1.5 union-find

CMakeLists.txt

@@ -69,4 +69,8 @@ add_executable(algs4
         PrimMST.cpp
         PrimMST.h
         tests/testGraph.cpp
+        UF.cpp
+        UF.h
+        tests/testUF.h
+        tests/testUF.cpp
 )

README.md

@@ -6,6 +6,10 @@ incorporating modern C++ practices.
 
 ## List of Algorithms
 
+### Fundamentals
+
+- **1.5** Union-find: [UF.h](UF.h) | [UF.cpp](UF.cpp)
+
 ### Sorting
 
 - **2.1** Selection sort: [Selection.h](Selection.h)

UF.cpp

@@ -0,0 +1,27 @@
+#include "UF.h"
+
+UF::UF(int N) : id(N), sz(N), count_(N) {
+    for (int i = 0; i < N; i++) {
+        id[i] = i;
+        sz[i] = 1;
+    }
+}
+
+int UF::find(int p) const {
+    while (p != id[p]) p = id[p];
+    return p;
+}
+
+void UF::unionize(int p, int q) {
+    int i = find(p);
+    int j = find(q);
+    if (i == j) return;
+    if (sz[i] < sz[j]) {
+        id[i] = j;
+        sz[j] += sz[i];
+    } else {
+        id[j] = i;
+        sz[i] += sz[j];
+    }
+    --count_;
+}

UF.h

@@ -0,0 +1,25 @@
+#ifndef UF_H
+#define UF_H
+#include <vector>
+
+
+class UF {
+private:
+    std::vector<int> id; // 父链接数组（以触点为索引）
+    std::vector<int> sz; // 各个根节点对应的分量的大小（以触点为索引）
+    int count_;          // 分量数量
+
+public:
+    UF(int N);
+
+    int count() const { return count_; }
+
+    bool connected(int p, int q) const { return find(p) == find(q); }
+
+    int find(int p) const;
+
+    void unionize(int p, int q);
+};
+
+
+#endif //UF_H

data/tinyUF.txt

@@ -0,0 +1,12 @@
+10
+4 3
+3 8
+6 5
+9 4
+2 1
+8 9
+5 0
+7 2
+6 1
+1 0
+6 7

main.cpp

@@ -28,14 +28,21 @@
 #include "Topological.h"
 #include "KosarajuSCC.h"
 #include "PrimMST.h"
+#include "tests/testUF.h"
 #include "tests/testSort.h"
 #include "tests/testPQ.h"
 #include "tests/testST.h"
 #include "tests/testGraph.h"
 
 int main(int argc, char* argv[]) {
-    std::filesystem::path dataFilePath(argv[1]);
-    if (dataFilePath.filename() == "words3.txt") {
+    if (argc < 2) {
+        // 测试union-find
+        // ./algs4 < ../data/tinyUF.txt
+        std::cout << "Testing 1.5 union-find" << "\n";
+        std::cout << "================================================" << "\n";
+        testUF();
+        std::cout << "================================================" << "\n";
+    } else if (std::filesystem::path dataFilePath(argv[1]); dataFilePath.filename() == "words3.txt") {
         // 测试排序算法
         // ./algs4 ../data/words3.txt
         std::cout << "Testing 2.1 selection sort" << "\n";

tests/testUF.cpp

@@ -0,0 +1,16 @@
+#include "testUF.h"
+#include "UF.h"
+#include <iostream>
+
+void testUF() {
+    UF uf([]() {
+        int N;
+        return std::cin >> N, N;
+    }());
+    for (int p, q; std::cin >> p >> q;) {
+        if (uf.connected(p, q)) continue;
+        uf.unionize(p, q);
+        std::cout << p << " " << q << "\n";
+    }
+    std::cout << uf.count() << " components" << "\n";
+}

tests/testUF.h

@@ -0,0 +1,6 @@
+#ifndef TESTUF_H
+#define TESTUF_H
+
+void testUF();
+
+#endif //TESTUF_H