chapter of graph.

Author: aaron.liu

CMakeLists.txt

@@ -7,5 +7,8 @@ set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11 -pthread")
 ADD_SUBDIRECTORY(TwoPointers)
 ADD_SUBDIRECTORY(DFS)
 ADD_SUBDIRECTORY(BFS)
+ADD_SUBDIRECTORY(LinkedLists)
+ADD_SUBDIRECTORY(Trie)
+ADD_SUBDIRECTORY(Graph)
 
 add_executable(AlgoInCpp main.cpp)

DFS/LC1020NumberOfEnclaves.cpp

@@ -3,7 +3,6 @@
 //
 
 #include <vector>
-#include <unordered_map>
 using namespace std;
 
 class NumberOfEnclaves {

Graph/AW849DijkstraI.cpp

@@ -0,0 +1,31 @@
+//
+// Created by Aaron Liu on 4/13/20.
+//
+
+#include <cstring>
+#include <algorithm>
+#include <iostream>
+
+using namespace std;
+
+const int N = 505;
+int n,m;
+int g[N][N];
+int dist[N];
+bool st[N];
+
+int main() {
+    scanf("%d%d", &n, &m);
+
+    memset(g, 0x3f, sizeof g);
+
+    for ( ; m > 0; m--) {
+        int a, b,c;
+        scanf("%d%d%d", &a, &b, &c);
+        g[a][b] = min(g[a][b], c);
+    }
+
+}
+
+
+

Graph/AW850DijkstraII.cpp

@@ -0,0 +1,69 @@
+//
+// 850. Dijkstra求最短路 II
+// problem link: https://www.acwing.com/problem/content/852/
+//
+
+#include <cstring>
+#include <iostream>
+#include <algorithm>
+#include <queue>
+
+using namespace std;
+
+const int N = 1e6 + 5;
+
+typedef pair<int, int> PII; // 堆里存的是pair<int, int>
+int n, m;
+int h[N], w[N], e[N], ne[N], idx;
+int dist[N];
+bool st[N];
+
+
+void add (int a, int b, int c) {
+    e[idx] = b;
+    w[idx] = c;
+    ne[idx] = h[a];
+    h[a] = idx;
+    idx += 1;
+}
+
+int dijkstra() {
+    memset(dist, 0x3f, sizeof dist);
+    dist[1] = 0;
+    priority_queue<PII, vector<PII>, greater<PII>> heap;
+    heap.push({0,1});
+
+    for ( ; heap.size() > 0; ) {
+        auto t = heap.top();
+        heap.pop();
+
+        int ver = t.second, distance = t.first;
+        if (st[ver]) continue;
+        st[ver] = true;
+        for (int i = h[ver]; i != -1; i = ne[i]) {
+            int j = e[i];
+            if (dist[j] > distance + w[i]) {
+                dist[j] = distance + w[i];
+                heap.push({dist[j], j});
+            }
+        }
+    }
+
+    if (dist[n] == 0x3f3f3f3f) return -1;
+    return dist[n];
+}
+
+
+int main() {
+    scanf("%d%d", &n, &m);
+    memset(h, -1, sizeof h);
+
+    for ( ; m > 0; m--) {
+        int a, b, c;
+        scanf("%d%d%d", &a, &b, &c);
+        add(a, b, c);
+    }
+
+    cout << dijkstra() << endl;
+    return 0;
+}

Graph/AW851SPFA.cpp

@@ -0,0 +1,71 @@
+//
+// 851. spfa求最短路
+// problem link: https://www.acwing.com/problem/content/853/
+//
+#include <cstring>
+#include <algorithm>
+#include <queue>
+
+using namespace std;
+
+const int N = 100010;
+
+int n, m;
+int h[N], w[N], e[N], ne[N], idx;
+int dist[N];
+bool st[N];
+
+void add(int a, int b, int c) {
+    e[idx] = b;
+    w[idx] = c;
+    ne[idx] = h[a];
+    h[a] = idx;
+    idx += 1;
+}
+
+int spfa() {
+    memset(dist, 0x3f, sizeof dist);
+    dist[1] = 0;
+    queue<int> q;
+    q.push(1);
+    st[1] = true;
+
+    for ( ; q.size() != 0; ) {
+        int t = q.front();
+        q.pop();
+        st[t] = false;
+
+        for (int i = h[t]; i != -1; i = ne[i]) {
+            int j = e[i];
+            if (dist[j] > dist[t] + w[i]) {
+                dist[j] = dist[t] + w[i];
+                if (!st[j]) {
+                    q.push(j);
+                    st[j] = true;
+                }
+            }
+        }
+    }
+
+    if (dist[n] == 0x3f3f3f3f) return -1;
+    return dist[n];
+}
+
+int main()
+{
+    scanf("%d%d", &n, &m);
+
+    memset(h, -1, sizeof h);
+
+    for ( ; m > 0; m--) {
+        int a, b, c;
+        scanf("%d%d%d", &a, &b, &c);
+        add(a, b, c);
+    }
+
+    int t = spfa();
+    if (t == -1) puts("impossible");
+    else printf("%d\n", t);
+
+    return 0;
+}

Graph/AW852NegativeCycleSPFA.cpp

@@ -0,0 +1,67 @@
+//
+// AcWing 852. spfa判断负环
+// link: https://www.acwing.com/problem/content/854/
+
+#include <cstring>
+#include <algorithm>
+#include <queue>
+
+using namespace std;
+const int N = 100010;
+
+int n, m;
+int h[N], w[N], e[N], ne[N], idx;
+int dist[N], cnt[N];
+bool st[N];
+
+void add(int a, int b, int c) {
+    e[idx] = b;
+    w[idx] = c;
+    ne[idx] = h[a];
+    h[a] = idx;
+    idx += 1;
+}
+
+bool spfa() {
+    queue<int> q;
+    for (int i = 1; i <= n; i++) {
+        q.push(i);
+        st[i] = true;
+    }
+
+    for ( ; q.size() != 0; ) {
+        int t = q.front();
+        q.pop();
+        st[t] = false;
+
+        for (int i = h[t]; i != -1; i = ne[i]) {
+            int j = e[i];
+            if (dist[j] > dist[t] + w[i]) {
+                dist[j] = dist[t] + w[i];
+                cnt[j] = cnt[t] + 1;
+                if (cnt[j] >= n) return true;
+                if (!st[j]) {
+                    q.push(j);
+                    st[j] = true;
+                }
+            }
+        }
+    }
+    return false;
+}
+
+int main() {
+    scanf("%d%d", &n, &m);
+    memset(h, -1, sizeof h);
+
+    for (; m > 0; m--) {
+        int a, b, c;
+        scanf("%d%d%d", &a, &b, &c);
+        add(a, b, c);
+    }
+
+    if (spfa()) puts("Yes");
+    else puts("No");
+
+    return 0;
+}

Graph/AW853BFWithEdgeNumLimit.cpp

@@ -0,0 +1,49 @@
+//
+// 853. 有边数限制的最短路
+// problem link: https://www.acwing.com/problem/content/855/
+//
+
+#include <cstring>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+
+const int N = 510, M = 10010;
+int n, m, k;
+int backup[N], dist[N];
+struct Edge {
+    int a, b, w;
+} edges[M];
+
+int bellman_ford() {
+    memset(dist, 0x3f3f3f3f, sizeof dist);
+    dist[1] = 0;
+    for (int i = 0; i < k; i++) {
+    memcpy(backup, dist, sizeof dist);
+        for (int j = 0; j < m; j++) {
+
+            int a = edges[j].a, b = edges[j].b, w = edges[j].w;
+            dist[b] = min(dist[b], backup[a] + w);
+        }
+    }
+
+    if (dist[n] > 0x3f3f3f3f / 2) return -1;
+    return dist[n];
+}
+
+int main() {
+
+    scanf("%d%d%d", &n, &m, &k);
+
+    for (int i = 0; i < m; i++) {
+        int a, b, w;
+        scanf("%d%d%d", &a, &b, &w);
+        edges[i] = {a, b, w};
+    }
+
+    int t = bellman_ford();
+    if (t == -1) puts("impossible");
+    else printf("%d\n", t);
+    return 0;
+}

Graph/AW854Floyd.cpp

@@ -0,0 +1,53 @@
+//
+// 854. Floyd求最短路
+// link: https://www.acwing.com/problem/content/856/
+
+#include <cstring>
+#include <algorithm>
+
+using namespace std;
+
+const int N = 210, INF = 1e9;
+
+int n, m, q;
+int d[N][N];
+
+void floyd() {
+    for (int k = 1; k <= n; k++) {
+        for (int i = 1; i <= n; i++) {
+            for (int j = 1; j <= n; j++) {
+                d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
+            }
+        }
+    }
+}
+
+int main() {
+    scanf("%d%d%d", &n, &m, &q);
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <= n; j++) {
+            if (j == i) {
+                d[i][j] = 0;
+            } else {
+                d[i][j] = INF;
+            }
+        }
+    }
+
+    for (; m > 0; m--) {
+        int a, b, w;
+        scanf("%d%d%d", &a, &b, &w);
+        d[a][b] = min(d[a][b], w);
+    }
+    floyd();
+
+    for (; q > 0; q--) {
+        int a, b;
+        scanf("%d%d", &a, &b);
+        // 特殊情况: 负权边更新负最大
+        if (d[a][b] > INF / 2) puts("impossible");
+        else printf("%d\n", d[a][b]);
+    }
+
+    return 0;
+}