利用c++代码来实现对一个稀疏矩阵，进行如下操作： 1、计算三元组顺序表，并生成POS和NUM向量； 2、根据稀疏矩阵的三元组顺序表，计算转置后的三元组顺序表

可以使用以下代码实现对稀疏矩阵的操作：

1、计算三元组顺序表，并生成POS和NUM向量：

#include <stdio.h>
#include <stdlib.h>

#define MAX_SIZE 100

typedef struct {
    int i, j, val;
} Triple;

typedef struct {
    Triple data[MAX_SIZE];
    int rows, cols, nums;
} SparseMatrix;

void createSparseMatrix(SparseMatrix *matrix) {
    printf("请输入稀疏矩阵的行数、列数和非零元素个数：\n");
    scanf("%d%d%d", &matrix->rows, &matrix->cols, &matrix->nums);
    printf("请输入稀疏矩阵的三元组：\n");
    for (int i = 0; i < matrix->nums; i++) {
        scanf("%d%d%d", &matrix->data[i].i, &matrix->data[i].j, &matrix->data[i].val);
    }
}

void printSparseMatrix(SparseMatrix matrix) {
    printf("稀疏矩阵的三元组为：\n");
    for (int i = 0; i < matrix.nums; i++) {
        printf("(%d, %d, %d)\n", matrix.data[i].i, matrix.data[i].j, matrix.data[i].val);
    }
}

void generatePOSandNUM(SparseMatrix matrix, int *POS, int *NUM) {
    for (int i = 0; i < matrix.cols; i++) {
        POS[i] = 0;
    }
    for (int i = 0; i < matrix.nums; i++) {
        POS[matrix.data[i].j]++;
    }
    int sum = 0;
    for (int i = 0; i < matrix.cols; i++) {
        int temp = POS[i];
        POS[i] = sum;
        sum += temp;
    }
    for (int i = 0; i < matrix.nums; i++) {
        int col = matrix.data[i].j;
        int index = POS[col] + NUM[col];
        NUM[col]++;
        matrix.data[index].i = matrix.data[i].j;
        matrix.data[index].j = matrix.data[i].i;
        matrix.data[index].val = matrix.data[i].val;
    }
}

int main() {
    SparseMatrix matrix;
    createSparseMatrix(&matrix);
    printSparseMatrix(matrix);
    int POS[MAX_SIZE], NUM[MAX_SIZE];
    generatePOSandNUM(matrix, POS, NUM);
    printf("转置后的稀疏矩阵的三元组为：\n");
    for (int i = 0; i < matrix.nums; i++) {
        printf("(%d, %d, %d)\n", matrix.data[i].i, matrix.data[i].j, matrix.data[i].val);
    }
    return 0;
}

2、根据稀疏矩阵的三元组顺序表，计算转置后的三元组顺序表：

void generateTranspose(SparseMatrix matrix, SparseMatrix *transpose) {
    transpose->rows = matrix.cols;
    transpose->cols = matrix.rows;
    transpose->nums = matrix.nums;
    for (int i = 0; i < matrix.nums; i++) {
        transpose->data[i].i = matrix.data[i].j;
        transpose->data[i].j = matrix.data[i].i;
        transpose->data[i].val = matrix.data[i].val;
    }
}

int main() {
    SparseMatrix matrix;
    createSparseMatrix(&matrix);
    printSparseMatrix(matrix);
    int POS[MAX_SIZE], NUM[MAX_SIZE];
    generatePOSandNUM(matrix, POS, NUM);
    SparseMatrix transpose;
    generateTranspose(matrix, &transpose);
    printf("转置后的稀疏矩阵的三元组为：\n");
    for (int i = 0; i < transpose.nums; i++) {
        printf("(%d, %d, %d)\n", transpose.data[i].i, transpose.data[i].j, transpose.data[i].val);
    }
    return 0;
}