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螺旋矩阵是指一个呈螺旋状的矩阵，它的数字由第一行开始到右边不断变大，向下变大，向左变大，向上变大，如此循环。如下图所示：
此类题目经常出现在各大互联网公司的面试笔试这种，今天我用c++实现输入一个整N，就打印出N*N的螺旋矩阵。
解题思路：
这道题刚开始整的感觉还不太好操作，主要就是找规律，主要思路就是按照由外到内，一层一层进行for循环打印，最外层循环控制有多少层，每层分为（上方、右侧、下方、左侧）四个递增的循环，直到最后一层打印完。如果输入N为奇数，将会有N/2 + 1层，最内层为N平方一个数字；如果N为偶数，将会有N/2层。
Java实现源码：
import java.util.Arrays;
import java.util.Scanner;
public class SpiralMatrix {
private void printArray(int[][] arr) {
int length = arr.length - 1;
if (arr.length != 1) {
for (int i = 1; i <= length; ++i) {
for (int n, j = 1; j <= length; ++j) {
System.out.print(String.format("% -8d", arr[i][j]));
}
System.out.println();
}
} else {
System.out.print("input length error!");
}
}
private int[][] getArray(int n) {
int[][] arr = new int[n + 1][n + 1];
for (int[] a : arr) {
Arrays.fill(a, 0);
}
return arr;
}
//顺时针螺旋
private void clockwise(int[][] arr) {
System.out.println("clockwise print: ");
int i = 0, j = 0, k = 1, n = arr.length - 1, m = n / 2;
if (n % 2 != 0) arr[m + 1][m + 1] = n * n;
for (i = 1; i <= n / 2; ++i) {
//上方
for (j = i; j <= n - i; ++j) {
arr[i][j] = k++;
}
//右侧
for (j = i; j <= n - i; ++j) {
arr[j][n + 1 - i] = k++;
}
//下方
for (j = n - i + 1; j >= i + 1; j = j - 1) {
arr[n + 1 - i][j] = k++;
}
//左侧
for (j = n - i + 1; j >= i + 1; j = j - 1) {
arr[j][i] = k++;
}
}
}
//逆时针螺旋
private void anticlockwise(int[][] arr) {
System.out.println("anticlockwise print: ");
int i = 1, j = 0, k = 1, n = arr.length - 1, m = n / 2;
if (n % 2 != 0) arr[m + 1][m + 1] = n * n;
//一层一层去打印，从外往里打印
for (i = 1; i <= n / 2; ++i) {
//上方
for (j = n - i + 1; j > i; --j) {
arr[i][j] = k++;
}
//右侧
for (j = i; j <= n - i; ++j) {
arr[j][i] = k++;
}
//下方
for (j = i; j <= n - i; ++j) {
arr[n + 1 - i][j] = k++;
}
//左侧
for (j = n - i + 1; j >= i + 1; --j) {
arr[j][n - i + 1] = k++;
}
}
}
public static void main(String[] argv) {
SpiralMatrix spiralMatrix = new SpiralMatrix();
Scanner scanner = new Scanner(System.in);
System.out.print("please input a number n: ");
while (scanner.hasNext()) {
int n = scanner.nextInt();
int[][] arr = spiralMatrix.getArray(n);
//顺时针
spiralMatrix.clockwise(arr);
spiralMatrix.printArray(arr);
System.out.println();
//逆时针
spiralMatrix.anticlockwise(arr);
spiralMatrix.printArray(arr);
System.out.print("please input a number n: ");
}
}
}
运行结果：
C++实现源码：
#include <iostream>
#include<iomanip>
#include<vector>
using namespace std;
int input() {
int n = 0;
cout << "please input a number n:";
cin >> n;
return n;
}
void printArray(int n, vector<vector<int> >& arr) {
if (n != 1) {
for (int i = 1; i <= n; ++i) {
for (int j = 1; j <= n; ++j) {
cout << setw(5) << arr[i][j];
}
cout << endl;
}
}
else {
cout << setw(5) << n;
}
}
vector<vector<int> > getArray(int n) {
vector<vector<int> > arr(n + 1, vector<int>(n + 1));
return arr;
}
int** getArray1(int n) {
int** arr = new int* [n];
for (int i = 0; i < n + 1; i++) {
arr[i] = new int[n + 1];
}
for (int i = 1; i <= n; ++i) {
for (int j = i; j <= n; ++j)
arr[i][j] = 0;
}
return arr;
}
void deleteArray1(int n, int** a) {
for (int i = 0; i < n + 1; i++) {
delete[]a[i];
}
a = NULL;
}
//顺时针螺旋
void clockwise(int n, vector<vector<int>>& arr) {
cout << "clockwise print: " << endl;
int i = 0, j = 0, k = 1, m = n / 2;
if (n % 2 != 0) arr[m + 1][m + 1] = n * n;
for (i = 1; i <= n / 2; ++i) {
//上方
for (j = i; j <= n - i; ++j) {
arr[i][j] = k++;
}
//右侧
for (j = i; j <= n - i; ++j) {
arr[j][n + 1 - i] = k++;
}
//下方
for (j = n - i + 1; j >= i + 1; j = j - 1) {
arr[n + 1 - i][j] = k++;
}
//左侧
for (j = n - i + 1; j >= i + 1; j = j - 1) {
arr[j][i] = k++;
}
}
}
//逆时针螺旋
void anticlockwise(int n, vector<vector<int> >& arr) {
cout << "anticlockwise print: " << endl;
int i = 1, j = 0, k = 1, m = n / 2;
if (n % 2 != 0) arr[m + 1][m + 1] = n * n;
//一层一层去打印，从外往里打印
for (i = 1; i <= n / 2; ++i) {
//上方
for (j = n - i + 1; j > i; --j) {
arr[i][j] = k++;
}
//右侧
for (j = i; j <= n - i; ++j) {
arr[j][i] = k++;
}
//下方
for (j = i; j <= n - i; ++j) {
arr[n + 1 - i][j] = k++;
}
//左侧
for (j = n - i + 1; j >= i + 1; --j) {
arr[j][n - i + 1] = k++;
}
}
}
int main() {
int n = input();
vector<vector<int>> arr = getArray(n);
clockwise(n, arr);
printArray(n, arr);
anticlockwise(n, arr);
printArray(n, arr);
return 0;
}
运行结果 ：
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