[array] leetcode - 48. Rotate Image - Medium

leetcode - 48. Rotate Image - Medium

descrition

You are given an n x n 2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

Note:

You have to rotate the image in-place, which means you have to modify the input 2D matrix directly. DO NOT allocate another 2D matrix and do the rotation.

Example 1 :

Given input matrix =
[
  [1,2,3],
  [4,5,6],
  [7,8,9]
],

rotate the input matrix in-place such that it becomes:
[
  [7,4,1],
  [8,5,2],
  [9,6,3]
]

Example 2:

Given input matrix =
[
  [ 5, 1, 9,11],
  [ 2, 4, 8,10],
  [13, 3, 6, 7],
  [15,14,12,16]
], 

rotate the input matrix in-place such that it becomes:
[
  [15,13, 2, 5],
  [14, 3, 4, 1],
  [12, 6, 8, 9],
  [16, 7,10,11]
]

解析

参见代码。小技巧：矩阵的对角线可以唯一确定一个矩阵。

code

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

class Solution{
public:
	void rotate(vector<vector<int> >& matrix){
		//rotateNonInplace(matrix);
		rotateNonInplace(matrix);
	}
	/*
		(si,sj) ** (si,sj+k) *** (si,ej)
		*                          *
		*                          *
		*                        (si+k,ej)
		(ei-k,sj)                  *
		*                          *
		*                          *
		(ei,sj)*** (ei,ej-k)  ** (ei,ej)
	*/
	// time-O(n^2), space-O(1)
	void rotateInplace(vector<vector<int> >& matrix){
		int n = matrix.size();
		int si = 0, sj = 0; // the top-left corner
		int ei = n-1, ej = n-1; // the down-right corner
		// (si, sj), (ei, ej)

		while(si <= ei && sj<=ej){
			for(int k=0; sj+k<=ej; k++){
				int temp = matrix[si][sj+k];
				matrix[si][sj+k] = matrix[ei-k][sj];
				matrix[ei-k][sj] = matrix[ei][ej-k];
				matrix[ei][ej-k] = matrix[si+k][ej];
				matrix[si+k][ej] = temp;
			}
			si++;
			sj++;
			ei--;
			ej--;
		}
	}

	// time-O(n^2), space-O(n^2)
	void rotateNonInplace(vector<vector<int> >& matrix){
		int n = matrix.size();
		vector<vector<int> > assit(n, vector<int>(n, 0));

		// put the i-row in matrix to (n-1-i)-column in assit
		for(int i=0; i<n; i++){
			for(int k=0; k<n; k++){
				assit[k][n-1-i] = matrix[i][k];
			}
		}

		// copy assit to matrix
		for(int i=0; i<n; i++){
			for(int j=0; j<n; j++){
				matrix[i][j] = assit[i][j];
			}
		}
	}
};

int main()
{
	return 0;
}