given a nn matrix full of integers.
now we know matrix has many layers, so for nn, we have n/2 layers.

now, we need to sort each layer, and relocate them clockwise, starting from the top left position.

idea: of course we can get every element for each layer, sort them and put them back.
but that means we need to use some extra space to store them.
but what about i use a PQ to iterate each element and sort them at the same time.

public class bordersort {
    public void solution(int[][] matrix){

        int m = matrix.length;
        int n = matrix[0].length;
        List<PriorityQueue<Integer>> temp = new ArrayList<>();

        int rowstart = 0;
        int rowend = m-1;
        int colstart = 0;
        int colend = n-1;
        while(rowstart<=rowend && colstart<=colend){
            PriorityQueue<Integer> pq = new PriorityQueue<>();
            for(int i=colstart; i<=colend; i++){
                pq.offer(matrix[rowstart][i]);
            }
            rowstart++;
            for(int i=rowstart; i<=rowend; i++){
                pq.offer(matrix[i][colend]);
            }
            colend--;
            if(rowstart<=rowend) {
                for (int i = colend; i >= colstart; i--) {
                    pq.offer(matrix[rowend][i]);
                }
                rowend--;
            }

            if(colstart<=colend) {
                for (int i = rowend; i>=rowstart; i--){
                    pq.offer(matrix[i][colstart]);
                }
                colstart++;
            }
            temp.add(pq);
        }

        rowstart = 0;
        rowend = m-1;
        colstart = 0;
        colend = n-1;

        int j = 0;
        while(rowstart<=rowend && colstart<=colend){ //this while - for - for - if(for) - if(for) is template of iterate a matrix in spiral way
            PriorityQueue<Integer> pq = temp.get(j);
            for(int i=colstart; i<=colend; i++){
                matrix[rowstart][i]=pq.poll();
            }
            rowstart++;
            for(int i=rowstart; i<=rowend; i++){
                matrix[i][colend]=pq.poll();
            }
            colend--;
            if(rowstart<=rowend) {
                for (int i = colend; i >= colstart; i--) {
                    matrix[rowend][i]=pq.poll();
                }
                rowend--;
            }

            if(colstart<=colend) {
                for (int i = rowend; i>=rowstart; i--){
                    matrix[i][colstart]=pq.poll();
                }
                colstart++;
            }
            j++;
        }



    }

    public static void main(String[] args){
        bordersort bs = new bordersort();
        int[][] matrix = new int[][]{{7,3,4,9,55},{6,8,10,30,33},{5,11,12,15,77},{16,20,77,888,909},{87,62,54,30,21}};
        bs.solution(matrix);
        for(int[] ma: matrix){
            for(int i=0; i<ma.length; i++){
                System.out.print(ma[i]);
                System.out.print(", ");
            }
            System.out.print("\n");
        }
    }
}