数据结构

稀疏矩阵(三元组,行逻辑连接)

本次代码将关于基本三元组和行逻辑链接表示的三元组进行了封装,还附加了两个系数矩阵的乘法和加法，欢迎大家参考测试代码。

#pragma once
#include <iostream>
#include <queue>
#include <vector>
#define MAXSIZE 100
using namespace std;

typedef struct node {
	int val;
	int row;
	int col;
	node(int v, int r, int c) :val(v), row(r), col(c) {}
	node() {}
}LinkNode;

class Triad 
{
public:
	Triad(int x, int y) :rn(x), cn(y) {}
	Triad() {}      //无参构造
	void input();   //输入矩阵
	void show();    //展示稀疏矩阵
	void GetRopt(); //获取行逻辑链接
	void GetCopt(); //获取列逻辑链接
	int  find(int r, int c); //查找矩阵中的某一个值
	Triad FastTranspose();   //转置返回一个三元组类
	Triad operator*(Triad &b);//乘法运算
	Triad operator+(Triad &b);//加法运算
private:
	LinkNode arr[MAXSIZE + 1];    //存储非零元素
	int rn; //行
	int cn; //列
	int tn; //非零元素个数
	int copt[MAXSIZE + 1];
	int ropt[MAXSIZE + 1];
};

void Triad::input()
{
	int x = 0,k = 1;
	for (int i = 1; i <= rn; i++)
	{
		for (int j = 1; j <= cn; j++)
		{
			cin >> x;
			if (x != 0)
			{
				LinkNode n(x, i, j);
				arr[k++] = n;
			}
		}
	}
	tn = k - 1;
}


void Triad::show()
{
	for (int i = 1; i <= this->tn; i++)
	{
		printf("arr[%d][%d] = %d
", this->arr[i].row, this->arr[i].col, this->arr[i].val);
	}
}

int Triad::find(int i, int j)
{
	for (int i = 1; i <= tn; i++)
	{
		if (arr[i].row == i && arr[i].col == j)
			return arr[i].val;
	}
	return 0;
}
//获取行逻辑链接
void Triad::GetRopt()
{
	if (this->tn) {
		int nums[MAXSIZE];
		fill(nums, nums + MAXSIZE, 0);
		fill(ropt, ropt + MAXSIZE + 1, 0);
		for (int i = 1; i <= this->tn; i++)
			++nums[this->arr[i].row];
		this->ropt[1] = 1;
		for (int i = 2; i <= this->tn; i++)
			this->ropt[i] = this->ropt[i - 1] + nums[i - 1];
	}
}
void Triad::GetCopt()
{
	if (this->tn) {
		int nums[MAXSIZE];
		fill(nums, nums + MAXSIZE, 0);
		fill(copt, copt + MAXSIZE + 1, 0);
		for (int i = 1; i <= this->tn; i++)
			++nums[this->arr[i].col];
		this->copt[1] = 1;
		for (int i = 2; i <= this->tn; i++)
			this->copt[i] = this->copt[i - 1] + nums[i - 1];
	}
}
//进行转置
Triad Triad::FastTranspose()
{
	Triad newmaxtri;
	this->GetCopt(); //获取列链接
	for (int i = 1; i <= tn; i++)
	{
		int col = arr[i].col;
		int   q = copt[col];
		newmaxtri.arr[q].row = arr[i].col;
		newmaxtri.arr[q].col = arr[i].row;
		newmaxtri.arr[q].val = arr[i].val;
		++copt[col];
	}
	newmaxtri.tn = this->tn;
	newmaxtri.cn = this->rn;
	newmaxtri.rn = this->cn;
	return newmaxtri;
}

Triad Triad::operator*(Triad &b)
{
	Triad ans;
	if (this->cn != b.rn)
	{
		cout << "矩阵 a 的列数不等于矩阵 b 的行数，不能计算矩阵乘法 ab" << endl;
		exit(1);
	}

	//矩阵ans初始化
	this->GetRopt();
	b.GetRopt();
	ans.rn = this->rn; //初始化行
	ans.cn = b.cn;     //初始化列
	ans.tn = 0;

	int ctemp[MAXSIZE + 1];
	//逐行求积
	if (this->tn * b.tn != 0)
	{
		for (int arow = 1; arow <= this->rn; ++arow)
		{
			//累加器清零
			fill(ctemp, ctemp + MAXSIZE + 1, 0);

			//计算c中第arow行的积并存入ctemp[]中
			ans.ropt[arow]= ans.tn + 1;
			int tp;//this中的某一行的最后一个非零元素在copt中的位置
			if (arow < this->rn) tp = this->ropt[arow + 1];
			else tp = this->tn + 1;

			//拿出this中当前行的每个非零元素
			for (int i = this->ropt[arow]; i < tp; ++i)
			{
				int brow = this->arr[i].col;
				int t;
				if (brow < b.rn)t = b.ropt[brow + 1];
				else t = b.tn + 1;
				for (int q = b.ropt[brow]; q < t; ++q)
				{
					int ccol = b.arr[q].col;
					ctemp[ccol] += this->arr[i].val * b.arr[q].val;
				}
			}
			for (int ccol = 1; ccol <= ans.cn; ++ccol)
			{
				if (ctemp[ccol])
				{
					if (++ans.tn > MAXSIZE)
					{
						cout << "错误:元素个数大于最大设定值" << endl;
						exit(-1);
					}
					LinkNode tmp;
					tmp.row = arow;
					tmp.col = ccol;
					tmp.val = ctemp[ccol];
					ans.arr[ans.tn] = tmp;
				 }
			}
		}
    }
	return ans;
}

Triad Triad::operator+(Triad &b)
{
	Triad ans;
	int ia, ib,ic,ar,br,cr,ac,bc,cc;
	ia = ib = ic =1;
	while (ia <= this->tn && ib <= b.tn)
	{
		ar = this->arr[ia].row;
		br = this->arr[ib].row;
		if (ar > br)
		{
			cr = br;
			while (cr == b.arr[ib].row)
			{
				ans.arr[ic].row = cr;
				ans.arr[ic].col = b.arr[ib].col;
				ans.arr[ic].val = b.arr[ib].val;
				++ib; ++ic;
			}
		}
		else if (ar < br)
		{
			cr = ar;
			while (cr == this->arr[ia].row)
			{
				ans.arr[ic].row = cr;
				ans.arr[ic].col = this->arr[ia].col;
				ans.arr[ic].val = this->arr[ia].val;
				++ic; ++ia;
			}
		}
		else if (ar == br)
		{
			cr = ar;
			ac = this->arr[ia].col;
			bc = b.arr[ib].col;
			if (ac > bc)
			{
				ans.arr[ic].row = cr;
				ans.arr[ic].col = bc;
				ans.arr[ic].val = b.arr[ib].val;
				++ic; ++ib;
			}
			else if (ac < bc)
			{
				ans.arr[ic].row = cr;
				ans.arr[ic].col = ac;
				ans.arr[ic].val = this->arr[ia].val;
				++ic; ++ia;
			}
			else if (ac == bc)
			{
				if (this->arr[ia].val + b.arr[ib].val != 0)
				{
					ans.arr[ic].row = cr;
					ans.arr[ic].col = ac;
					ans.arr[ic].val = this->arr[ia].val + b.arr[ib].val;
					++ic;
				}
				++ia;
				++ib;
			}
		}
	}
	while (ia <= this->tn)
	{
		ans.arr[ic].row = this->arr[ia].row;
		ans.arr[ic].col = this->arr[ia].col;
		ans.arr[ic].val = this->arr[ia].val;
		++ic; ++ia;
	}
	while (ib <= b.tn)
	{
		ans.arr[ic].row = b.arr[ib].row;
		ans.arr[ic].col = b.arr[ib].col;
		ans.arr[ic].val = b.arr[ib].val;
		++ic; ++ib;
	}
	ans.tn = --ic;
	return ans;
}

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