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Vladimir-Chan · Sep 18, 2020 · d224052 · d224052
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diff --git a/算法设计与分析/作业/Assignment_1.docx b/算法设计与分析/作业/Assignment_1.docx
diff --git a/算法设计与分析/作业/Assignment_1.pdf b/算法设计与分析/作业/Assignment_1.pdf
diff --git a/算法设计与分析/作业/Assignment_1.txt b/算法设计与分析/作业/Assignment_1.txt
@@ -0,0 +1,80 @@
+/*
+#include <iostream> 
+using namespace std;
+//3d5 凸多边形最优三角剖分
+const int N = 9;//凸多边形边数+1
+int weight[][N] = { { 0,14,25,27,10,11,24,16 },
+					{ 14,0,18,15,27,28,16,14 },
+					{ 25,18,0,19,14,19,16,10 },
+					{ 27,15,19,0,22,23,15,14 },
+					{ 10,27,14,22,0,14,13,20 },
+					{ 11,28,19,23,14,0,15,18 },
+					{ 24,16,16,15,13,15,0,27 },
+					{ 16,14,10,14,20,18,27,0 }, };//凸多边形的权
+
+int MinWeightTriangulation(int n, int **t, int **s);
+void Traceback(int i, int j, int **s);//构造最优解
+int Weight(int a, int b, int c);//权函数
+
+int main()
+{
+	int **s = new int *[N];
+	int **t = new int *[N];
+	for (int i = 0; i<N; i++)
+	{
+		s[i] = new int[N];
+		t[i] = new int[N];
+	}
+
+	cout << "g：" << MinWeightTriangulation(N - 1, t, s) << endl;
+	cout << "最优三角剖分结构为：" << endl;
+	Traceback(1, 8, s); //s[i][j]记录了Vi-1和Vj构成三角形的第3个顶点的位置
+	system("pause");
+	return 0;
+}
+
+int MinWeightTriangulation(int n, int **t, int **s)
+{
+	for (int i = 1; i <= n; i++)
+	{
+		t[i][i] = 0;
+	}
+	for (int r = 2; r <= n; r++) //r为当前计算的链长（子问题规模）  
+	{
+		for (int i = 1; i <= n - r + 1; i++)//n-r+1为最后一个r链的前边界  
+		{
+			int j = i + r - 1;//计算前边界为r，链长为r的链的后边界  
+
+			t[i][j] = t[i + 1][j] + Weight(i - 1, i, j);//将链ij划分为A(i) * ( A[i+1:j] )这里实际上就是k=i
+
+			s[i][j] = i;
+
+			for (int k = i + 1; k<j; k++)
+			{
+				//将链ij划分为( A[i:k] )* (A[k+1:j])   
+				int u = t[i][k] + t[k + 1][j] + Weight(i - 1, k, j);
+				if (u<t[i][j])
+				{
+					t[i][j] = u;
+					s[i][j] = k;
+				}
+			}
+		}
+	}
+	return t[1][N - 2];
+}
+
+void Traceback(int i, int j, int **s)
+{
+	if (i == j) return;
+	Traceback(i, s[i][j], s);
+	Traceback(s[i][j] + 1, j, s);
+	cout << "三角剖分顶点：V" << i - 1 << ",V" << j << ",V" << s[i][j] << endl;
+}
+
+int Weight(int a, int b, int c)
+{
+	return weight[a][b] + weight[b][c] + weight[a][c];
+}
+
+*/
diff --git a/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1.sdf b/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1.sdf
diff --git a/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1.sln b/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1.sln
@@ -0,0 +1,28 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio 14
+VisualStudioVersion = 14.0.24720.0
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "ConsoleApplication1", "ConsoleApplication1\ConsoleApplication1.vcxproj", "{EC05B173-879A-4BAE-A260-C1269A382392}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|x64 = Debug|x64
+		Debug|x86 = Debug|x86
+		Release|x64 = Release|x64
+		Release|x86 = Release|x86
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Debug|x64.ActiveCfg = Debug|x64
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Debug|x64.Build.0 = Debug|x64
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Debug|x86.ActiveCfg = Debug|Win32
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Debug|x86.Build.0 = Debug|Win32
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Release|x64.ActiveCfg = Release|x64
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Release|x64.Build.0 = Release|x64
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Release|x86.ActiveCfg = Release|Win32
+		{EC05B173-879A-4BAE-A260-C1269A382392}.Release|x86.Build.0 = Release|Win32
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+EndGlobal
diff --git a/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1/ConsoleApplication1.cpp b/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1/ConsoleApplication1.cpp
@@ -0,0 +1,112 @@
+#include "stdafx.h"
+#include<iostream>
+#include<vector>
+using namespace std;
+
+const int N = 8; //八边形
+
+//权值函数
+vector<vector<int>> weight = {
+	{ 0,14,25,27,10,11,24,16 },
+	{ 14,0,18,15,27,28,16,14 },
+	{ 25,18,0,19,14,19,16,10 },
+	{ 27,15,19,0,22,23,15,14 },
+	{ 10,27,14,22,0,14,13,20 },
+	{ 11,28,19,23,14,0,15,18 },
+	{ 24,16,16,15,13,15,0,27 },
+	{ 16,14,10,14,20,18,27,0 }};
+
+//初始化存储数组
+vector<int> tempweight(N, 0);
+vector<int> temppoint(N, -1);
+// bestweight[i][j] 记录凸子多边形 {Vi, ..., Vj} 三角剖分的最优权值。
+vector<vector<int>> bestweight(N, tempweight);
+// bestpoint[i][j] 记录与 Vi、Vj 构成三角形第三个顶点 Vk 。
+vector<vector<int>> bestpoint(N, temppoint);
+
+
+//计算Vi,Vk,Vj组成的三角形的权重之和
+int GetWeight(int i, int k, int j);
+
+//自底向上动态规划计算n变形最优三角形的权值之和
+int MinWeightTriangulation(int n);
+
+//打印凸子多边形 {Vi, ..., Vj} 的最优三角剖分结果
+void Traceback(int i, int j);
+
+int main() {
+	cout << "凸多边形权重矩阵为："  << endl;
+	for (int i = 0; i < N; i++) {
+		for (int j = 0; j < N; j++) {
+			cout << weight[i][j] << " ";
+		}
+		cout << endl;
+	}
+	cout << endl;
+	cout <<"动态规划算法计算结果：" << MinWeightTriangulation(N) << endl;
+	cout << endl;
+	cout << "最优三角剖分结构为：" << endl;
+	Traceback(0, N - 1);
+	cout << endl;
+
+	cout << "bestPoint[i][j] 记录与 Vi、Vj 构成三角形第三个顶点 Vk 为："  << endl;
+	for (int i = 0; i < N; i++) {
+		for (int j = 0; j < N; j++) {
+			cout << bestpoint[i][j] << "\t";
+		}
+		cout << endl;
+	}
+
+	system("pause");
+	return 0;
+}
+
+
+int GetWeight(int i, int k, int j)
+{
+	return weight[i][k] + weight[k][j] + weight[i][j];
+}
+
+int MinWeightTriangulation(int n)
+{
+	//对动态规划数组初始化,这里初始化其实可以不做，前面已经初始化过了
+	bestweight[n - 1][n - 1] = 0;//下面初始化会漏掉[n-1][n-1]点
+	for (int i = 0; i < n - 1; i++) {
+		bestweight[i][i] = bestweight[i][i + 1] = 0;
+	}
+
+	//scale代表子问题的规模大小，例如子问题{V0,V1,V2}的规模为2,子问题{V0,V1...V5}的规模为5
+	for (int scale = 2; scale < n; scale++) {
+		//求解子问题的最后一个为n-scale-1，例如scale=2，最后一个子问题为i=6,j+8,{V6,V7,V8}
+		for (int i = 0; i < n - scale; i++) {
+			// j 代表当前以 Vi 为起点的子问题的后边界 Vj
+			int j = i + scale;
+
+			//先处理 k = i+1的情况，这是为了有一开始的初值方便对比，这里也可以选择初始化最大值9999
+			bestweight[i][j] = bestweight[i][i + 1] + bestweight[i + 1][j] + GetWeight(i, i + 1, j);
+			bestpoint[i][j] = i + 1;
+
+			//有了基准值之后，可以开始循环处理k=i+2的情况
+			for (int k = i + 2; k < j; k++) {
+				int temp = bestweight[i][k] + bestweight[k][j] + GetWeight(i, k, j);
+				if (temp < bestweight[i][j]) {
+					bestweight[i][j] = temp;
+					bestpoint[i][j] = k;
+				}
+			}
+		}
+	}
+
+	//返回右上角的最佳数值。
+	return bestweight[0][n - 1];
+}
+
+void Traceback(int i, int j)
+{
+	//注意回溯查找的返回条件,i+1=j表示中间没有任何点存在，bestpoint[i][j]内部的值为出始化-1
+	if (i+1 == j)
+		return;
+	Traceback(i,bestpoint[i][j]);
+	cout << "V" << i << " -- V" << bestpoint[i][j] << " -- V" << j << " = " << GetWeight(i,bestpoint[i][j],j) << endl;
+	Traceback(bestpoint[i][j],j);
+}
diff --git a/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1/ConsoleApplication1.vcxproj b/算法设计与分析/作业/Assignment_1/ConsoleApplication1/ConsoleApplication1/ConsoleApplication1.vcxproj
@@ -0,0 +1,163 @@
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