|
| 1 | +package main |
| 2 | + |
| 3 | +import "fmt" |
| 4 | + |
| 5 | +type intSet struct { |
| 6 | + size int |
| 7 | + elements map[int]struct{} |
| 8 | +} |
| 9 | + |
| 10 | +func NewIntSet() intSet { |
| 11 | + return intSet{size: 0, elements: make(map[int]struct{})} |
| 12 | +} |
| 13 | + |
| 14 | +func (s *intSet) Add(elem int) { |
| 15 | + if _, exists := s.elements[elem]; !exists { |
| 16 | + s.elements[elem] = struct{}{} |
| 17 | + s.size++ |
| 18 | + } |
| 19 | + |
| 20 | + return |
| 21 | +} |
| 22 | + |
| 23 | +func (s *intSet) Remove(elem int) { |
| 24 | + if _, exists := s.elements[elem]; exists { |
| 25 | + delete(s.elements, elem) |
| 26 | + s.size-- |
| 27 | + } |
| 28 | + |
| 29 | + return |
| 30 | +} |
| 31 | + |
| 32 | +func (s *intSet) Contains(elem int) bool { |
| 33 | + _, exists := s.elements[elem] |
| 34 | + |
| 35 | + return exists |
| 36 | +} |
| 37 | + |
| 38 | +func (s *intSet) GetAnyElement() (int, error) { |
| 39 | + if len(s.elements) == 0 { |
| 40 | + return 0, fmt.Errorf("set is empty") |
| 41 | + } |
| 42 | + |
| 43 | + var elem int |
| 44 | + for k, _ := range s.elements { |
| 45 | + elem = k |
| 46 | + |
| 47 | + break |
| 48 | + } |
| 49 | + |
| 50 | + return elem, nil |
| 51 | +} |
| 52 | + |
| 53 | +// Return true if cycle exists. |
| 54 | +func checkCycleFrom(start int, adjs [][]int, whiteSet, graySet, blackSet intSet) bool { |
| 55 | + if blackSet.Contains(start) { |
| 56 | + return false |
| 57 | + } |
| 58 | + |
| 59 | + if graySet.Contains(start) { |
| 60 | + return true |
| 61 | + } |
| 62 | + |
| 63 | + if whiteSet.Contains(start) { |
| 64 | + whiteSet.Remove(start) |
| 65 | + graySet.Add(start) |
| 66 | + } |
| 67 | + |
| 68 | + // Explore all adjacencies |
| 69 | + for i := 0; i < len(adjs[start]); i++ { |
| 70 | + cycleExists := checkCycleFrom(adjs[start][i], adjs, whiteSet, graySet, blackSet) |
| 71 | + |
| 72 | + if cycleExists { |
| 73 | + return true |
| 74 | + } |
| 75 | + } |
| 76 | + |
| 77 | + graySet.Remove(start) |
| 78 | + blackSet.Add(start) |
| 79 | + |
| 80 | + return false |
| 81 | +} |
| 82 | + |
| 83 | +func checkCycle(adjs [][]int) bool { |
| 84 | + whiteSet, graySet, blackSet := NewIntSet(), NewIntSet(), NewIntSet() |
| 85 | + |
| 86 | + for i := 0; i < len(adjs); i++ { |
| 87 | + whiteSet.Add(i) |
| 88 | + } |
| 89 | + |
| 90 | + for { |
| 91 | + elem, err := whiteSet.GetAnyElement() |
| 92 | + |
| 93 | + if err != nil { |
| 94 | + break |
| 95 | + } |
| 96 | + |
| 97 | + if checkCycleFrom(elem, adjs, whiteSet, graySet, blackSet) { |
| 98 | + return true |
| 99 | + } |
| 100 | + } |
| 101 | + |
| 102 | + return false |
| 103 | +} |
| 104 | + |
| 105 | +func topologicalTraversal(start int, adjs [][]int, visited map[int]struct{}, traversal []int) []int { |
| 106 | + if _, exists := visited[start]; exists { |
| 107 | + return traversal |
| 108 | + } |
| 109 | + |
| 110 | + for _, to := range adjs[start] { |
| 111 | + traversal = topologicalTraversal(to, adjs, visited, traversal) |
| 112 | + } |
| 113 | + |
| 114 | + visited[start] = struct{}{} |
| 115 | + traversal = append(traversal, start) |
| 116 | + |
| 117 | + return traversal |
| 118 | +} |
| 119 | + |
| 120 | +func findOrder(numCourses int, prerequisites [][]int) []int { |
| 121 | + adjs := make([][]int, numCourses) |
| 122 | + |
| 123 | + for i, _ := range adjs { |
| 124 | + adjs[i] = []int{} |
| 125 | + } |
| 126 | + |
| 127 | + visited := make(map[int]struct{}) |
| 128 | + leafCheck := make([]bool, numCourses) |
| 129 | + |
| 130 | + for i, _ := range leafCheck { |
| 131 | + leafCheck[i] = true |
| 132 | + } |
| 133 | + |
| 134 | + for _, pair := range prerequisites { |
| 135 | + from, to := pair[0], pair[1] |
| 136 | + |
| 137 | + adjs[from] = append(adjs[from], to) |
| 138 | + |
| 139 | + leafCheck[to] = false |
| 140 | + } |
| 141 | + |
| 142 | + if checkCycle(adjs) { |
| 143 | + return []int{} |
| 144 | + } |
| 145 | + |
| 146 | + order := []int{} |
| 147 | + |
| 148 | + for i := 0; i < numCourses; i++ { |
| 149 | + if leafCheck[i] { |
| 150 | + // leaf course - this is a course that no other course depends on |
| 151 | + order = topologicalTraversal(i, adjs, visited, order) |
| 152 | + } |
| 153 | + } |
| 154 | + |
| 155 | + for i := 0; i < numCourses; i++ { |
| 156 | + if _, exists := visited[i]; !exists { |
| 157 | + return []int{} |
| 158 | + } |
| 159 | + } |
| 160 | + |
| 161 | + return order |
| 162 | +} |
| 163 | + |
| 164 | +type testcase struct { |
| 165 | + numCourses int |
| 166 | + preReqs [][]int |
| 167 | +} |
| 168 | + |
| 169 | +func tests() { |
| 170 | + testcases := []testcase{ |
| 171 | + testcase{numCourses: 2, preReqs: [][]int{[]int{1, 0}}}, |
| 172 | + testcase{numCourses: 4, preReqs: [][]int{[]int{1, 0}, []int{2, 0}, []int{3, 1}, []int{3, 2}}}, |
| 173 | + testcase{numCourses: 3, preReqs: [][]int{[]int{0, 2}, []int{1, 2}, []int{2, 0}}}, |
| 174 | + } |
| 175 | + |
| 176 | + for i, tc := range testcases { |
| 177 | + order := findOrder(tc.numCourses, tc.preReqs) |
| 178 | + |
| 179 | + fmt.Printf("Test case: %d; order: %v\n", i, order) |
| 180 | + } |
| 181 | +} |
| 182 | + |
| 183 | +func main() { |
| 184 | + // tests() |
| 185 | + s1 := NewIntSet() |
| 186 | + |
| 187 | + s1.Add(4) |
| 188 | + |
| 189 | + fmt.Printf("s1.size = %d\n", s1.size) |
| 190 | +} |
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