順序表實現稀疏矩陣

*****************************稀疏矩陣.h*******************************

#include<stdio.h>
#include<stdlib.h>
#include<malloc.h>
typedef int ElemType;

// 稀疏矩陣的三元組順序表存儲表示 

#define MAXSIZE 100 // 非零元個數的最大值 
typedef struct
{
    int i, j;        // 行下標,列下標 
    ElemType e; // 非零元素值 
}Triple;

typedef struct
{
    Triple data[MAXSIZE + 1]; // 非零元三元組表,data[0]未用 
    int mu, nu, tu;                   // 矩陣的行數、列數和非零元個數 
}TSMatrix;

//接口定義
int CreateSMatrix(TSMatrix *M);
void DestroySMatrix(TSMatrix *M);
void PrintSMatrix(TSMatrix M);
int CopySMatrix(TSMatrix M, TSMatrix *T);
int comp(int c1, int c2);
int AddSMatrix(TSMatrix M, TSMatrix N, TSMatrix *Q);
int SubtSMatrix(TSMatrix M, TSMatrix N, TSMatrix *Q);
int MultSMatrix(TSMatrix M, TSMatrix N, TSMatrix *Q);
int TransposeSMatrix(TSMatrix M, TSMatrix *T);
int FastTransposeSMatrix(TSMatrix M, TSMatrix *T);

*********************************************源代碼.cpp************************************************

#include"稀疏矩陣.h"


// 創建稀疏矩陣M
int CreateSMatrix(TSMatrix *M)
{
    int i, m, n;
    ElemType e;
    int k;

    printf("請輸入矩陣的行數,列數,非零元素個數：（逗號）\n");
    scanf_s("%d,%d,%d", &(*M).mu, &(*M).nu, &(*M).tu);
    (*M).data[0].i = 0;       // 爲以下比較順序做準備 
    for (i = 1; i <= (*M).tu; i++)
    {
        do
        {
            printf("請按行序順序輸入第%d個非零元素所在的行(1～%d),"
                "列(1～%d),元素值：(逗號)\n", i, (*M).mu, (*M).nu);
            scanf_s("%d,%d,%d", &m, &n, &e);
            k = 0;//錯誤提示變量
            // 行或列超出範圍 
            if (m < 1 || m >(*M).mu || n < 1 || n >(*M).nu)
                k = 1;
            if (m < (*M).data[i - 1].i || m == (*M).data[i - 1].i
                && n <= (*M).data[i - 1].j) // 行或列的順序有錯 
                k = 1;
        } while (k);
        (*M).data[i].i = m;     //行下標
        (*M).data[i].j = n;     //列下標
        (*M).data[i].e = e;     //該下標所對應的值
    }
    return 1;
}

// 銷燬稀疏矩陣M，所有元素置空
void DestroySMatrix(TSMatrix *M)
{
    (*M).mu = 0;
    (*M).nu = 0;
    (*M).tu = 0;
}

// 輸出稀疏矩陣M
void PrintSMatrix(TSMatrix M)
{
    int i;
    printf("\n%d行%d列%d個非零元素。\n", M.mu, M.nu, M.tu);
    printf("%4s%4s%8s\n", "行", "列", "元素值");
    for (i = 1; i <= M.tu; i++)
        printf("%4d%4d%8d\n", M.data[i].i, M.data[i].j, M.data[i].e);
}

// 由稀疏矩陣M複製得到T
int CopySMatrix(TSMatrix M, TSMatrix *T)
{
    (*T) = M;
    return 1;
}

// AddSMatrix函數要用到
int comp(int c1, int c2)
{
    int i;
    if (c1<c2)
        i = 1;
    else if (c1 == c2)
        i = 0;
    else
        i = -1;
    return i;
}

// 求稀疏矩陣的和Q=M+N
int AddSMatrix(TSMatrix M, TSMatrix N, TSMatrix *Q)
{
    Triple *Mp, *Me, *Np, *Ne, *Qh, *Qe;
    if (M.mu != N.mu)
        return 0;
    if (M.nu != N.nu)
        return 0;
    (*Q).mu = M.mu;
    (*Q).nu = M.nu;
    Mp = &M.data[1];          // Mp的初值指向矩陣M的非零元素首地址 
    Np = &N.data[1];          // Np的初值指向矩陣N的非零元素首地址 
    Me = &M.data[M.tu];       // Me指向矩陣M的非零元素尾地址 
    Ne = &N.data[N.tu];       // Ne指向矩陣N的非零元素尾地址 
    Qh = Qe = (*Q).data;      // Qh、Qe的初值指向矩陣Q的非零元素首地址的前一地址 
    while (Mp <= Me && Np <= Ne)
    {
        Qe++;
        switch (comp(Mp->i, Np->i))
        {
        case  1:
            *Qe = *Mp;
            Mp++;
            break;
        case  0:
            // M、N矩陣當前非零元素的行相等,繼續比較列
            switch (comp(Mp->j, Np->j))
            {
            case  1:
                *Qe = *Mp;
                Mp++;
                break;
            case  0:
                *Qe = *Mp;
                Qe->e += Np->e;
                if (!Qe->e) // 元素值爲0，不存入壓縮矩陣 
                    Qe--;
                Mp++;
                Np++;
                break;
            case -1:
                *Qe = *Np;
                Np++;
            }
            break;
        case -1:
            *Qe = *Np;
            Np++;
        }
    }
    if (Mp>Me) // 矩陣M的元素全部處理完畢 
        while (Np <= Ne)
        {
            Qe++;
            *Qe = *Np;
            Np++;
        }
    if (Np>Ne) // 矩陣N的元素全部處理完畢 
        while (Mp <= Me)
        {
            Qe++;
            *Qe = *Mp;
            Mp++;
        }
    (*Q).tu = Qe - Qh; // 矩陣Q的非零元素個數 
    return 1;
}

// 求稀疏矩陣的差Q=M-N
int SubtSMatrix(TSMatrix M, TSMatrix N, TSMatrix *Q)
{
    int i;
    for (i = 1; i <= N.tu; i++)
        N.data[i].e *= -1;
    AddSMatrix(M, N, Q);
    return 1;
}

// 求稀疏矩陣的乘積Q=M*N
int MultSMatrix(TSMatrix M, TSMatrix N, TSMatrix *Q)
{
    int i, j, h = M.mu, l = N.nu, Qn = 0;
    // h,l分別爲矩陣Q的行、列值,Qn爲矩陣Q的非零元素個數，初值爲0 
    ElemType *Qe;
    if (M.nu != N.mu)
        return 0;
    (*Q).mu = M.mu;
    (*Q).nu = N.nu;
    Qe = (ElemType *)malloc(h*l * sizeof(ElemType)); // Qe爲矩陣Q的臨時數組 
                                                     // 矩陣Q的第i行j列的元素值存於*(Qe+(i-1)*l+j-1)中，初值爲0
    for (i = 0; i<h*l; i++)
        *(Qe + i) = 0; // 賦初值0 
    for (i = 1; i <= M.tu; i++) // 矩陣元素相乘，結果累加到Qe 
        for (j = 1; j <= N.tu; j++)
            if (M.data[i].j == N.data[j].i)
                *(Qe + (M.data[i].i - 1)*l + N.data[j].j - 1) +=
                M.data[i].e * N.data[j].e;
    for (i = 1; i <= M.mu; i++)
        for (j = 1; j <= N.nu; j++)
            if (*(Qe + (i - 1)*l + j - 1) != 0)
            {
                Qn++;
                (*Q).data[Qn].e = *(Qe + (i - 1)*l + j - 1);
                (*Q).data[Qn].i = i;
                (*Q).data[Qn].j = j;
            }
    free(Qe);
    (*Q).tu = Qn;
    return 1;
}

// 求稀疏矩陣M的轉置矩陣T。
int TransposeSMatrix(TSMatrix M, TSMatrix *T)
{
    int p, q, col;
    (*T).mu = M.nu;
    (*T).nu = M.mu;
    (*T).tu = M.tu;
    if ((*T).tu)
    {
        q = 1;
        for (col = 1; col <= M.nu; ++col)      //先將列轉換成行
            for (p = 1; p <= M.tu; ++p)    //再將行轉換成列
                if (M.data[p].j == col)
                {
                    (*T).data[q].i = M.data[p].j;
                    (*T).data[q].j = M.data[p].i;
                    (*T).data[q].e = M.data[p].e;
                    ++q;
                }
    }
    return 1;
}

// 快速求稀疏矩陣M的轉置矩陣T。
int FastTransposeSMatrix(TSMatrix M, TSMatrix *T)
{
    int p, q, t, col, *num, *cpot;
    num = (int *)malloc((M.nu + 1) * sizeof(int));        // 生成數組（[0]不用） 
    cpot = (int *)malloc((M.nu + 1) * sizeof(int));       // 生成數組（[0]不用） 
    (*T).mu = M.nu;
    (*T).nu = M.mu;
    (*T).tu = M.tu;
    if ((*T).tu)
    {
        for (col = 1; col <= M.nu; ++col)
            num[col] = 0; // 設初值 
        for (t = 1; t <= M.tu; ++t) // 求M中每一列含非零元素個數 
            ++num[M.data[t].j];
        cpot[1] = 1;
        // 求第col列中第一個非零元在(*T).data中的序號
        for (col = 2; col <= M.nu; ++col)
            cpot[col] = cpot[col - 1] + num[col - 1];
        for (p = 1; p <= M.tu; ++p)
        {
            col = M.data[p].j;
            q = cpot[col];
            (*T).data[q].i = M.data[p].j;
            (*T).data[q].j = M.data[p].i;
            (*T).data[q].e = M.data[p].e;
            ++cpot[col];
        }
    }
    free(num);
    free(cpot);
    return 1;
}

**************************************************Test.cpp****************************************************

#include"稀疏矩陣.h"

int main()
{
    TSMatrix A, B, C;

    printf("創建矩陣A: ");
    CreateSMatrix(&A);
    PrintSMatrix(A);

    printf("由矩陣A複製矩陣B: ");
    CopySMatrix(A, &B);
    PrintSMatrix(B);

    DestroySMatrix(&B);
    printf("銷燬矩陣B後:\n");
    PrintSMatrix(B);

    printf("重建矩陣B:(注意與矩陣A的行、列數相同，這樣方便後面的測試"
        "行、列分別爲%d,%d)\n", A.mu, A.nu);
    CreateSMatrix(&B);
    PrintSMatrix(B);

    printf("矩陣C1(A+B): ");
    AddSMatrix(A, B, &C);
    PrintSMatrix(C);
    DestroySMatrix(&C);

    printf("矩陣C2(A-B): ");
    SubtSMatrix(A, B, &C);
    PrintSMatrix(C);
    DestroySMatrix(&C);

    printf("矩陣C3(A的轉置): ");
    TransposeSMatrix(A, &C);
    PrintSMatrix(C);
    DestroySMatrix(&A);
    DestroySMatrix(&B);
    DestroySMatrix(&C);

    printf("創建矩陣A2: ");
    CreateSMatrix(&A);
    PrintSMatrix(A);

    printf("創建矩陣B3:(行數應與矩陣A2的列數相同=%d)\n", A.nu);
    CreateSMatrix(&B);
    PrintSMatrix(B);

    printf("矩陣C5(A*B): ");
    MultSMatrix(A, B, &C);
    PrintSMatrix(C);
    DestroySMatrix(&A);
    DestroySMatrix(&B);
    DestroySMatrix(&C);

    printf("創建矩陣A: ");
    CreateSMatrix(&A);
    PrintSMatrix(A);

    FastTransposeSMatrix(A, &B);
    printf("矩陣B(A的快速轉置): ");
    PrintSMatrix(B);

    DestroySMatrix(&A);
    DestroySMatrix(&B);

    system("pause");
    return 0;
}