具有周期性边界的2d随机游走

Question

我在2d中模拟随机游走，周期性边界。我的代码如下：

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

/**
*creates the environment in the form of a matrix of ones and zeros, random walk
*/

#define ROWS 3
#define COLS 3
#define MOVES 1
#define DIRECTIONS 4

int main(void)
{
    srand(time(NULL)); //seed for the random number generator
    int array[ROWS][COLS]; //array for the environment
    int x, y; //row and column for loop purposes
    int min = 0; //min number in the array
    int max = 1; // max number in the array

    for(x = 0; x < ROWS; x++) //loop to fill array
        {
            for(y = 0; y < COLS; y++)
            {
                array[x][y] = min + rand() % (max - min + 1);
                printf("%d", array[x][y]);
            }
            printf("\n");
        }

    int steps = 0; //step counter
    int direction; //direction will be chosen at random

    int i = rand() % ROWS;  //Assign start position row
    int j = rand() % COLS;  //Assign start position column
    printf("initial position: %d %d \n", i, j);

    while (steps < MOVES)
        {
            direction = rand() % DIRECTIONS; // 0 = N, 1 = S, 2 = E, 3 = W
            printf("direction: %d \n", direction);
            switch (direction) 
                {
                    case 0: // north
                        i = ((i - 1) % ROWS); 
                    break;

                    case 1: // south
                        i = ((i + 1) % ROWS);
                    break; 

                    case 2: // east
                        j = ((j + 1) % COLS);
                    break;

                    case 3: // west
                        j = ((j - 1) % COLS);
                    break; 
                }
                printf("new position: %d %d \n", i, j);

            steps++; //update step counter
            printf("number of steps: %d \n", steps);    
        }

    return 0;
}

当我获得方向S或E时，边界条件正常。初始位置1 2的E的结果是新位置1 0.但是如果我得到位置N或W，则边界条件不起作用。初始位置为0 1的N的结果是新位置-1 1，应该是2 1.如何修复我的代码？谢谢。