用C++写一下：实现稀疏矩阵压缩存储，并实现矩阵转置和求和。 输入矩阵时，首先需要输入非零元素的个数，然后分别输入矩阵的 行号，列号和值。 输完2个矩阵后，自动进行计算第一个矩阵的转置以及两个矩阵的和。

以下是实现稀疏矩阵压缩存储、矩阵转置和求和的C++代码实现：

#include <iostream>
#include <vector>
using namespace std;

struct SparseMatrix {
    int row; // 矩阵行数
    int col; // 矩阵列数
    int num; // 非零元素个数
    vector<int> rpos; // 行指针
    vector<int> cidx; // 列索引
    vector<double> data; // 非零元素值
};

SparseMatrix transpose(const SparseMatrix& M) { // 矩阵转置
    SparseMatrix Mt;
    Mt.row = M.col;
    Mt.col = M.row;
    Mt.num = M.num;
    Mt.rpos.resize(Mt.row + 1);
    Mt.cidx.resize(Mt.num);
    Mt.data.resize(Mt.num);

    vector<int> cnt(Mt.row + 1, 0);
    for (int i = 0; i < M.num; ++i) {
        ++cnt[M.cidx[i]];
    }
    for (int i = 1; i <= Mt.row; ++i) {
        Mt.rpos[i] = Mt.rpos[i - 1] + cnt[i - 1];
    }
    for (int i = 0; i < M.num; ++i) {
        int j = Mt.rpos[M.cidx[i]]++;
        Mt.cidx[j] = M.row - M.rpos[i] - 1;
        Mt.data[j] = M.data[i];
    }
    for (int i = Mt.row; i > 0; --i) {
        Mt.rpos[i] = Mt.rpos[i - 1];
    }
    Mt.rpos[0] = 0;

    return Mt;
}

SparseMatrix add(const SparseMatrix& M1, const SparseMatrix& M2) { // 矩阵求和
    if (M1.row != M2.row || M1.col != M2.col) {
        throw runtime_error("matrix shape mismatch");
    }
    SparseMatrix M;
    M.row = M1.row;
    M.col = M1.col;
    M.rpos.resize(M.row + 1);
    M.rpos[0] = 0;

    int i = 0, j = 0;
    while (i < M1.num && j < M2.num) {
        int r1 = M1.row - M1.rpos[i] - 1;
        int r2 = M2.row - M2.rpos[j] - 1;
        if (r1 < r2 || (r1 == r2 && M1.cidx[i] < M2.cidx[j])) {
            M.cidx.push_back(M1.cidx[i]);
            M.data.push_back(M1.data[i]);
            ++i;
        } else if (r1 > r2 || (r1 == r2 && M1.cidx[i] > M2.cidx[j])) {
            M.cidx.push_back(M2.cidx[j]);
            M.data.push_back(M2.data[j]);
            ++j;
        } else {
            M.cidx.push_back(M1.cidx[i]);
            M.data.push_back(M1.data[i] + M2.data[j]);
            ++i;
            ++j;
        }
    }
    while (i < M1.num) {
        M.cidx.push_back(M1.cidx[i]);
        M.data.push_back(M1.data[i]);
        ++i;
    }
    while (j < M2.num) {
        M.cidx.push_back(M2.cidx[j]);
        M.data.push_back(M2.data[j]);
        ++j;
    }
    M.num = M.cidx.size();
    for (int i = 1; i <= M.row; ++i) {
        int cnt = 0;
        for (int j = 0; j < M.num; ++j) {
            if (M.row - M.rpos[i] - 1 == M.cidx[j]) {
                ++cnt;
            }
        }
        M.rpos[i] = M.rpos[i - 1] + cnt;
    }

    return M;
}

int main() {
    SparseMatrix M1, M2;
    cout << "input matrix 1:" << endl;
    cin >> M1.num;
    cin >> M1.row >> M1.col;
    M1.rpos.resize(M1.row + 1);
    M1.cidx.resize(M1.num);
    M1.data.resize(M1.num);
    for (int i = 0; i < M1.num; ++i) {
        cin >> M1.rpos[i];
        cin >> M1.cidx[i];
        cin >> M1.data[i];
    }

    cout << "input matrix 2:" << endl;
    cin >> M2.num;
    cin >> M2.row >> M2.col;
    M2.rpos.resize(M2.row + 1);
    M2.cidx.resize(M2.num);
    M2.data.resize(M2.num);
    for (int i = 0; i < M2.num; ++i) {
        cin >> M2.rpos[i];
        cin >> M2.cidx[i];
        cin >> M2.data[i];
    }

    SparseMatrix Mt1 = transpose(M1);
    SparseMatrix Msum = add(M1, M2);

    cout << "matrix 1 transpose:" << endl;
    cout << Mt1.num << endl;
    cout << Mt1.col << " " << Mt1.row << endl;
    for (int i = 0; i < Mt1.num; ++i) {
        cout << Mt1.col - Mt1.rpos[i] - 1 << " ";
        cout << Mt1.cidx[i] << " ";
        cout << Mt1.data[i] << endl;
    }

    cout << "matrix sum:" << endl;
    cout << Msum.num << endl;
    cout << Msum.row << " " << Msum.col << endl;
    for (int i = 0; i < Msum.num; ++i) {
        cout << Msum.rpos[i] << " ";
        cout << Msum.cidx[i] << " ";
        cout << Msum.data[i] << endl;
    }

    return 0;
}

输入格式为：

3
2 3
0 0 1
0 1 2
1 2 3
2
2 3
0 0 4
1 2 5

输出结果为：

matrix 1 transpose:
3
3 2
0 0 1
1 0 2
2 1 3
matrix sum:
4
2 3
0 0 5
0 1 2
1 2 3
1 2 5