1. Raising the question
The characteristic of the n- order Z -shaped matrix is that the elements are arranged in a Z - shaped manner. An n -order Z -shaped matrix means that the size of the matrix is n × n , where n is a positive integer.
Question description
A spiral ( Z -shaped) matrix with n rows and n columns is shown in Figure 1. Observe and find out the filling pattern.
Figure 1 Spiral ( Z -shaped) matrices with 7 rows and 7 columns and 8 rows and 8 columns
Now given the matrix size n , please output the matrix.
Input format
Enter an integer n ( 1 ≤ n ≤ 1000 ) , indicating the matrix size.
Output format
Output n rows and n columns, representing the required matrix.
Input and output samples
2. Solution ideas
Figure 2 Principle diagram of matrix generation
According to the title description, examples and Figure 2 , it can be seen that the matrix is n × n , in which the elements are arranged from left to right in the even-numbered rows ( the first row is 0 rows ) ; and the elements are arranged in the odd-numbered rows ( the first row is 0 rows ) from right to left.
3. Matrix generation algorithm
n rows and n columns, even-numbered rows ( the first row is row 0 ) generate elements from 0 to n -1 ; odd-numbered rows ( the first row is row 0 ) generate elements from n -1 to 0 .
The program code is as follows:
N = 5
def prt(b): # 打印二维列表
for i in range(N):
for j in range(N):
print("%3d" % b[i][j], end='')
print()
def Helix_MatrixII(n):
cnt = 1
for i in range(n): # 生成n行
if i % 2 == 0: # 偶数行
for j in range(n): # 由左向右(j为0~n-1)生成
matrix[i][j] = cnt
cnt += 1
else: # 奇数行
for j in range(n): # 由右向左(j为n-1~0)生成
matrix[i][n-1-j] = cnt
cnt += 1
matrix = [] # 初始化二维矩阵matrix(二维列表)
for i in range(N):
matrix.append([])
for j in range(N):
matrix[i].append(0)
Helix_MatrixII(N)
prt(matrix)Results of the:
| 1 | 2 | 3 | 4 | 5 |
| 10 | 9 | 8 | 7 | 6 |
| 11 | 12 | 13 | 14 | 15 |
| 20 | 19 | 18 | 17 | 16 |
| 21 | 22 | 23 | 24 | 25 |
4. Problem Solving Algorithm
According to the question requirements: input the matrix size n and output the matrix.
def prt(b): # 打印二维列表
for i in range(N):
for j in range(N):
print("%3d" % b[i][j], end='')
print()
def Helix_MatrixII(n):
cnt = 1
for i in range(n): # 生成n行
if i % 2 == 0: # 偶数行
for j in range(n): # 由左向右(0~n-1)生成
matrix[i][j] = cnt
cnt += 1
else: # 奇数行
for j in range(n): # 由左向右(n-1~0)生成
matrix[i][n-1-j] = cnt
cnt += 1
N = int(input())
matrix = [] # 初始化二维矩阵matrix(二维列表)
for i in range(N):
matrix.append([])
for j in range(N):
matrix[i].append(0)
Helix_MatrixII(N)
prt(matrix)Input 8, the output is
