Get the time complexity function from the pseudocode for adding 2 matrices below // add two matrices for(i = 0 ; i < rows; i++){ for(j = 0; j < columns; j++) matrix2[i][j] = matrix1[i][j] + matrix2[i][j]; } // display the result for(i = 0 ; i < rows; i++){ for(j = 0; j < columns; j++){ printf("%d ", matrix2[i][j]); } printf("\n"); }
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Get the time complexity function from the pseudocode for adding 2 matrices below
// add two matrices
for(i = 0 ; i < rows; i++){
for(j = 0; j < columns; j++)
matrix2[i][j] = matrix1[i][j] + matrix2[i][j];
}
// display the result
for(i = 0 ; i < rows; i++){
for(j = 0; j < columns; j++){
printf("%d ", matrix2[i][j]);
}
printf("\n");
}
Step by step
Solved in 2 steps
- please add comments for each matrix algorithms below START OF MATRIX ADDITIONInput no. of rows m1 and columns n1 of first matrixFor i = 0 to m1-1 For j=0 to n1-1 Input a[i][j] End forEnd forInput no. of rows m2 and columns n2 of second matrixFor i = 0 to m2-1 For j=0 to n2-1 Input b[i][j] End forEnd forIf (m1 != n1 and m2!=n2) Print "Addition is not possible"Else Initialize sum matrix sum[m1][n1] as 0 matrix For i = 0 to m1-1 For j=0 to n1-1 sum[i][j] =a[i][j]+b[i][j] End for End forEnd IfFor i = 0 to m1-1 For j=0 to n1-1 Print sum[i][j] End forEnd forEND OF MATRIX ADDITION START OF SCALAR MULTIPLICATIONInput no. of rows m and columns n of matrixFor i = 0 to m-1 For j=0 to n-1 Input a[i][j] End forEnd forInput scalar value kInitialize result matrix res[m][n] as 0 matrixFor i = 0 to m-1 For j=0 to n-1 res[i][j] = k *a[i][j] End forEnd forEnd IfFor i = 0 to m-1 For j=0 to n-1…Can you answer with the Python programming language without using input ? A 2D matrix can be represented as a list and a column count value in Python. For example, the 3x3 matrix 1 2 3 4 5 6 7 8 9 can be row-wise represented as ([1,2,3,4,5,6,7,8,9], 3), where the number 3 represents the number of columns in the matrix. Similarly, 1 3 5 2 4 6 becomes ([1,3,5,2,4,6], 3). A submatrix can be defined as an (l,r,t,b) tuple, where l and r are left and right column indices, and t and b are top and bottom row indices (all inclusive). Write a function that takes a tuple containing the list representing a matrix, and the column count of the matrix, along with another tuple representing a specific submatrix, and returns the list representation of the submatrix along with its column count as a tuple. For example, given submatrix(([1,2,3,4,5,6,7,8,9,10,11,12], 4), (1,2,0,1)) returns: ([2,3,6,7], 2) because, ([1,2,3,4,5,6,7,8,9,10,11,12], 4) represents: 1 2 3 4 5 6 7 8 9 10 11 12 and (1,2,0,1)…Can you ask with the python software language? A 2D matrix can be represented as a list and a column count value in Python. For example, the 3x3 matrix 1 2 3 4 5 6 7 8 9 can be row-wise represented as ([1,2,3,4,5,6,7,8,9], 3), where the number 3 represents the number of columns in the matrix. Similarly, 1 3 5 2 4 6 becomes ([1,3,5,2,4,6], 3). A submatrix can be defined as an (l,r,t,b) tuple, where l and r are left and right column indices, and t and b are top and bottom row indices (all inclusive). Write a function that takes a tuple containing the list representing a matrix, and the column count of the matrix, along with another tuple representing a specific submatrix, and returns the list representation of the submatrix along with its column count as a tuple. For example, given submatrix(([1,2,3,4,5,6,7,8,9,10,11,12], 4), (1,2,0,1)) returns: ([2,3,6,7], 2) def submatrix(matrix, indices):
- Get the time complexity function from the pseudocode for the addition of the 2 matrices below, and prove whether the big-oh is O(n^2) so that it satisfies the rule f(n) <= c g(n); / add two matricesfor(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++)matrix2[i][j] = matrix1[i][j] + matrix2[i][j];}// display the resultfor(i = 0 ; i < rows; i++){for(j = 0; j < columns; j++){printf("%d ", matrix2[i][j]);}printf("\n");}Convert the algorithm to a Python program. ALGORITHM Matrix Multiplication(A[0..n-1, 0..n -1], B(0,n-1,0..n -1)//Multiplies two square matrices of order n by the definition-based algorithm //input: Two n x n matrices A and B //Output: Matrix C = AB for i← 0 to n-1 dofor j ←0 to n- 1 doC[i. j] =0.0 for k 0 to n - 1 doC[i. jl ←C[i. j] + A[. k]* B|k. j] return CFor the program below, calculate its worst-case complexity as a function of the size n of the input array A. Explain your answer by giving a detailed calculation.def initialCommon (A,B): # initial common component of A, B for i in range (len(A) ,-1,-1): same = True for j in range (i): if A[j] != B[j]: same = False if same : return [A[j] for j in range (i)]
- Given an n x n matrix where each of the rows and columns is sorted in ascending order, return the kth smallest element in the matrix. Note that it is the kth smallest element in the sorted order, not the kth distinct element. You must find a solution with a memory complexity better than O(n2). Example 1: Input: matrix = [[1,5,9],[10,11,13],[12,13,15]], k = 8 Output: 13 Explanation: The elements in the matrix are [1,5,9,10,11,12,13,13,15], and the 8th smallest number is 13 Example 2: Input: matrix = [[-5]], k = 1 Output: -5A 2D matrix can be represented as a list and a column count value in Python. For example, the 3x3 matrix 1 2 34 5 67 8 9 can be row-wise represented as ([1,2,3,4,5,6,7,8,9], 3), where the number 3 represents the number of columns in the matrix. Similarly, 1 3 52 4 6 becomes ([1,3,5,2,4,6], 3). A submatrix can be defined as an (l,r,t,b) tuple, where l and r are left and right column indices, and t and b are top and bottom row indices (all inclusive). Write a function that takes a tuple containing the list representing a matrix, and the column count of the matrix, along with another tuple representing a specific submatrix, and returns the list representation of the submatrix along with its column count as a tuple. For example, given submatrix(([1,2,3,4,5,6,7,8,9,10,11,12], 4), (1,2,0,1)) returns: ([2,3,6,7], 2) because, ([1,2,3,4,5,6,7,8,9,10,11,12], 4) represents: 1 2 3 45 6 7 89 10 11 12 and (1,2,0,1) represents the submatrix between column indices 1 and 2 (both inclusive), and row…A 2D matrix can be represented as a list and a column count value in Python. For example, the 3x3 matrix 1 2 34 5 67 8 9 can be row-wise represented as ([1,2,3,4,5,6,7,8,9], 3), where the number 3 represents the number of columns in the matrix. Similarly, 1 3 52 4 6 becomes ([1,3,5,2,4,6], 3). A submatrix can be defined as an (l,r,t,b) tuple, where l and r are left and right column indices, and t and b are top and bottom row indices (all inclusive). Write a function that takes a tuple containing the list representing a matrix, and the column count of the matrix, along with another tuple representing a specific submatrix, and returns the list representation of the submatrix along with its column count as a tuple. For example, given submatrix(([1,2,3,4,5,6,7,8,9,10,11,12], 4), (1,2,0,1)) returns: ([2,3,6,7], 2) because, ([1,2,3,4,5,6,7,8,9,10,11,12], 4) represents: 1 2 3 45 6 7 89 10 11 12 and (1,2,0,1) represents the submatrix between column indices 1 and 2 (both inclusive), and row…
- Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example 1: Input: nums1 = [1,3], nums2 = [2] Output: 2.00000 Explanation: merged array = [1,2,3] and median is 2. Example 2: Input: nums1 = [1,2], nums2 = [3,4] Output: 2.50000 Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Constraints: nums1.length == m nums2.length == n 0 <= m <= 1000 0 <= n <= 1000 1 <= m + n <= 2000 -106 <= nums1[i], nums2[i] <= 106 Write the whole code in python language Attach the code outputs also and explain the implementation.Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example 1: Input: nums1 = [1,3], nums2 = [2] Output: 2.00000 Explanation: merged array = [1,2,3] and median is 2. Example 2: Input: nums1 = [1,2], nums2 = [3,4] Output: 2.50000 Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5. Constraints: nums1.length == m nums2.length == n 0 <= m <= 1000 0 <= n <= 1000 1 <= m + n <= 2000 -106 <= nums1[i], nums2[i] <= 106Using Java Modify the program 1 to compute the multiplication of two vectors with the sizes mx1 and 1xn. The result is a matrix mxn computed as follows: the element on the position r and c in the product will be equal with m1[r][0]*m2[0][c].