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![Max Heap #include <bits/stdc++.h>
using namespace std;
int main () {
int a[] = {2,4,8,9,7,10,9,15,20,13};
vector<int> v1(a, a+5);
vector<int> v2 = {2,4,8,9,7,10,9,15,20,13};
make_heap (v1.begin(), v1.end());
cout << "initial max heap : " << v.front() << 'n’;
pop_heap (v.begin(),v.end());
v.pop_back(); cout << "max heap after pop : " << v.front() << 'n’;
v.push_back(99);
push_heap (v.begin(),v.end());
cout << "max heap after push: " << v.front() << 'n’;
sort_heap (v.begin(),v.end());
cout << "final sorted range :";
for (unsigned i=0; i<v.size(); i++)
cout << ' ' << v[i]; cout << 'n’;
return 0;
}](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-15-320.jpg)
![Representation
► Vertices
►[0] ubonratchathani
►[1] amnatcharoen
►[2] srisaket
►[3] yasothon
►…
► Edges
►0 1
►0 2
►1 2
►1 3
►…](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-30-320.jpg)
![Representation
► Vertices
►[0] อุบลราชธานี
►[1] อานาจเจริญ
►[2] ศรีสะเกษ
►[3] ยโสธร
►…
► Edges
► 0 1
► 0 2
► 1 2
► 1 3
► …](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-31-320.jpg)
![(1) Adjacency Matrix
0 1 1 0 0 0
0 0 1 1 0 0
0 0 0 0 1 1
0 0 0 0 1 1
0 0 0 0 0 0
0
1
2
3
4
0 1 2 3 4 5
0 0 0 0 1 0
5
1.int m[][6] = {
2. { 0, 1, 1, 0, 0, 0 },
3. { 0, 0, 1, 1, 0, 0 },
4. { 0, 0, 0, 0, 1, 1 },
5. { 0, 0, 0, 0, 1, 1 },
6. { 0, 0, 0, 0, 0, 0 },
7. { 0, 0, 0, 0, 1, 0 }
8.};](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-35-320.jpg)
![(1) Adjacency Matrix
1.int m[][6] = {
2. { 0, 1.17, 1.05, 0, 0, 0 },
3. { 0, 0, 1.10, 0.77, 0, 0 },
4. { 0, 0, 0, 0, 1.53, 2.15 },
5. { 0, 0, 0, 0, 2.03, 0.88 },
6. { 0, 0, 0, 0, 0, 0 },
7. { 0, 0, 0, 0, 2.08, 0 }
8.};
0 1.17 1.05 0 0 0
0 0 1.10 0.77 0 0
0 0 0 0 1.53 2.15
0 0 0 0 2.03 0.88
0 0 0 0 0 0
0
1
2
3
4
0 1 2 3 4 5
0 0 0 0 2.08 0
5](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-42-320.jpg)
![Depth First Traversal - iterative
1.# iterative depth first traversal
2.def dfti(graph, src=0):
3. stack = [ src ]
4. while len(stack) > 0:
5. current = stack.pop()
6. print(current)
7. for neighbor in graph[current]:
8. stack.append(neighbor)](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-62-320.jpg)
![Depth First Traversal - recursive
1.# recursive depth first traveral
2.def dftr(graph, src=0):
3. print(src)
4. for neighbor in graph[src]:
5. dftr(graph, neighbor)
6.](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-63-320.jpg)
![Depth First Traversal - iterative
1.// iterative depth first traversal
2.void dfti(mivi graph, int src) {
3. stack<int> s({src});
4. int current;
5. while (!s.empty()) {
6. current = s.top(); s.pop();
7. cout << "pop: " << current << endl;
8. for (auto neighbor : graph[current]) {
9. s.push(neighbor);
10. }
11. }
12.}
13.](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-64-320.jpg)
![Depth First Traversal - recursive
1.// recursive depth first traversal
2.void dftr(mivi graph, int src) {
3. cout << "pop: " << src << endl;
4. for (auto neighbor : graph[src]) {
5. dftr(graph, neighbor);
6. }
7.}
8.](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-65-320.jpg)
![Breadth First Traversal - iterative
1.# iterative breadth first traversal
2.def bfti(graph, src=0):
3. q = [ src ]
4. while len(q) > 0:
5. current = q.pop(0)
6. print(current)
7. for neighbor in graph[current]:
8. q.append(neighbor)
9.](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-78-320.jpg)
![Breadth First Traversal - iterative
1.void bft(mivi graph, int src) {
2. queue<int> q({ src });
3. int current;
4. while (!q.empty()) {
5. current = q.front(); q.pop();
6. cout << "pop: " << current << endl;
7. for (auto neighbor : graph[current]) {
8. q.push(neighbor);
9. }
10. }
11.}
12.](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-79-320.jpg)
![Depth First Traversal – iterative 2
1.void dft2(mivi graph, int src) {
2. stack<int> s({src});
3. map<int, bool> visited;
4. int current;
5.
6. visited[src] = true;
7. while (!s.empty()) {
8. current = s.top(); s.pop();
9. cout << "pop: " << current << endl;
10. for (auto neighbor : graph[current]) {
11. if (visited.find(neighbor) == visited.end()) {
12. visited[neighbor] = true;
13. s.push(neighbor);
14. }
15. }
16. }
17.}](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-88-320.jpg)
![Depth First Traversal – recursive 2
1.void dftr2(mivi graph, int src, map<int, bool>& visited) {
2. if (visited.find(src) == visited.end()) {
3. cout << "pop: " << src << endl;
4. visited[src] = true;
5. for (auto neighbor : graph[src]) {
6. dftr2(graph, neighbor, visited);
7. }
8. }
9.}](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-89-320.jpg)
![Breadth First Traversal – iterative 2
1.void bft2(mivi graph, int src) {
2. queue<int> q({ src });
3. map<int, bool> visited;
4. int current;
5.
6. visited[src] = true;
7. while (!q.empty()) {
8. current = q.front(); q.pop();
9. cout << "pop: " << current << endl;
10. for (auto neighbor : graph[current]) {
11. if (visited.find(neighbor) == visited.end()) {
12. visited[neighbor] = true;
13. q.push(neighbor);
14. }
15. }
16. }
17.}](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-90-320.jpg)
![hasPath มีเส ้นทางจาก 1 ไป 4?
1
0
2
3
4
5
def hasPath(graph, src, dst): # depth first
if src == dst: return True
for neigbor in graph[src]:
if hasPath(graph, neigbor, dst):
return True
return False](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-91-320.jpg)
![hasPath มีเส ้นทางจาก 1 ไป 4?
1
0
2
3
4
5
def hasPath(graph, src, dst): # breadth first
queue = [ src ]
while len(queue) > 0:
current = queue.pop()
if current == dst: return True
for neighbor in graph[current]:
queue.push(neighbor)
return False](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-92-320.jpg)
![Explore() พิมพ์ชื่อจังหวัดแยกกลุ่มที่เชื่อมกันกลุ่มละ
บรรทัด
def explore(graph, current, visited):
if current in visited: return False
visited.add(current)
for neighbor in graph[current]:
explore(graph, neighbor, visited)
return True](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-97-320.jpg)
![largestComponent() กลุ่มที่เชื่อมกันมากที่สุดกี่
จังหวัด
def largestComponent(graph):
largest = 0
visited = set()
for node in graph:
size = exploreSize(graph, node,
visited)
if size > largest: largest = size
return largest
def exploreSize(graph, node, visited):
if node in visited: return 0
visited.add(node)
size = 1
for neighbor of graph[node]:
size += exploreSize(graph, neighbor,
visited)
return size](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-99-320.jpg)
![Explore()
def explore(grid, r, c, visited):
if !(0 <= r < len(grid)) || !(0 <= c < len(grid[r])): return 0
if grid[r][c] == ‘W’: return 0
if (r,c) in visited: return 0
visited.add( (r,c) )
explore(grid, r-1, c, visited)
explore(grid, r+1, c, visited)
explore(grid, r, c-1, visited)
explore(grid, r, c+1, visited)
return 1](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-101-320.jpg)
![islandCount()
def islandCount(grid):
visited, count = set(), 0
for r in range(0, len(grid)):
for c in range(0, len(grid[r]):
count += explore(grid, r, c, visited)
return count](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-102-320.jpg)
![Shortest Path – เส ้นทางสั้นที่สุด (Prelim)
def shortestPath(graph, src, dst): # bread first
queue = [ [src, 0] ]
visited = { src }
while len(queue) > 0:
node, distance = queue.pop()
if node == dst: return distance
for neighbor in graph[node]:
if node not in visited:
visited.add(node)
queue.push( [neighbor, distance+1] )
return -1 # path not found](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-107-320.jpg)
![Prim’s Algorithm
1.typedef vector<int> vi;
2.typedef pair<int, int> ii;
3.
4.vi taken;
5.priority_queue<ii> pq;
6.
7.void process(int vtx) {
8. taken[vtx] = 1;
9. for (int j=0; j < (int)graph[vtx].size(); j++) {
10. ii v = graph[vtx][j];
11. if (!taken[v.first])
12. pq.push(ii(-v.second, -v.first));
13. }
14.}
15.](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-109-320.jpg)
![Prim’s Algorithm
1.int main() {
2. ios_base::sync_with_stdio(false);
3. cin.tie(NULL);
4. taken.assign(V, 0);
5. process(0);
6. long mst_cost = 0;
7. while (!pq.empty()) {
8. ii front = pq.top(); pq.pop();
9. u = -front.second;
10. w = -front.first;
11. if (!taken[u]) {
12. mst_cost += w;
13. process(u);
14. }
15. }
16. cout << mst_cost << endl;
17. return 0;
18.}](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-110-320.jpg)
![Prim’s Algorithm
1.int main() {
2. ios_base::sync_with_stdio(false);
3. cin.tie(NULL);
4. taken.assign(V, 0);
5. process(0);
6. long mst_cost = 0;
7. while (!pq.empty()) {
8. ii front = pq.top(); pq.pop();
9. u = -front.second;
10. w = -front.first;
11. if (!taken[u]) {
12. mst_cost += w;
13. process(u);
14. }
15. }
16. cout << mst_cost << endl;
17. return 0;
18.}](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-111-320.jpg)
![Dijkstra
1.typedef vector<int> vi;
2.int main() {
3. vi dist(V, INF);
4. dist[s] = 0;
5. priority_queue<ii, vector<ii>, greater<ii>> pq;
6. pq.push(ii(0, s));
7. while (!pq.empty()) {
8. ii front = pq.top(); pq.pop();
9. int d = front.first, u = front.second;
10. if (d > dist[u]) continue;
11. for (int j=0; j<(int)graph[u].size(); j++) {
12. ii v = graph[u][j];
13. if (dist[u] + v.second < dist[v.first]) {
14. dist[v.first] = dist[u] + v.second;
15. pq.push(ii(dist[v.first], v.first));
16. }
17. }
18. }
19.}](https://image.slidesharecdn.com/treeandgraph-240317005318-211ee753/85/Tree-and-Graph-Algorithms-and-Implementation-112-320.jpg)
![Java Programming [8/12] : Arrays and Collection](https://cdn.slidesharecdn.com/ss_thumbnails/chapter8-130103205430-phpapp01-thumbnail.jpg?width=640&height=640&fit=bounds)
Tree and Graph Algorithms and Implementation
- 1.
- 2. Data Structure Primitive Non-primitive LinearNon-Linear Static Dynamic array Linked list stack queue Tree Graph map list vector pair set deque priority_queue
- 3. Big-O (time complexity/spacecomplexity) top push pop empty priority_queue 1/1 log(n)/1 log(n)/1 1/1 find insert erase empty clear size map log(n)/1 log(n)/1 log(n)/1 1/1 n/1 1/1 find insert erase empty size set log(n)/1 log(n)/1 log(n)/1 1/1 1/1 top pop empty push stack 1/1 1/1 1/1 1/1 front back pop push empty size queue 1/1 1/1 1/1 1/1 1/1 1/1 sort reverse push_back erase clear size vector n*log(n)/log(n) n/1 1/1 n/1 n/1 1/1 https://leetcode.com/discuss/study-guide/1327203/c-stl-guide-stl-operations-and-time-complexities
- 4. Recap ► Vector https://www.cplusplus.com/reference/vector/vector/ 1.#include<bits/stdc++.h> 2.using namespace std; 3.int main() { 4. int n, x; 5. vector<int> a; 6. cin >> n; 7. for (auto i=0; i<n; i++) { 8. cin >> x; 9. a.push_back(x); 10. } 11. a.erase(a.begin()+3, a.begin()+5); 12. for (auto t=a.begin(); t!=a.end(); t++) 13. cout << *t << endl; 14. return 0; 15.}
- 5. Recap ► Queue https://www.cplusplus.com/reference/queue/queue/ 1.#include<bits/stdc++.h> 2.using namespace std; 3.int main() { 4. int n, q; 5. queue<string> names; 6. string name; 7. cin >> n; 8. for (int i=0; i<n; i++) { 9. cin >> name; 10. names.push(name); 11. } 12. while (!names.empty()) { 13. cout << names.front() << endl; 14. names.pop(); 15. } 16. return 0; 17.}
- 6. Trees ต้นไม้ (Trees) เป็นโครงสร้างข้อมูลที่มีลักษณะเป็นกิ่งไม้ที่มีลำาต้น(Root) และกิ่งลูก (Child Nodes) ที่เชื่อมต่อกันโดยใช้เส้นเชื่อม (Edges) ► โหนด (Nodes): จุดบนต้นไม้ที่เก็บข้อมูล ► เส้นเชื่อม (Edges): ลูกศรที่เชื่อมต่อระหว่างโหนดเพื่อแสดงความสัมพันธ์ ► ราก (Root): โหนดบนสุดของต้นไม้ที่ไม่มีแม่ ► แม่ (Parent): โหนดที่อยู่เหนือโหนดลูกในโครงสร้างต้นไม้ ► ลูก (Child): โหนดที่ตำ่ากว่าโหนดแม่ในโครงสร้างต้นไม้ ► ใบ (Leaf): โหนดที่ไม่มีโหนดลูก ► ต้นไม้ย่อย (Subtree): ต้นไม้ที่มีรากเป็นลูกของโหนดอื่น ► ความสูง (Height): จำานวนเส้นเชื่อมจากใบถึงรากของต้นไม้ 1 2 3 4 5 6 8
- 7. Types of Trees ►Binary Tree ► Binary Search Tree ► Balanced Tree (AVL Tree, Red-Black Tree) ► Multi-way Tree (n-ary Tree)
- 8.
- 9. Binary Search Tree ต้นไม้ค้นหาแบบทวิภาคที่มีการเรียงลำาดับ ข้อมูลของโหนด คุณสมบัติ ►Left Subtree < Parent Node ► Parent Node < Right Subtree 8 3 10 1 6 14 4 7 13
- 10. Balanced Binary searchTree ต้นไม้ที่กระจายโหนดอย่างสมดุล ช่วยให้การ เข้าถึงข้อมูล มีประสิทธิภาพมากขึ้น คุณสมบัติ ► ค้นหาได้เร็ว ► อัลกอริทึมทำางานได้เร็ว AVL Tree, Red-Black Tree 8 3 10 1 6 14 4 7 13
- 11. AVL Tree Adelson-Velsky andLandis Tree is a self-balancing binary search tree. ► abs(h(left subtree) – h(right subtree)) <= 1 12 8 18 5 11 4 17 https://www.geeksforgeeks.org/introduction-to-avl-tree/
- 12. Red-Black Tree a self-balancingbinary search tree. ► Every node is either red or black. ► Root node is black. ► Red node can’t have red parent or red child. ► Every path from a node to descendant leaf has same number of black nodes. ► Every leaf must be colored black. 7 3 18 8 10 11 22 https://www.geeksforgeeks.org/introduction-to-red-black-tree/ 26
- 13. Heap ► โครงสร ้างข้อมูลที่เก็บค่าในลักษณะต ้นไม ้ที่มีคุณสมบัติของ complete binary tree ช่วยให ้ค ้นหาข ้อมูลได ้เร็วขึ้น 10 15 30 40 50 70 70 45 50 10 15 50 เลขบนน้อยกว่าเลขล่าง สองเลข เลขบนมากกว่าเลขล่าง สองเลข Min Heap Max Heap น้อย ที่สุด มาก ที่สุด
- 14. สร ้าง 2 4 8 97 10 9 15 20 13 i=0 i=1 i=2 i=3 i=4 i=5 i=6 i=7 i=8 i=9
- 15. Max Heap #include<bits/stdc++.h> using namespace std; int main () { int a[] = {2,4,8,9,7,10,9,15,20,13}; vector<int> v1(a, a+5); vector<int> v2 = {2,4,8,9,7,10,9,15,20,13}; make_heap (v1.begin(), v1.end()); cout << "initial max heap : " << v.front() << 'n’; pop_heap (v.begin(),v.end()); v.pop_back(); cout << "max heap after pop : " << v.front() << 'n’; v.push_back(99); push_heap (v.begin(),v.end()); cout << "max heap after push: " << v.front() << 'n’; sort_heap (v.begin(),v.end()); cout << "final sorted range :"; for (unsigned i=0; i<v.size(); i++) cout << ' ' << v[i]; cout << 'n’; return 0; }
- 16. Min Heap #include<bits/stdc++.h> using namespace std; void print(vector<int> const& v = {}) { for (const auto& e : v) cout << e << ' ‘; cout << 'n’; } int main () { vector<int> v = {2,4,8,9,7,10,9,15,20,13}; print(v); make_heap(v.begin(), v.end(), greater<>{}); pop_heap(v.begin(), v.end(), greater<>{}); auto top = v.back(); v.pop_back(); print({top}); print(v1); return 0; }
- 17. Multi-way Tree ต้นไม้หลายทาง (Multi-wayTree) เป็นโครงสร้างข้อมูลที่โหนด แต่ละตัวอาจมีโหนดลูกมากกว่าหนึ่งโหนด ► โหนดลูกอาจมีจำานวนที่ไม่แน่นอน ► แต่ละโหนดอาจมีความสัมพันธ์กับโหนดอื่นๆ ในโครงสร้าง ต้นไม้ ประโยชน์ของต้นไม้หลายทาง ► ช่วยให้สามารถจัดการข้อมูลแบบลำาดับการเชื่อมต่อได้อย่างมี ประสิทธิภาพ ► เหมาะสำาหรับการจัดเก็บข้อมูลที่มีลำาดับการเชื่อมต่อที่ซับซ้อน B-tree, Trie
- 18. B-Tree โครงสร้างข้อมูลที่ใช้ในการจัดเก็บข้อมูลแบบเชิงลำาดับที่มีการ แบ่งช่วงข้อมูลเป็นส่วนย่อยเพื่อให้สามารถเข้าถึงข้อมูลอย่างมี ประสิทธิภาพ ► โหนดมีจำานวนลูกได้มากกว่า 2 ►จำานวนลูกคงที่ที่กำาหนดไว้ล่วงหน้า ► จัดเก็บข้อมูลตามลำาดับที่กำาหนด https://www.geeksforgeeks.org/introduction-of-b-tree-2/ 100 35 65 130 180 10 20 40 50 70 80 90 10 20 40 50 70 80 90
- 19.
- 20. เก็บด ้วย arrayเหมือนเดิมได ้ไหม?
- 21.
- 22. Graph ► Vertex ข้อมูลตาแหน่ง (plural: vertices)
- 23. Graph ► Edge ข้อมูลความสัมพันธ์ระหว่าง Vertex
- 24. Types ► Undirected Graph► Directed Graph
- 25. Types ► Unweighted Graph► Weighted Graph 1.17 1.05 1.10 0.77 0.88 2.15 2.03 1.53 2.08
- 26.
- 27. Camp2_Tasks: GraphInput01 (directedgraph) 9 ubonratchathani,sisaket ubonratchathani,amnatcharoen amnatcharoen,sisaket amnatcharoen,yasothon sisaket,roiet sisaket,surin yasothon,surin yasothon,roiet roiet,surin surin,sisaket no ► Input ► Input
- 28. Camp2_Tasks: GraphInput02 (undirectedgraph) 9 ubonratchathani,sisaket ubonratchathani,amnatcharoen amnatcharoen,sisaket amnatcharoen,yasothon sisaket,roiet sisaket,surin yasothon,surin yasothon,roiet roiet,surin surin,sisaket yes ► Input ► Input
- 29. Representation ► Vertices ► ubonratchathani ►amnatcharoen ► srisaket ► yasothon ► … ► Edges ► ubonratchathani amnatcharoen ► ubonratchathani srisaket ► amnatcharoen srisaket ► amnatcharoen yasothon ► …
- 30. Representation ► Vertices ►[0] ubonratchathani ►[1]amnatcharoen ►[2] srisaket ►[3] yasothon ►… ► Edges ►0 1 ►0 2 ►1 2 ►1 3 ►…
- 31. Representation ► Vertices ►[0] อุบลราชธานี ►[1]อานาจเจริญ ►[2] ศรีสะเกษ ►[3] ยโสธร ►… ► Edges ► 0 1 ► 0 2 ► 1 2 ► 1 3 ► …
- 32. Representations (1) Adjacency Matrix (2)Adjacency List
- 33.
- 34. (1) Adjacency Matrix 01 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 2 3 4 0 1 2 3 4 5 0 0 0 0 1 0 5
- 35. (1) Adjacency Matrix 01 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 2 3 4 0 1 2 3 4 5 0 0 0 0 1 0 5 1.int m[][6] = { 2. { 0, 1, 1, 0, 0, 0 }, 3. { 0, 0, 1, 1, 0, 0 }, 4. { 0, 0, 0, 0, 1, 1 }, 5. { 0, 0, 0, 0, 1, 1 }, 6. { 0, 0, 0, 0, 0, 0 }, 7. { 0, 0, 0, 0, 1, 0 } 8.};
- 36. (2) Adjacency List(neighbors) 1 2 2 4 5 4 5 0 1 2 3 4 4 5 3
- 37. (2) Adjacency List 12 2 4 5 4 5 0 1 2 3 4 4 5 3 1.vector<vector<int>> m = { 2. {1, 2}, 3. {2, 3}, 4. {4, 5}, 5. {4, 5}, 6. {}, 7. {4}, 8.};
- 38. (2) Adjacency List 12 2 4 5 4 5 0 1 2 3 4 4 5 3 1.typedef vector<int> vi; 2.typedef vector<vi> vvi; 3.vvi m = { 4. {1, 2}, 5. {2, 3}, 6. {4, 5}, 7. {4, 5}, 8. {}, 9. {4}, 10.};
- 39. (2) Adjacency List 12 2 4 5 4 5 0 1 2 3 4 4 5 3 1.typedef vector<int> vi; 2.typedef map<int, vi> mivi; 3.mivi m = { 4. {0, {1, 2}}, 5. {1, {2, 3}}, 6. {2, {4, 5}}, 7. {3, {4, 5}}, 8. {5, {4}} 9.};
- 40.
- 41. (1) Adjacency Matrix 01.17 1.05 0 0 0 0 0 1.10 0.77 0 0 0 0 0 0 1.53 2.15 0 0 0 0 2.03 0.88 0 0 0 0 0 0 0 1 2 3 4 0 1 2 3 4 5 0 0 0 0 2.08 0 5
- 42. (1) Adjacency Matrix 1.intm[][6] = { 2. { 0, 1.17, 1.05, 0, 0, 0 }, 3. { 0, 0, 1.10, 0.77, 0, 0 }, 4. { 0, 0, 0, 0, 1.53, 2.15 }, 5. { 0, 0, 0, 0, 2.03, 0.88 }, 6. { 0, 0, 0, 0, 0, 0 }, 7. { 0, 0, 0, 0, 2.08, 0 } 8.}; 0 1.17 1.05 0 0 0 0 0 1.10 0.77 0 0 0 0 0 0 1.53 2.15 0 0 0 0 2.03 0.88 0 0 0 0 0 0 0 1 2 3 4 0 1 2 3 4 5 0 0 0 0 2.08 0 5
- 43. (2) Adjacency List <1,1.17><2,1.05> <2,1.10> <4,1.53> <5,2.15> <4,2.03> <5,0.88> 0 1 2 3 4 <4,2.08> 5 <3,0.77>
- 44. (2) Adjacency List <1,1.17><2,1.05> <2,1.10> <4,1.53> <5,2.15> <4,2.03> <5,0.88> 0 1 2 3 4 <4,2.08> 5 <3,0.77> 1.typedef pair<float, int> fi; 2.typedef vector<fi> vfi; 3.typedef vector<vfi> vvfi; 4.vector<vector<pair<float,i>>> m = { 5. {(1,1.17), (2,1.05)}, 6. {(2,1.10), (3,0.77)}, 7. {(4,1.53), (5,2.15)}, 8. {(4,2.03), (5,0.88)}, 9. {}, 10. {(4,2.08)}, 11.};
- 45. (2) Adjacency List <1,1.17><2,1.05> <2,1.10> <4,1.53> <5,2.15> <4,2.03> <5,0.88> 0 1 2 3 4 <4,2.08> 5 <3,0.77> 1.typedef pair<int,int> ii; 2.typedef vector<ii> vii; 3.typedef vector<vii> vvii; 4.vvii m = { 5. {(1,1.17), (2,1.05)}, 6. {(2,1.10), (3,0.77)}, 7. {(4,1.53), (5,2.15)}, 8. {(4,2.03), (5,0.88)}, 9. {}, 10. {(4,2.08)}, 11.};
- 46. (2) Adjacency List <1,1.17><2,1.05> <2,1.10> <4,1.53> <5,2.15> <4,2.03> <5,0.88> 0 1 2 3 4 <4,2.08> 5 <3,0.77> 1.typedef pair<int,int> ii; 2.typedef vector<ii> vii; 3.typedef map<int,<vii>> mivii; 4.mivii m = { 5. {0, {(1,1.17), (2,1.05)}}, 6. {1, {(2,1.10), (3,0.77)}}, 7. {2, {(4,1.53), (5,2.15)}}, 8. {3, {(4,2.03), (5,0.88)}}, 9. {4, {}}, 10. {5, {(4,2.08)}}, 11.};
- 47. Traversal – การไล่ดูสมาชิกของกราฟ ►Depth First (ลึก) ► stack ► Breadth First (กว ้าง) ► queue
- 48.
- 49. Representation 1 3 4 5 0 1 2 3 4 5 1.typedef vector<int> vi; 2.typedefmap<int, vi> mivi; 3.mivi m = { 4. {0, {1, 2}}, 5. {1, {3}}, 6. {2, {4}}, 7. {3, {5}}, 8. {4, {}}, 9. {5, {}} 10.}; 2
- 50. Depth First Traversal 1 0 2 3 4 5 0 stack<int>current pop()
- 51. Depth First Traversal 1 0 2 3 4 5 0 2 1 stack<int>current push( neighbors(0) ) 0
- 52. Depth First Traversal 1 0 2 3 4 5 2 1 stack<int>current pop() 0
- 53. Depth First Traversal 1 0 2 3 4 5 2 4 1 stack<int>current push( neighbors(2) ) 0 2
- 54. Depth First Traversal 1 0 2 3 4 5 4 1 stack<int>current pop() 0 2
- 55. Depth First Traversal 1 0 2 3 4 5 4 1 stack<int>current push( neighbors(4) ) 0 2 4
- 56. Depth First Traversal 1 0 2 3 4 5 1 stack<int>current pop() 0 2 4
- 57. Depth First Traversal 1 0 2 3 4 5 1 3 stack<int>current push( neighbors(1) ) 0 2 4 1
- 58. Depth First Traversal 1 0 2 3 4 5 3 stack<int>current pop() 0 2 4 1
- 59. Depth First Traversal 1 0 2 3 4 5 3 5 stack<int>current push( neighbors(3) ) 0 2 4 1 3
- 60. Depth First Traversal 1 0 2 3 4 5 5 stack<int>current pop() 0 2 4 1 3
- 61. Depth First Traversal 1 0 2 3 4 5 5 stack<int>current push( neighbors(5) ) 0 2 4 1 3 5
- 62. Depth First Traversal- iterative 1.# iterative depth first traversal 2.def dfti(graph, src=0): 3. stack = [ src ] 4. while len(stack) > 0: 5. current = stack.pop() 6. print(current) 7. for neighbor in graph[current]: 8. stack.append(neighbor)
- 63. Depth First Traversal- recursive 1.# recursive depth first traveral 2.def dftr(graph, src=0): 3. print(src) 4. for neighbor in graph[src]: 5. dftr(graph, neighbor) 6.
- 64. Depth First Traversal- iterative 1.// iterative depth first traversal 2.void dfti(mivi graph, int src) { 3. stack<int> s({src}); 4. int current; 5. while (!s.empty()) { 6. current = s.top(); s.pop(); 7. cout << "pop: " << current << endl; 8. for (auto neighbor : graph[current]) { 9. s.push(neighbor); 10. } 11. } 12.} 13.
- 65. Depth First Traversal- recursive 1.// recursive depth first traversal 2.void dftr(mivi graph, int src) { 3. cout << "pop: " << src << endl; 4. for (auto neighbor : graph[src]) { 5. dftr(graph, neighbor); 6. } 7.} 8.
- 66. Breadth First Traversal 1 0 2 3 4 5 0 queue<int>current pop()
- 67. Breadth First Traversal 1 0 2 3 4 5 0 2 1 queue<int>current push( neighbors(0) ) 0
- 68. Breadth First Traversal 1 0 2 3 4 5 2 1 queue<int>current 0 pop()
- 69. Breadth First Traversal 1 0 2 3 4 5 1 3 2 queue<int>current push( neighbors(1) ) 0 1
- 70. Breadth First Traversal 1 0 2 3 4 5 3 2 queue<int>current 0 1 pop()
- 71. Breadth First Traversal 1 0 2 3 4 5 2 4 3 queue<int>current push( neighbors(2) ) 0 1 2
- 72. Breadth First Traversal 1 0 2 3 4 5 4 3 queue<int>current 0 1 2 pop()
- 73. Breadth First Traversal 1 0 2 3 4 5 3 5 4 queue<int>current push( neighbors(3) ) 0 1 2 3
- 74. Breadth First Traversal 1 0 2 3 4 5 5 4 queue<int>current 0 1 2 3 pop()
- 75. Breadth First Traversal 1 0 2 3 4 5 4 5 queue<int>current push( neighbors(4) ) 0 1 2 3 4
- 76. Breadth First Traversal 1 0 2 3 4 5 5 queue<int>current 0 1 2 3 4 pop()
- 77. Breadth First Traversal 1 0 2 3 4 5 5 queue<int>current push( neighbors(5) ) 0 1 2 3 4 5
- 78. Breadth First Traversal- iterative 1.# iterative breadth first traversal 2.def bfti(graph, src=0): 3. q = [ src ] 4. while len(q) > 0: 5. current = q.pop(0) 6. print(current) 7. for neighbor in graph[current]: 8. q.append(neighbor) 9.
- 79. Breadth First Traversal- iterative 1.void bft(mivi graph, int src) { 2. queue<int> q({ src }); 3. int current; 4. while (!q.empty()) { 5. current = q.front(); q.pop(); 6. cout << "pop: " << current << endl; 7. for (auto neighbor : graph[current]) { 8. q.push(neighbor); 9. } 10. } 11.} 12.
- 80.
- 81. Representation 1 2 2 4 5 45 0 1 2 3 4 4 5 3 1.typedef vector<int> vi; 2.typedef map<int, vi> mivi; 3.mivi m = { 4. {0, {1, 2} }, 5. {1, {2, 3} }, 6. {2, {4, 5} }, 7. {3, {4, 5} }, 8. {4, {} }, 9. {5, {4} }, 10.};
- 82. Depth First Traversal 1 0 2 3 4 5 stack<int>current 0 pop()
- 83. Depth First Traversal 1 0 2 3 4 5 0 2 1 stack<int>current push( neighbors(0) ) 0
- 84. Depth First Traversal 1 0 2 3 4 5 2 1 stack<int>current pop() 0
- 85. Depth First Traversal 1 0 2 3 4 5 2 4 1 stack<int>current push( neighbors(2) ) pop() 5 0 2
- 86. Depth First Traversal 1 0 2 3 4 5 4 1 stack<int>current pop() 0 2 5
- 87. Depth First Traversal 1 0 2 3 4 5 5 4 1 stack<int>current push( neighbors(5) ) pop() 4 ??? 0 2 5
- 88. Depth First Traversal– iterative 2 1.void dft2(mivi graph, int src) { 2. stack<int> s({src}); 3. map<int, bool> visited; 4. int current; 5. 6. visited[src] = true; 7. while (!s.empty()) { 8. current = s.top(); s.pop(); 9. cout << "pop: " << current << endl; 10. for (auto neighbor : graph[current]) { 11. if (visited.find(neighbor) == visited.end()) { 12. visited[neighbor] = true; 13. s.push(neighbor); 14. } 15. } 16. } 17.}
- 89. Depth First Traversal– recursive 2 1.void dftr2(mivi graph, int src, map<int, bool>& visited) { 2. if (visited.find(src) == visited.end()) { 3. cout << "pop: " << src << endl; 4. visited[src] = true; 5. for (auto neighbor : graph[src]) { 6. dftr2(graph, neighbor, visited); 7. } 8. } 9.}
- 90. Breadth First Traversal– iterative 2 1.void bft2(mivi graph, int src) { 2. queue<int> q({ src }); 3. map<int, bool> visited; 4. int current; 5. 6. visited[src] = true; 7. while (!q.empty()) { 8. current = q.front(); q.pop(); 9. cout << "pop: " << current << endl; 10. for (auto neighbor : graph[current]) { 11. if (visited.find(neighbor) == visited.end()) { 12. visited[neighbor] = true; 13. q.push(neighbor); 14. } 15. } 16. } 17.}
- 91. hasPath มีเส ้นทางจาก1 ไป 4? 1 0 2 3 4 5 def hasPath(graph, src, dst): # depth first if src == dst: return True for neigbor in graph[src]: if hasPath(graph, neigbor, dst): return True return False
- 92. hasPath มีเส ้นทางจาก1 ไป 4? 1 0 2 3 4 5 def hasPath(graph, src, dst): # breadth first queue = [ src ] while len(queue) > 0: current = queue.pop() if current == dst: return True for neighbor in graph[current]: queue.push(neighbor) return False
- 93.
- 94. Representation 1 2 0 0 1 14 0 1 2 3 4 3 5 2 1.typedef vector<int> vi; 2.typedef vector<vi> vvi; 3.vvi m = { 4. {1, 2}, 5. {0, 2, 3}, 6. {0, 1, 4, 5}, 7. {1, 4, 5}, 8. {2, 3, 5}, 9. {3, 4}, 10.}; 3 4 5 5 2 3 5 4
- 95. Homework ► Search ► DepthFirst ► Iterative & Recursive ► Breadth First ► iterative ► hasPath ► Depth First ► Iterative & Recursive ► Breadth First ► iterative
- 96.
- 97. Explore() พิมพ์ชื่อจังหวัดแยกกลุ่มที่เชื่อมกันกลุ่มละ บรรทัด def explore(graph,current, visited): if current in visited: return False visited.add(current) for neighbor in graph[current]: explore(graph, neighbor, visited) return True
- 98. islandCount() นับจานวนกลุ่มจังหวัดที่เชื่อมกัน def islandCount(graph): visited,count = set(), 0 for node in graph: if explore(graph, node, visited): count += 1 return count
- 99. largestComponent() กลุ่มที่เชื่อมกันมากที่สุดกี่ จังหวัด def largestComponent(graph): largest= 0 visited = set() for node in graph: size = exploreSize(graph, node, visited) if size > largest: largest = size return largest def exploreSize(graph, node, visited): if node in visited: return 0 visited.add(node) size = 1 for neighbor of graph[node]: size += exploreSize(graph, neighbor, visited) return size
- 100. Exercise: W เป็นน้าL เป็นที่ดิน มีกี่เกาะ? W L W W L W L L W W L W W L W W W W W W W L L W W L W L L W W W W W W W W L W W L W L L W W L W W L W W W W W W W L L W W L W L L W W W W W W W
- 101. Explore() def explore(grid, r,c, visited): if !(0 <= r < len(grid)) || !(0 <= c < len(grid[r])): return 0 if grid[r][c] == ‘W’: return 0 if (r,c) in visited: return 0 visited.add( (r,c) ) explore(grid, r-1, c, visited) explore(grid, r+1, c, visited) explore(grid, r, c-1, visited) explore(grid, r, c+1, visited) return 1
- 102. islandCount() def islandCount(grid): visited, count= set(), 0 for r in range(0, len(grid)): for c in range(0, len(grid[r]): count += explore(grid, r, c, visited) return count
- 103. Exercise: W เป็นน้าL เป็นที่ดิน ที่ดินติดกัน มากที่สุดกี่ช่อง? W L W W L W L L W W L W W L W W W W W W W L L W W L W L L W W W W W W W W L W W L W L L W W L W W L W W W W W W W L L W W L W L L W W W W W W W
- 104.
- 105. Exercise: W เป็นน้าL เป็นที่ดิน ที่ดินติดกัน น้อยที่สุดกี่ช่อง? W L W W L W L L W W L W W L W W W W W W W L L W W L W L L W W W W W W W W L W W L W L L W W L W W L W W W W W W W L L W W L W L L W W W W W W W
- 106.
- 107. Shortest Path –เส ้นทางสั้นที่สุด (Prelim) def shortestPath(graph, src, dst): # bread first queue = [ [src, 0] ] visited = { src } while len(queue) > 0: node, distance = queue.pop() if node == dst: return distance for neighbor in graph[node]: if node not in visited: visited.add(node) queue.push( [neighbor, distance+1] ) return -1 # path not found
- 108. Others shortest pathalgorithms? ► Minimum Spanning Tree ► Kruskal’s Algorithm ► Prim’s Algorithm ► Shortest Path Algorithms ► Dijkstra’s Algorithm ► Bellman Ford’s Algorithm ► Floyd Warshall’s Algorithm
- 109. Prim’s Algorithm 1.typedef vector<int>vi; 2.typedef pair<int, int> ii; 3. 4.vi taken; 5.priority_queue<ii> pq; 6. 7.void process(int vtx) { 8. taken[vtx] = 1; 9. for (int j=0; j < (int)graph[vtx].size(); j++) { 10. ii v = graph[vtx][j]; 11. if (!taken[v.first]) 12. pq.push(ii(-v.second, -v.first)); 13. } 14.} 15.
- 110. Prim’s Algorithm 1.int main(){ 2. ios_base::sync_with_stdio(false); 3. cin.tie(NULL); 4. taken.assign(V, 0); 5. process(0); 6. long mst_cost = 0; 7. while (!pq.empty()) { 8. ii front = pq.top(); pq.pop(); 9. u = -front.second; 10. w = -front.first; 11. if (!taken[u]) { 12. mst_cost += w; 13. process(u); 14. } 15. } 16. cout << mst_cost << endl; 17. return 0; 18.}
- 111. Prim’s Algorithm 1.int main(){ 2. ios_base::sync_with_stdio(false); 3. cin.tie(NULL); 4. taken.assign(V, 0); 5. process(0); 6. long mst_cost = 0; 7. while (!pq.empty()) { 8. ii front = pq.top(); pq.pop(); 9. u = -front.second; 10. w = -front.first; 11. if (!taken[u]) { 12. mst_cost += w; 13. process(u); 14. } 15. } 16. cout << mst_cost << endl; 17. return 0; 18.}
- 112. Dijkstra 1.typedef vector<int> vi; 2.intmain() { 3. vi dist(V, INF); 4. dist[s] = 0; 5. priority_queue<ii, vector<ii>, greater<ii>> pq; 6. pq.push(ii(0, s)); 7. while (!pq.empty()) { 8. ii front = pq.top(); pq.pop(); 9. int d = front.first, u = front.second; 10. if (d > dist[u]) continue; 11. for (int j=0; j<(int)graph[u].size(); j++) { 12. ii v = graph[u][j]; 13. if (dist[u] + v.second < dist[v.first]) { 14. dist[v.first] = dist[u] + v.second; 15. pq.push(ii(dist[v.first], v.first)); 16. } 17. } 18. } 19.}