]]);
    }
    return ans;
  }
}

class Solution {
public:
  vector<bool> checkIfPrerequisite(int n, vector<vector<int>>& prerequisites, vector<vector<int>>& queries) {
    bool f[n][n];
    memset(f, false, sizeof(f));
    vector<int> g[n];
    vector<int> indeg(n);
    for (auto& p : prerequisites) {
      g[p[0]].push_back(p[1]);
      ++indeg[p[1]];
    }
    queue<int> q;
    for (int i = 0; i < n; ++i) {
      if (indeg[i] == 0) {
        q.push(i);
      }
    }
    while (!q.empty()) {
      int i = q.front();
      q.pop();
      for (int j : g[i]) {
        f[i][j] = true;
        for (int h = 0; h < n; ++h) {
          f[h][j] |= f[h][i];
        }
        if (--indeg[j] == 0) {
          q.push(j);
        }
      }
    }
    vector<bool> ans;
    for (auto& qry : queries) {
      ans.push_back(f[qry[0]][qry[1]]);
    }
    return ans;
  }
};

func checkIfPrerequisite(n int, prerequisites [][]int, queries [][]int) (ans []bool) {
  f := make([][]bool, n)
  for i := range f {
    f[i] = make([]bool, n)
  }
  g := make([][]int, n)
  indeg := make([]int, n)
  for _, p := range prerequisites {
    a, b := p[0], p[1]
    g[a] = append(g[a], b)
    indeg[b]++
  }
  q := []int{}
  for i, x := range indeg {
    if x == 0 {
      q = append(q, i)
    }
  }
  for len(q) > 0 {
    i := q[0]
    q = q[1:]
    for _, j := range g[i] {
      f[i][j] = true
      for h := 0; h < n; h++ {
        f[h][j] = f[h][j] || f[h][i]
      }
      indeg[j]--
      if indeg[j] == 0 {
        q = append(q, j)
      }
    }
  }
  for _, q := range queries {
    ans = append(ans, f[q[0]][q[1]])
  }
  return
}

function checkIfPrerequisite(n: number, prerequisites: number[][], queries: number[][]): boolean[] {
  const f = Array.from({ length: n }, () => Array(n).fill(false));
  const g: number[][] = Array.from({ length: n }, () => []);
  const indeg: number[] = Array(n).fill(0);
  for (const [a, b] of prerequisites) {
    g[a].push(b);
    ++indeg[b];
  }
  const q: number[] = [];
  for (let i = 0; i < n; ++i) {
    if (indeg[i] === 0) {
      q.push(i);
    }
  }
  while (q.length) {
    const i = q.shift()!;
    for (const j of g[i]) {
      f[i][j] = true;
      for (let h = 0; h < n; ++h) {
        f[h][j] ||= f[h][i];
      }
      if (--indeg[j] === 0) {
        q.push(j);
      }
    }
  }
  return queries.map(([a, b]) => f[a][b]);
}