引言
对于矩阵我们应该并不陌生吧,在大学线性代数里面每天对它相加,相乘,转置等等,那么在计算机中该怎么实现呢?
首先,先定义一个矩阵的结构体。
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| const int MAXN = 100;
struct Matrix{ int row,col; int matrix[MAXN][MAXN]; Matrix(){} Matrix(int r,int c):row(r),col(c){} };
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矩阵相加
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| Matrix Add(Matrix x,Matrix y){ Matrix answer = Matrix(x.row, x.col); for (int i = 0; i < x.row; ++i) { for (int j = 0; j < y.col; ++j) { answer.matrix[i][j] = x.matrix[i][j] + y.matrix[i][j]; } } return answer; }
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矩阵相乘
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| Matrix Multiply(Matrix x,Matrix y){ Matrix answer = Matrix(x.row, y.col); for (int i = 0; i < x.row; ++i) { for (int j = 0; j < y.col; ++j) { answer.matrix[i][j] = 0; for (int k = 0; k < x.col; ++k) { answer.matrix[i][j] += x.matrix[i][k] * y.matrix[k][j]; } } } return answer; }
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矩阵转置
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| Matrix Transpose(Matrix x){ Matrix answer = Matrix(x.col, x.row); for (int i = 0; i < x.row; ++i) { for (int j = 0; j < x.col; ++j) { answer.matrix[i][j] = answer.matrix[j][i]; } } return answer; }
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矩阵求幂
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| Matrix QuickPower(Matrix x,int n){ Matrix answer = Matrix(x.row, x.col); for (int i = 0; i < x.row; ++i) { for (int j = 0; j < x.col; ++j) { if (i == j) { answer.matrix[i][j] = 1; } else { answer.matrix[i][j] = 0; } } } while (n != 0) { if (n % 2 == 1) { answer = Multiply(answer, x); } n /= 2; x = Multiply(x, x); } return answer;
}
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