Twodimensional arrays (matrices)
Twodimensional arrays (matrices): creation
Matrix1. Given two positive integers M and N, create and output an M × N matrix of integers such that all its elements of the Ith row are equal to 10·I (I = 1, …, M).
Matrix2. Given two positive integers M and N, create and output an M × N matrix of integers such that all its elements of the Jth column are equal to 5·J (J = 1, …, N).
Matrix3. Two positive integers M, N and a sequence of M real numbers are given. Create and output an M × N matrix of real numbers such that each of its columns contains all numbers from the given sequence (in the same order).
Matrix4. Two positive integers M, N and a sequence of M real numbers are given. Create and output an M × N matrix of real numbers such that each of its rows contains all numbers from the given sequence (in the same order).
Matrix5. Two positive integers M and N, a real number D, and a sequence of M real numbers are given. Create and output an M × N matrix of real numbers such that its first column contains all numbers from the given sequence (in the same order), and elements of each next column are equal to the sum of the corresponding element of the previous column and the number D (so each row of the matrix will be an arithmetic sequence with the common difference D).
Matrix6. Two positive integers M and N, a real number D, and a sequence of M real numbers are given. Create and output an M × N matrix of real numbers such that its first row contains all numbers from the given sequence (in the same order), and elements of each next row are equal to the sum of the corresponding element of the previous row and the number R (so each column of the matrix will be a geometric sequence with the common ratio R).
Twodimensional arrays (matrices): output
Matrix7°. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ M). Output elements of the matrix row with the order number K.
Matrix8. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ M). Output elements of the matrix column with the order number K.
Matrix9. An M × N matrix of real numbers is given. Output elements of its rows with even order numbers (2, 4, …). An output of matrix elements must be performed in the order of rows. Do not use conditional statements.
Matrix10. An M × N matrix of real numbers is given. Output elements of its columns with odd order numbers (1, 3, …). An output of matrix elements must be performed in the order of columns. Do not use conditional statements.
Matrix11. An M × N matrix of real numbers is given. Output elements of the matrix in the following order: the first row from left to right, the second row from right to left, the third row from left to right, the fourth row from right to left, and so on.
Matrix12. An M × N matrix of real numbers is given. Output elements of the matrix in the following order: the first column from up to down, the second column from down to up, the third column from up to down, the fourth column from down to up, and so on.
Matrix13. A realvalued square matrix A of order M is given. Starting with the element A_{1,1}, output its elements as follows: all elements of the first row, all elements of the Mth column except the element A_{1,M} (which is already output), all remaining elements of the second row, all remaining elements of the (M−1)th column, and so on; the element A_{M,1} must be output in the end. All rows must be output from left to right, all columns must be output from up to down.
Matrix14. A realvalued square matrix A of order M is given. Starting with the element A_{1,1}, output its elements as follows: all elements of the first column, all elements of the Mth row except the element A_{M,1} (which is already output), all remaining elements of the second column, all remaining elements of the (M−1)th row, and so on; the element A_{1,M} must be output in the end. All rows must be output from left to right, all columns must be output from up to down.
Matrix15. A realvalued square matrix A of order M is given (M is an odd number). Starting with the element A_{1,1} and moving clockwise, output all matrix elements in the spiral order: the first row from left to right, the last column from up to down, the last row from right to left, the first column from down to up, all remaining elements of the second row (from left to right), and so on; the central element of the matrix must be output in the end.
Matrix16. A realvalued square matrix A of order M is given (M is an odd number). Starting with the element A_{1,1} and moving counterclockwise, output all matrix elements in the spiral order: the first column from up to down, the last row from left to right, the last column from down to up, the first row from right to left, all remaining elements of the second column (from up to down), and so on; the central element of the matrix must be output in the end.
Twodimensional arrays (matrices): analysis
Matrix17. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ M). Find the sum and the product of elements of the matrix row with the order number K.
Matrix18. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ N). Find the sum and the product of elements of the matrix column with the order number K.
Matrix19. An M × N matrix of real numbers is given. Find the sum of elements for each matrix row.
Matrix20. An M × N matrix of real numbers is given. Find the product of elements for each matrix column.
Matrix21. An M × N matrix of real numbers is given. Find the average of elements for each matrix row with odd order number (1, 3, …). Do not use conditional statements.
Matrix22. An M × N matrix of real numbers is given. Find the sum of elements for each matrix column with even order number (2, 4, …). Do not use conditional statements.
Matrix23. An M × N matrix of real numbers is given. Find the minimal element for each matrix row.
Matrix24°. An M × N matrix of real numbers is given. Find the maximal element for each matrix column.
Matrix25. An M × N matrix of real numbers is given. Find the order number of the matrix row with the maximal sum of elements. Output this order number and the maximal sum value.
Matrix26. An M × N matrix of real numbers is given. Find the order number of the matrix column with the minimal product of elements. Output this order number and the minimal product value.
Matrix27. An M × N matrix of real numbers is given. Find the maximal value among the minimal elements of matrix rows.
Matrix28. An M × N matrix of real numbers is given. Find the minimal value among the maximal elements of matrix columns.
Matrix29. An M × N matrix of real numbers is given. For each matrix row find the amount of elements that are smaller than the average of all elements of this row.
Matrix30. An M × N matrix of real numbers is given. For each matrix column find the amount of elements that are greater than the average of all elements of this column.
Matrix31. An M × N matrix of real numbers is given. Find the order numbers of row and column for an element whose value is the closest to the average of all matrix elements.
Matrix32. An M × N matrix of integers is given. Find the order number of the first matrix row that contains the equal amount of positive and negative elements (zero elements are not considered). If the matrix does not contain the required rows then output 0.
Matrix33. An M × N matrix of integers is given. Find the order number of the last matrix column that contains the equal amount of positive and negative elements (zero elements are not considered). If the matrix does not contain the required columns then output 0.
Matrix34. An M × N matrix of integers is given. Find the order number of the last matrix row that contains even numbers only. If the matrix does not contain the required rows then output 0.
Matrix35. An M × N matrix of integers is given. Find the order number of the first matrix column that contains odd numbers only. If the matrix does not contain the required columns then output 0.
Matrix36°. An M × N matrix of integers is given, values of its elements are in the range 0 to 100. A matrix row is called the similar with the other row if these rows contain the same set of numbers. For example, rows (1, 3, 3, 2) and (2, 2, 1, 3) contain the same set {1, 2, 3} and therefore they are the similar rows. Find the amount of matrix rows that are the similar with the first row.
Matrix37. An M × N matrix of integers is given, values of its elements are in the range 0 to 100. A matrix column is called the similar with the other column if these columns contain the same set of numbers. For example, columns (1, 3, 3, 2) and (2, 2, 1, 3) contain the same set {1, 2, 3} and therefore they are the similar columns. Find the amount of matrix columns that are the similar with the last column.
Matrix38. An M × N matrix of integers is given. Find the amount of its rows that contain no elements with equal values.
Matrix39. An M × N matrix of integers is given. Find the amount of its columns that contain no elements with equal values.
Matrix40. An M × N matrix of integers is given. Find the order number of the last row that contains the maximal amount of elements with equal values.
Matrix41. An M × N matrix of integers is given. Find the order number of the first column that contains the maximal amount of elements with equal values.
Matrix42. An M × N matrix of real numbers is given. Find the amount of its rows whose values of elements are sorted in ascending order.
Matrix43. An M × N matrix of real numbers is given. Find the amount of its columns whose values of elements are sorted in descending order.
Matrix44. An M × N matrix of real numbers is given. Find minimal element among elements of all matrix rows whose values of elements are sorted in ascending or descending order. If the matrix does not contain the required rows then output 0 (as a real number).
Matrix45. An M × N matrix of real numbers is given. Find maximal element among elements of all matrix columns whose values of elements are sorted in ascending or descending order. If the matrix does not contain the required columns then output 0 (as a real number).
Matrix46. An M × N matrix of integers is given. Find the matrix element that is the maximum in its row and the minimum in its column. If the matrix does not contain such elements then output 0.
Twodimensional arrays (matrices): changing
Matrix47. An M × N matrix of real numbers and two integers K_{1}, K_{2} are given (1 ≤ K_{1} < K_{2} ≤ M). Exchange matrix rows with the order numbers K_{1} and K_{2}.
Matrix48. An M × N matrix of real numbers and two integers K_{1}, K_{2} are given (1 ≤ K_{1} < K_{2} ≤ N). Exchange matrix columns with the order numbers K_{1} and K_{2}.
Matrix49. An M × N matrix of real numbers is given. For each matrix row exchange values of its minimal and maximal element.
Matrix50. An M × N matrix of real numbers is given. For each matrix column exchange values of its minimal and maximal element.
Matrix51. An M × N matrix of real numbers is given. Exchange matrix rows containing the minimal and the maximal element of the matrix.
Matrix52. An M × N matrix of real numbers is given. Exchange matrix columns containing the minimal and the maximal element of the matrix.
Matrix53°. An M × N matrix of real numbers is given. Exchange the column with the order number 1 and the last column that contains positive numbers only. If the matrix does not contain the required columns then do not change it.
Matrix54. An M × N matrix of real numbers is given. Exchange the column with the order number N and the first column that contains negative numbers only. If the matrix does not contain the required columns then do not change it.
Matrix55. An M × N matrix of real numbers is given (M is an even number). Exchange the upper and lower half of the matrix.
Matrix56. An M × N matrix of real numbers is given (N is an even number). Exchange the left and right half of the matrix.
Matrix57. An M × N matrix of real numbers is given (M and N are even numbers). Exchange the upper left and lower right quarter of the matrix.
Matrix58. An M × N matrix of real numbers is given (M and N are even numbers). Exchange the upper right and lower left quarter of the matrix.
Matrix59. An M × N matrix of real numbers is given. Reflect its elements about the horizontal axis of symmetry of the matrix (that is, exchange matrix rows with the order numbers 1 and M, 2 and M − 1, and so on).
Matrix60. An M × N matrix of real numbers is given. Reflect its elements about the vertical axis of symmetry of the matrix (that is, exchange matrix columns with the order numbers 1 and N, 2 and N − 1, and so on).
Matrix61. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ M). Remove the matrix row with the order number K.
Matrix62. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ N). Remove the matrix column with the order number K.
Matrix63. An M × N matrix of real numbers is given. Remove the matrix row that contains the minimal matrix element.
Matrix64. An M × N matrix of real numbers is given. Remove the matrix column that contains the maximal matrix element.
Matrix65. An M × N matrix of real numbers is given. Remove its first column that contains positive numbers only. If the matrix does not contain the required columns then do not change it.
Matrix66. An M × N matrix of real numbers is given. Remove its last column that contains negative numbers only. If the matrix does not contain the required columns then do not change it.
Matrix67. An M × N matrix of real numbers is given. The matrix contains both positive and negative numbers. Remove all matrix columns that contain positive numbers only. If the matrix does not contain the required columns then do not change it.
Matrix68. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ M). Insert a new row of elements with zero value before the matrix row with the order number K.
Matrix69. An M × N matrix of real numbers and an integer K are given (1 ≤ K ≤ N). Insert a new column of elements with the value 1 after the matrix column with the order number K.
Matrix70. An M × N matrix of real numbers is given. Double the occurrence of the matrix row that contains the maximal matrix element.
Matrix71. An M × N matrix of real numbers is given. Double the occurrence of the matrix column that contains the minimal matrix element.
Matrix72. An M × N matrix of real numbers is given. Insert a new column of elements with the value 1 before the first matrix column that contains positive numbers only. If the matrix does not contain the required columns then do not change it.
Matrix73. An M × N matrix of real numbers is given. Insert a new column of elements with zero value after the last matrix column that contains negative numbers only. If the matrix does not contain the required columns then do not change it.
Matrix74°. An M × N matrix of real numbers is given. A matrix element is called the local minimum if it is smaller than all its neighbors. Replace all local minimums of the matrix by zero values. An additional matrix may be used for performing the required replacement.
Matrix75. An M × N matrix of real numbers is given. A matrix element is called the local maximum if it is greater than all its neighbors. Replace values of all local maximums of the matrix by opposite values. An additional matrix may be used for performing the required replacement.
Matrix76. An M × N matrix of real numbers is given. Rearrange the matrix rows so that values of their first elements were in ascending order.
Matrix77. An M × N matrix of real numbers is given. Rearrange the matrix columns so that values of their last elements were in descending order.
Matrix78. An M × N matrix of real numbers is given. Rearrange the matrix rows so that minimal values of their elements were in descending order.
Matrix79. An M × N matrix of real numbers is given. Rearrange the matrix columns so that maximal values of their elements were in ascending order.
Twodimensional arrays (matrices): diagonals
Matrix80. A realvalued square matrix A of order M is given. Find the sum of elements of its main diagonal: A_{1,1}, A_{2,2}, A_{3,3}, …, A_{M,M}.
Matrix81. A realvalued square matrix A of order M is given. Find the average of elements of its secondary diagonal: A_{1,M}, A_{2,M−1}, A_{3,M−2}, …, A_{M,1}.
Matrix82°. A realvalued square matrix A of order M is given. Find the sum of elements of each matrix diagonal that is parallel to the main diagonal. Begin with the singleelement diagonal A_{1,M}.
Matrix83. A realvalued square matrix A of order M is given. Find the sum of elements of each matrix diagonal that is parallel to the secondary diagonal. Begin with the singleelement diagonal A_{1,1}.
Matrix84. A realvalued square matrix A of order M is given. Find the average of elements of each matrix diagonal that is parallel to the main diagonal. Begin with the singleelement diagonal A_{1,M}.
Matrix85. A realvalued square matrix A of order M is given. Find the average of elements of each matrix diagonal that is parallel to the secondary diagonal. Begin with the singleelement diagonal A_{1,1}.
Matrix86. A realvalued square matrix A of order M is given. Find the minimal value of elements of each matrix diagonal that is parallel to the main diagonal. Begin with the singleelement diagonal A_{1,M}.
Matrix87. A realvalued square matrix A of order M is given. Find the maximal value of elements of each matrix diagonal that is parallel to the secondary diagonal. Begin with the singleelement diagonal A_{1,1}.
Matrix88°. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie below the main diagonal. Do not use conditional statements.
Matrix89. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie above the secondary diagonal. Do not use conditional statements.
Matrix90. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie on the secondary diagonal or below it. Do not use conditional statements.
Matrix91. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie on the main diagonal or above it. Do not use conditional statements.
Matrix92. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie above the main diagonal and above the secondary diagonal simultaneously. Do not use conditional statements.
Matrix93. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie above the main diagonal and below the secondary diagonal simultaneously. Do not use conditional statements.
Matrix94. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie below the main diagonal (or on it) and above the secondary diagonal (or on it) simultaneously. Do not use conditional statements.
Matrix95. A realvalued square matrix of order M is given. Assign zero value to the matrix elements that lie below the main diagonal (or on it) and below the secondary diagonal (or on it) simultaneously. Do not use conditional statements.
Matrix96. A realvalued square matrix A of order M is given. Reflect its elements about the main diagonal (that is, exchange values of matrix elements A_{1,2} and A_{2,1}, A_{1,3} and A_{3,1}, and so on). Do not use an additional matrix.
Matrix97. A realvalued square matrix A of order M is given. Reflect its elements about the secondary diagonal (that is, exchange values of matrix elements A_{1,1} and A_{M,M}, A_{1,2} and A_{M−1,M}, and so on). Do not use an additional matrix.
Matrix98. A realvalued square matrix A of order M is given. Rotate its elements by 180° (that is, exchange values of matrix elements A_{1,1} and A_{M,M}, A_{1,2} and A_{M,M−1}, and so on). Do not use an additional matrix.
Matrix99. A realvalued square matrix A of order M is given. Rotate its elements counterclockwise by 90° (that is, assign an initial value of A_{1,1} to A_{M,1}, an initial value of A_{M,1} to A_{M,M}, and so on). Do not use an additional matrix.
Matrix100°. A realvalued square matrix A of order M is given. Rotate its elements clockwise by 90° (that is, assign an initial value of A_{1,1} to A_{1,M}, an initial value of A_{1,M} to A_{M,M}, and so on). Do not use an additional matrix.
