# The problem statement is at # https://cw.felk.cvut.cz/brute/data/ae/release/2019l_be5b33pge/pge19/evaluation/input.php?task=lpaths # and also at the end of this file as a comment. # Be careful with indices, the matrix size in this implementation # is N+2 x N+2, # it has an additional artificial border of width 1, # filled with big values in rows and columns 0 and N+1. # The artificial border helps to manipulate the cell which are # at the border of the original matrix in the same way and by # the same code as the "regular" cells which are inside the matrix. import time N = 0 matrix = [] maxval = 9 def rotateLeft90deg( arr ): b = [[0] * (N+2) for i in range(N+2)] for i in range(N+2): for j in range(N+2): b[i][j] = arr[j][N+1-i] return b def tryFindL( a, i ): # in direction East and North origi = i # start at the West border of the matrix val = a[i][1] # can we go East? if a[i-1][1] == val or a[i+1][1] == val: return 0,0,0, 0 # yes, we can j = 2 while True: # obvious fails: if j > N or a[i][j] != val: return 0,0,0, 0 # can move one step East? if a[i-1][j] != val and a[i+1][j] != val: j += 1; continue; # found corner down to South? if a[i+1][j] != val and a[i][j+1] != val and a[i-1][j] == val: break return 0,0,0, 0 # in all other cases # now try move North i -= 2 while True: # happily arrived to North border? if i < 1 : return origi, j, val, (origi+j-1)*val # can continue North? if a[i][j-1] != val and a[i][j] == val and a[i][j+1] != val: i -= 1; continue return 0,0,0, 0 # in all other cases # Instead of looking for L-shaped regions in all 4 possible directions # we implement only the search in one direction and rotate # the matrix 3 times by 90 degrees. def mxValue(arr): value = 0 for k in range(4): for i in range (2, N+1): ii, jj, val, valsum = tryFindL( arr, i ) #if val > 0: print( k, ii, jj, val, valsum) value += valsum if k < 3: arr = rotateLeft90deg( arr ) return value # Note the creation of the artificial border def loadOneMx(): mx = [] border = [maxval] * (N+2) mx.append( border ) for i in range(N): row = list( map( int, input().split() ) ) mxrow = [maxval]+row +[maxval] mx.append(mxrow) mx.append( border ) return mx # ----------------------------------------------------------------------- # M A I N # ----------------------------------------------------------------------- t1 = time.time() N, K = map(int, input().split()) for k in range(K): matrix = loadOneMx() print( mxValue(matrix) ) t2 = time.time() #print( "time %6.3f" % (t2-t1) ) # --------------------------------------------------------------------------- # P R O B L E M S T A T E M E N T # with examples # --------------------------------------------------------------------------- ''' L-paths in a Matrix In this problem, we consider integer square matrices consisting of N×N cells. The indices of the rows and the columns are 0,1,2, ..., N−1. Two cells in a matrix are neighbours if they are in the same row or in the same column and either their row coordinates differ by 1 or their column coordinates differ by 1. A cell in the matrix interior has four neighbour cells, a cell in the corner of a matrix has two neighbour cells and a cell at the border of the matrix and not in the corner has three neighbour cells. An L-path in a matrix is a set LP of cells with the following properties: 1. All cells in LP contain the same value. 2. Any cell which is not in LP and which is a neighbour of some cell in LP contains a different value from the value of cells in LP. 3. There is one specific cell D in LP with coordinates [r, c] such that exactly one of the four following conditions is satisfied: 3.1. All cells with coordinates [r-1, c], [r-2, c], ..., [0, c] and [r, c+1], [r, c+2], ..., [r, N-1] are in LP. 3.2. All cells with coordinates [r-1, c], [r-2, c], ..., [0, c] and [r, c-1], [r, c-2], ..., [r, 0] are in LP. 3.3. All cells with coordinates [r+1, c], [r+2, c], ..., [N-1, c] and [r, c-1], [r, c-2], ..., [r, 0] are in LP. 3.4. All cells with coordinates [r+1, c], [r+2, c], ..., [N-1, c] and [r, c+1], [r, c+2], ..., [r, N-1] are in LP. 4. No other cells in the matrix than those specified in 3. are part of LP. 5. LP consists of at least 3 cells. The value of an L-path is the sum of values in all its cells. The L-value of a matrix is the sum of all values of L-paths in the matrix. If there is no L-path in the matrix, the L-value of the matrix is defined to be 0. The task -------- Determine the L-value of each input matrix. Input ----- The first input line contains two integers N and K. Integer N specifies the size of all matrices in the input. Integer K specifies the number of matrices in the input. Next, there are exactly K matrices of size N×N occupying K×N lines. First N lines specify the first matrix, next N lines specify the second matrix and so on. Each line contains N values, the values correspond to the values in a particular row in the current matrix. All values are separated by single space. It holds 1 ≤ N, K ≤ 100, all values in all matrices are positive integers less than 100. Output ------ The output contains as many text lines as there are matrices in the input. Each line contains the L-value of the corresponding matrix. The order of the output values is the same as the order of the input matrices. Example 1 Input 8 1 4 5 2 3 1 2 2 2 2 2 2 3 1 1 1 1 4 3 3 3 3 3 3 3 7 7 7 7 6 5 5 5 1 1 1 7 6 6 6 6 8 8 1 7 5 5 5 5 3 8 1 7 5 1 1 1 3 3 1 7 5 1 1 1 Output 105 Comment: The region with 3's in the upper right part of the matrix is not an L-path. Example 2 Input 5 3 1 8 1 8 1 8 8 1 8 1 1 1 1 8 1 8 8 8 8 1 1 1 1 1 1 4 4 4 4 4 5 5 5 5 4 5 5 5 5 4 1 1 5 5 4 5 1 5 5 4 7 7 7 2 7 7 7 7 2 2 2 2 2 7 7 7 7 2 7 7 7 7 2 7 7 Output 94 39 16 Example 3 Input 6 2 2 1 2 2 1 2 1 1 2 2 1 1 2 2 6 6 2 2 2 2 6 6 2 2 1 1 2 2 1 1 2 1 2 2 1 2 4 4 4 4 4 4 8 8 8 8 8 8 8 5 5 5 5 1 8 3 3 3 6 1 8 1 1 1 1 1 4 4 4 4 4 4 Output 12 0 '''