Table of Contents
Problem Statement
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 bi first if you want to take course ai.
- For example, the pair
[0, 1], indicates that to take course0you have to first take course1.
Return true if you can finish all courses. Otherwise, return false.
Example 1:
Input: numCourses = 2, prerequisites = [[1,0]] Output: true Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So it is possible.
Example 2:
Input: numCourses = 2, prerequisites = [[1,0],[0,1]] Output: false Explanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.
Constraints:
1 <= numCourses <= 20000 <= prerequisites.length <= 5000prerequisites[i].length == 20 <= ai, bi < numCourses- All the pairs prerequisites[i] are unique.
Golang Solution
DFS
type edge struct {
source int
destination int
}
func createEdge(graph map[int][]edge, s, d int) {
graph[s] = append(graph[s], edge{
source: s,
destination: d,
})
}
func createGraph() map[int][]edge {
graph := map[int][]edge{}
return graph
}
func topoSort(graph map[int][]edge, visited []bool, current int, recursion []bool) bool {
visited[current] = true
recursion[current] = true
for _, edge := range graph[current] {
if recursion[edge.destination] {
return true
}
if !visited[edge.destination] {
isCyclePresent := topoSort(graph, visited, edge.destination, recursion)
if isCyclePresent {
return true
}
}
}
recursion[current] = false
return false
}
func canFinish(numCourses int, preRequisites [][]int) bool {
visited := make([]bool, numCourses)
recursion := make([]bool, numCourses)
graph := createGraph()
for _, edge := range preRequisites {
createEdge(graph, edge[1], edge[0])
}
for i := 0; i < numCourses; i++ {
if !visited[i] {
isCyclePresent := topoSort(graph, visited, i, recursion)
// early return for cycle detection
if isCyclePresent {
return false
}
}
}
return true
}Output
func main() {
numCourses := 2
preRequisites := [][]int{
{0, 1},
//{1, 0},
}
ans := canFinish(numCourses, preRequisites)
fmt.Printf("Answer=%t\n", ans)
}
true
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