README_EN.md

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

DFS.

Python3

class Solution:
    def checkIfPrerequisite(
        self, numCourses: int, prerequisites: List[List[int]], queries: List[List[int]]
    ) -> List[bool]:
        @cache
        def dfs(a, b):
            if b in g[a] or a == b:
                return True
            for c in g[a]:
                if dfs(c, b):
                    return True
            return False

        g = defaultdict(set)
        for a, b in prerequisites:
            g[a].add(b)
        return [dfs(a, b) for a, b in queries]

Java

class Solution {
    public List<Boolean> checkIfPrerequisite(
        int numCourses, int[][] prerequisites, int[][] queries) {
        int[][] g = new int[numCourses][numCourses];
        for (int i = 0; i < numCourses; ++i) {
            Arrays.fill(g[i], -1);
        }
        for (int[] e : prerequisites) {
            int a = e[0], b = e[1];
            g[a][b] = 1;
        }
        List<Boolean> ans = new ArrayList<>();
        for (int[] e : queries) {
            int a = e[0], b = e[1];
            ans.add(dfs(a, b, g));
        }
        return ans;
    }

    private boolean dfs(int a, int b, int[][] g) {
        if (g[a][b] != -1) {
            return g[a][b] == 1;
        }
        if (a == b) {
            g[a][b] = 1;
            return true;
        }
        for (int i = 0; i < g[a].length; ++i) {
            if (g[a][i] == 1 && dfs(i, b, g)) {
                g[a][b] = 1;
                return true;
            }
        }
        g[a][b] = 0;
        return false;
    }
}

C++

class Solution {
public:
    vector<bool> checkIfPrerequisite(int numCourses, vector<vector<int>>& prerequisites, vector<vector<int>>& queries) {
        vector<vector<int>> g(numCourses, vector<int>(numCourses, -1));
        for (auto& e : prerequisites) {
            int a = e[0], b = e[1];
            g[a][b] = 1;
        }
        vector<bool> ans;
        for (auto& e : queries) {
            int a = e[0], b = e[1];
            ans.push_back(dfs(a, b, g));
        }
        return ans;
    }

    bool dfs(int a, int b, vector<vector<int>>& g) {
        if (g[a][b] != -1) return g[a][b] == 1;
        if (a == b) {
            g[a][b] = 1;
            return true;
        }
        for (int i = 0; i < g[a].size(); ++i) {
            if (g[a][i] == 1 && dfs(i, b, g)) {
                g[a][b] = 1;
                return true;
            }
        }
        g[a][b] = 0;
        return false;
    }
};

Go

func checkIfPrerequisite(numCourses int, prerequisites [][]int, queries [][]int) []bool {
	g := make([][]int, numCourses)
	for i := range g {
		g[i] = make([]int, numCourses)
		for j := range g[i] {
			g[i][j] = -1
		}
	}
	for _, e := range prerequisites {
		a, b := e[0], e[1]
		g[a][b] = 1
	}
	var ans []bool
	var dfs func(a, b int) bool
	dfs = func(a, b int) bool {
		if g[a][b] != -1 {
			return g[a][b] == 1
		}
		if a == b {
			g[a][b] = 1
			return true
		}
		for i, c := range g[a] {
			if c == 1 && dfs(i, b) {
				g[a][b] = 1
				return true
			}
		}
		g[a][b] = 0
		return false
	}
	for _, e := range queries {
		a, b := e[0], e[1]
		ans = append(ans, dfs(a, b))
	}
	return ans
}

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