我的实现有一个越界错误 mergeSort ，我不知道为什么。这是确切的错误消息： Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: Index 1 out of bounds for length 1" 以下是我对 mergeSort :

public static void mergeSort(int[] arr, int n) {
    if (n < 2) {
        return;
    }

    int mid_index = n / 2; 
    int[] left = new int[mid_index];
    int[] right = new int[n - mid_index];

    for (int i = 0; i < mid_index; i++) {
        left[i] = arr[i];
    }

    for (int i = mid_index; i < n; i++) {
        right[i - mid_index] = arr[i];
    }

    mergeSort(left, mid_index);
    mergeSort(right, n - mid_index);
    merge(arr, left, right, mid_index, n - mid_index);
}

public static void merge(int[] arr, int[] left, int[] right, int left_length, int right_length) {
    int i = 0;
    int j = 0; 
    int k = 0; 

    while (j < left_length && k < right_length) {
        if (left[i] < right[j]) {
            arr[k] = left[i];
            k++;
            i++;
        } else {
            arr[k] = right[j];
            k++;
            j++;
        }
    }

    while (j < left_length) {
        arr[k] = left[i];
        k++;
        i++;
    }

    while (i < right_length) {
        arr[k] = right[j];
        k++;
        j++;
    }
}