matrices precalculus

/*F (i,j) indicates the edge length of the maximum full 0 sub-matrix (I,J) in the lower right cornerIf A[i][j]==1,f (i,j) =0Otherwise: f (i,j) =min{F (i-1,j), F (i,j-1), F (i-1,j-1)}+1This is the maximum full 0 square sub-matrixRequires a rectangular matrix, the above ideas do not workAssume that (I,J) is the largest matrix in the lower right corner =12It could be 3*4, 4*3, 2*6, 6*2, 1*12, 12*1According to the above-mentioned idea of state transfer, the scheme to obtain the optimal value is not

Variants-matrix matrices ()matrix () is a six-value (A,B,C,D,E,F) transformation matrix that specifies a 2D transformation that is equivalent to applying a [a B c D E F] transformation matrix directly. is to reposition the element based on the horizontal (x-axis) and vertical (Y-axis), this property value uses a matrix that involves mathematics, and I'm just saying here that the transform in CSS3 has such a property value, and if you need to understan

progression summation formula, find the number of remaining elements, with the total number of elements minus the number of elements remaining is the first element value on the current slash. The number of elements is n*n, and the remaining number of elements is M * (M + 1)/2, where m= (n-1-i) + (N-1-J). The value of the first element of the slash is n*n-m* (m+1)/2.Code 1#include #include #include using namespace STD;intMain () {intNCin>> N;// vectorint>VEC (N*n);intS,m,smax = n * N; for(in

Topic:the font traversal of a matrixGive you a matrix of M x n elements (m rows, n columns), to find the font traversal of the matrix.Sample ExampleFor the following matrices:[ [1, 2, 3, 4], [5, 6, 7, 8], [9,10, 11, 12]]Return[1, 2, 5, 9, 6, 3, 4, 7, 10, 11, 8, 12]Solving:Feel very simple, is not to get out, program source, here is first right up, I change first to go sideways is wrong, said do not understand. Another way to express or not und

Reference : http://wenku.baidu.com/view/193f8a8fbceb19e8b8f6baf6.html(Owed by: Spring Night rain Http://blog.csdn.net/chunyexiyu reprint please indicate the source)Common geometric transformation matrices: translation (translate), rotation (rotate), scaling (scale), and simple compositing, such as rotation around a specified point, scalingMultiplicative reference Http://blog.csdn.net/chunyexiyu/article/details/44671737-Matrix matrix multiplication fo

An introduction to the graph of adjacency matricesA graph of adjacency matrices refers to a direction graph represented by an adjacency matrix.The above figure G2 contains "a,b,c,d,e,f,g" a total of 7 vertices, and contains "The matrix on the right is the adjacency matrix of the G2 in memory. A[i][j]=1 indicates that the first vertex to the J Vertex is an edge, a[i][j]=0 is not an edge, and A[i][j] represents the value of column J of Line I, for examp

line has three integers a, B, K, which indicates that you can walk the repeating edge from point A to point B (K Enter end when n, M are all 0Output calculates the number of scenarios per query, as a result of a large number of methods, outputs its 1000 moduloSample INPUT4 3 3 2 1 0Sample Output2013 analysis: When I see this problem using matrices to solve my first feeling is incredible, this with the matrix has what Chicken feather relationship?!! B

Test Instructions:LinkMethod:Bsgs+ Matrix Inversionparsing:The problem is to A x =B(mod c ) A and B are replaced by matrices. But there is no change anywhere else. So it involves the inverse of the matrix. How do you find the inverse of a matrix? First, after the original matrix followed by a unit matrix, it is advisable to set the right diagonal first to Gaussian elimination of the original matrix and to elimin

Diag:diagonal matrices and diagonals of a matrixSyntaxX = Diag (v,k)X = Diag (v)v = diag (x,k)v = diag (X)Descriptionx = Diag (v,k) when V was a vector of n components, returns a square matrix X of order N+abs (k), with the elements of V on tHe kth diagonal. K = 0 Represents the main diagonal, K > 0 above the main diagonal, and K X = Diag (v) puts V on the main diagonal, same as above with k = 0.v = diag (x,k) for matrix X, returns a column vectors v

Topicsearch for two-dimensional Matrix IIWrite an efficient algorithm to search for values in the MXN matrix, returning the number of occurrences of this value.This matrix has the following characteristics: The integers in each row are sorted from left to right. The integers of each column are sorted from top to bottom. There are no duplicate integers in each row or column. Sample ExampleConsider the following matrices:[[1, 3, 5,

The Sum of Sub-matricesDescriptionSeen draw a big 3*n matrix, whose entries ai,j is all integer numbers (1 InputThere is multiple test cases.For each test case, the first line contains an integer n, k (1 OutputFor each test case, the print one line with an integer.Sample Input5 31 2-10 3 53-2-10 2-10-10-10 1-10-10 2 3-1-2-3-42 3Sample Output144The maximum and the K-sub-matrices inside the 3*n matrix are obtained.State compression on a column#include #

Android custom controls-3D galleries and image matrices 1.3D gallery implementation We know that the android system has provided us with a "Container" for displaying images-Gallery. However, this Gallery shows flat effects and does not have a strong dynamic effect. Here, we are working on a custom Gallery component to display the 3D effects of images. Think about it. Let's take a look: What should I do with Gallery that achieves this 3D effect? First

)From PoIntS to EdMs and backX is the d*n matrix,The average distance between Xi and XJ is, and defines||.|| Represents the Euclidean norm, i.e.1 represents the column vector of the n*1, that is, the transpose of [1 1 1...1], and the 1 transpose is the line vector of the 1*n; the EDM (X) is actuallySimilarly, to make, thenFormulas 3 and 4 reveal an important attribute: the rank of X is up to D, the rank of the most is D, and the other two addend rank 1 for Equation 3, thus getting: the rank of a

know the point (x, y) coordinates, to find the coordinates of the symmetric point (x ', y ')?Very simple, one is vertical, the second is the center point on the axis, so there are:(y-y')/(x-x') =-1/k→ky-ky' =-x+x' //Two straight lines perpendicular to each other with negative slope Countdown + x')/2 * k = (y + y')/2 →kx+kx' = y+y 'Very simple, put x‘ and y‘ put forward, there are:X' = (1-k*k)/(k*k+1) *x + 2k/(k*k+1) *y; Y' = 2k/(k*k+1) *x + (k*k-1)/(k*k+1) *y;And then combine the matrix

Nine Chapters count judges Net-original websitehttp://www.jiuzhang.com/problem/29/TopicsGiven the n*n matrix, you need to query the greatest common divisor of all the numbers in any sub-matrices. Please give a design idea, preprocessing the matrix, speed up the query. Additional space complexity is required within O (n^2).AnswerConstructs a two-dimensional line segment tree. Preprocessing time O (n^2), each query O (log n)Interviewer AngleThis topic n

#CODING=GBK fromPILImportImageImportNumPy as NP#Import scipydefLoadImage ():#Reading Picturesim = Image.open ("lena.jpg") #Show Picturesim.show () im= Im.convert ("L") Data=im.getdata () data=Np.matrix (data)#Print Data #transform into 512*512data = Np.reshape (data, (512,512)) New_im=Image.fromarray (data)#Show Picturesnew_im.show () LoadImage ( )Above to first to remove the color of the picture, is to become black and white, converted into two-dimensional data matrix, not to color to sav

angle will change, after rotating and scaling, the new coordinate system is P-Q, and the new vector is obtained.BThe relative position of the new coordinate system is similar to that of the west of the Cartesian coordinate system ).MBefore transformation,AIs the diagonal line,MAfter conversion,BOr diagonal lines. AM = BIt can also be understood that there is an object in which an object coordinate system is established. A point in an object connects to the origin of an object coordinate syste

A 10*10 matrix (which can be understood as a chessboard), generates a set of data at any time and fills in the Matrix. Numbers at any position are calculated except 4 and colored by the remainder, if the remainder is 0, the color is red, 1 is blue, 2 is green, and 3 is black. It can be understood that the color of 4 is generated and placed on the board, if one of the five stars with the same color is connected (The rule goes through wuziqi), find any group and output the position and bottom valu

Child matrix of Row A and column B, or the child matrix of Row B and column. A non-Intersecting rectangle indicates that two rectangles have no common elements. Format input format The first line contains four positive integers n, m, A, and B, which are separated by spaces. In the following n rows, each row has m integers separated by spaces, which represent each element of the Two-dimensional matrix in sequence. Output Format Output a row with an integer representing the answer. If two non-

Take the second-order matrix as an example. A typical Fibonacci series can be solved by multiplication of matrices. If multiplication is not considered, the complexity should be lgn. The following describes how to calculate the power of a matrix. # Include