数据结构值行逻辑链接表实现矩阵运算(参考整理严蔚敏数据结构)

#include<iostream>#include<iomanip>using namespace std;#define MAXSIZE 100#define MAXRC 20typedef int ElemType;typedef struct Triple{int i;int j;ElemType e;}Triple;typedef struct RLSMatrix{Triple data[MAXSIZE];int rpos[MAXRC + 1];//各行第一个非零元所在的位置int rows;int cols;int nums;}RLSMatrix;void CreateRLSM(RLSMatrix &M){int t;Triple T;bool k;cout << "请输入矩阵的行数,列数,非零元素数：";cin >> M.rows >> M.cols >> M.nums;M.data[0].i = 0; //为计算rpos[]做准备for (t = 1; t <= M.nums; ++t){do{cout << "请按行序顺序输入第" << t << "个非零元素所在的行,列,元素值：";cin >> T.i >> T.j >> T.e;k = false;if (T.i<1 || T.i>M.rows || T.j<1 || T.j>M.cols)// 行、列超出范围k = true;if (T.i < M.data[t - 1].i || T.i == M.data[t - 1].i&&T.j <= M.data[t - 1].j)// 没有按顺序输入非零元素k = true;} while (k);M.data[t] = T;}for (t = 1; t <= M.nums; ++t)// 计算rpos[]{if (M.data[t].i > M.data[t - 1].i){for (T.i = 0; T.i <M.data[t].i - M.data[t - 1].i; T.i++)M.rpos[M.data[t].i - T.i] = t;}}for (t = M.data[M.nums].i + 1; t <= M.rows; ++t) // 给最后没有非零元素的几行赋值M.rpos[t] = M.nums + 1;}void DestroyRLSM(RLSMatrix &M){M.rows = 0;M.cols = 0;M.nums = 0;}void CopyRLSM(RLSMatrix M, RLSMatrix &N){N = M;}void TransRLSM(RLSMatrix M, RLSMatrix &N){int p, q, t, col, *num;num = new int[M.cols + 1];N.cols = M.rows;N.rows = M.cols;N.nums = M.nums;if (N.nums){for (col = 1; col <= M.cols; ++col)num[col] = 0;for (t = 1; t <= M.nums; ++t)++num[M.data[t].j];N.rpos[1] = 1;for (col = 2; col <= M.cols; ++col)N.rpos[col] = N.rpos[col - 1] + num[col - 1];for (col = 1; col <= M.cols; ++col)num[col] = N.rpos[col];for (p = 1; p <= M.nums; ++p){col = M.data[p].j;q = num[col];N.data[q].i = M.data[p].j;N.data[q].j = M.data[p].i;N.data[q].e = M.data[p].e;++num[col];}}delete[]num;}bool AddRLSM(RLSMatrix M, RLSMatrix N, RLSMatrix &Q){int k, p, q;if (M.rows != N.rows || M.cols != N.cols)return false;Q.rows = M.rows;Q.cols = M.cols;Q.nums = 0;M.rpos[M.rows + 1] = M.nums + 1;// 为方便后面的while循环临时设置N.rpos[N.rows + 1] = N.nums + 1;for (k = 1; k <= M.rows; ++k)// 对于每一行，k指示行号{Q.rpos[k] = Q.nums + 1;p = M.rpos[k];// p指示M矩阵第k行当前元素的序号q = N.rpos[k];// q指示N矩阵第k行当前元素的序号while (p < M.rpos[k + 1] && q < N.rpos[k + 1]){// M,N矩阵均有第k行元素未处理if (M.data[p].j == N.data[q].j){// M矩阵当前元素和N矩阵当前元素的列相同Q.data[Q.nums + 1].e = M.data[p].e + N.data[q].e;if (Q.data[Q.nums + 1].e){++Q.nums;Q.data[Q.nums].i = k;Q.data[Q.nums].j = M.data[p].j;}++p;++q;}else if (M.data[p].j < N.data[q].j){ // M矩阵当前元素的列<N矩阵当前元素的列++Q.nums;Q.data[Q.nums].e = M.data[p].e;Q.data[Q.nums].i = k;Q.data[Q.nums].j = M.data[p].j;++p;}else{// M矩阵当前元素的列>N矩阵当前元素的列++Q.nums;Q.data[Q.nums].e = N.data[q].e;Q.data[Q.nums].i = k;Q.data[Q.nums].j = N.data[q].j;++q;}}while (p < M.rpos[k + 1]){// M矩阵还有k行的元素未处理++Q.nums;Q.data[Q.nums].e = M.data[q].e;Q.data[Q.nums].i = k;Q.data[Q.nums].j = M.data[q].j;++p;}while (q < N.rpos[k + 1]){// N矩阵还有k行的元素未处理++Q.nums;Q.data[Q.nums].e = N.data[q].e;Q.data[Q.nums].i = k;Q.data[Q.nums].j = N.data[q].j;++q;}}return true;}bool SubtractRLSM(RLSMatrix M, RLSMatrix N, RLSMatrix &Q){int t;if (M.rows != N.rows || M.cols != N.cols)return false;for (t = 1; t <= N.nums; ++t)N.data[t].e *= -1;AddRLSM(M, N, Q);return true;}bool MultiplyRLSM(RLSMatrix M, RLSMatrix N, RLSMatrix &Q){int arow, brow, p, q, ccol, ctemp[MAXRC + 1];if (M.cols != N.rows)return false;Q.rows = M.rows;Q.cols = N.cols;Q.nums = 0;M.rpos[M.rows + 1] = M.nums + 1;N.rpos[N.rows + 1] = N.nums + 1;if (M.nums*N.nums)//M,N都是非零矩阵{for (arow = 1; arow <= M.rows; ++arow){//从M的第一行开始到最后一行,arow是M的当前行for (ccol = 1; ccol <= Q.cols; ++ccol)ctemp[ccol] = 0; // Q的当前行的各列元素累加器清零Q.rpos[arow] = Q.nums + 1; // Q当前行的第1个元素位于上1行最后1个元素之后for (p = M.rpos[arow]; p < M.rpos[arow + 1]; ++p){brow = M.data[p].j;// 找到对应元在N中的行号(M当前元的列号)for (q = N.rpos[brow]; q < N.rpos[brow + 1]; ++q){ccol = N.data[q].j; // 乘积元素在Q中列号ctemp[ccol] += M.data[p].e*N.data[q].e;}}// 求得Q中第arow行的非零元for (ccol = 1; ccol <= Q.cols; ++ccol){if (ctemp[ccol]){if (++Q.nums > MAXSIZE)return false;Q.data[Q.nums].i = arow;Q.data[Q.nums].j = ccol;Q.data[Q.nums].e = ctemp[ccol];}}}}return true;}void PrintRLSM(RLSMatrix M){//打印矩阵int t;cout << "矩阵为:" << endl;cout << "元素的行数  " << "元素的列数  " << "内容" << endl;for (t = 1; t <= M.nums; ++t){cout << setw(8) << M.data[t].i << setw(8) << M.data[t].j<< setw(11) << M.data[t].e << endl;}for (t = 1; t <= M.rows; ++t)cout << "第" << t << "行的第一个非零元素是本矩阵第" << M.rpos[t] << "个元素"<<endl;}int main(void){RLSMatrix M,N,Q;CreateRLSM(M);CreateRLSM(N);SubtractRLSM(M, N, Q);PrintRLSM(Q);return(0);}