Spiral Matrix II#

Problem statement#

Given a positive integer n, generate an n x n matrix filled with elements from 1 to n^2 in spiral order.

Example 1#

Example 1

Input: n = 3
Output: [[1,2,3],[8,9,4],[7,6,5]]

Example 2#

Input: n = 1
Output: [[1]]

Constraints#

  • 1 <= n <= 20.

Solution#

  1. Starting from the top left of the matrix.

  2. Going along the spiral direction.

  3. Put the value to the matrix, starting from 1.

Code#

#include <vector>
#include <iostream>
using namespace std;
enum Direction {RIGHT, DOWN, LEFT, UP};
vector<vector<int>> generateMatrix(int n) {
    vector<vector<int>> m(n, vector<int>(n));
    int bottom = n - 1;
    int right = n - 1;
    int top = 0;
    int left = 0;
    int row = 0;
    int col = 0;
    Direction d = RIGHT;
    int a = 1;
    while (top <= bottom && left <= right) {
        m[row][col] = a++;
        switch (d) {
            case RIGHT: if (col == right) {
                            top++;
                            d = DOWN;
                            row++;
                        } else {
                            col++;
                        }
                        break;
            case DOWN:  if (row == bottom) {
                            right--;
                            d = LEFT;
                            col--;
                        } else {
                            row++;
                        }
                        break;
            case LEFT:  if (col == left) {
                            bottom--;
                            d = UP;
                            row--;
                        } else {
                            col--;
                        }
                        break;
            case UP:    if (row == top) {
                            left++;
                            d = RIGHT;
                            col++;
                        } else {
                            row--;
                        }
                        break;
        }
    }
    return m;
}
void printResult(const vector<vector<int>>& m) {
    cout << "[";
    for (auto& r : m) {
        cout << "[";
        for (int a : r) {
            cout << a << ",";
        }
        cout << "]";
    }
    cout << "]\n";
}
int main() {
    auto m = generateMatrix(3);
    printResult(m);
    m = generateMatrix(1);
    printResult(m);
}

Output:
[[1,2,3,][8,9,4,][7,6,5,]]
[[1,]]

This solution uses a Direction enum and boundary variables to iteratively fill the matrix in a spiral pattern. Updating the direction of movement based on the current position and boundaries efficiently populates the matrix with sequential values, traversing in a clockwise direction from the outer layer to the inner layer.

Complexity#

  • Runtime: O(n^2), where n x n is the size of the matrix.

  • Extra space: O(1).

Key Takeaway#

Enumerating directions with an enum (like Direction) can enhance code readability and maintainability, especially in algorithms involving traversal or movement. It aids in clearly defining and referencing the possible directions within the problem domain.

Exercise#

  • Spiral Matrix[1].