write the code in C++

sort.txt

161 8092 4548 2868 8740 3809 3638 5582 3195 1422 7161 665 6247 8171 6092 589 6345 8874 3711 8520 6001 6221 7180 213 25 8755 3374 2772 2476 7159 7659 2637 6251 559 46 3867 5422 613 8672 5868 4612 1542 6141 7789 1683 1904 5122 1169 7781 5909 6830 7057 5051 16 2551 8647 2119 3143 2968 7889 1833 715 377 7321 2647 6775 8540 5421 7389 5564 8642 353 7107 3135 8142 8790 2391 4265 960 1172 7526 5142 5582 3577 2510 5485 576 4630 8628 3544 871 7813 1611 7600 6135 1610 2728 5675 4384 7469 8592 4026 7822 6699 7161 4316 3841 6905 5933 2153 8077 4459 4647 2011 8036 7158 7496 5965 140 7125 509 7363 5938 8473 5964 425 1083 6044 3453 5467 4513 3045 493 687 7096 5007 5003 1937 264 1937 4091 8341 6396 8738 7705 2785 4248 6201 6102 4388 1678 6611 2752 7617 3436 6068 5394 4520 3112 8847 987 4977 2892 7833 5664 988 1192 1667 278 1456 956 4369 7149 4705 1459 5854 4842 5708 408 1944 7448 2086 5907 7552 703 344 4620 6098 4864 7732 3297 3203 1061 3542 8388 6725 1882 6932 5745 2160 8388 6701 3881 3890 8758 5341 7096 4600 8401 7504 6544 6849 591 804 5402 7646 1148 7374 2096 3364 3459 5394 6567 4520 8936 3308 2246 8170 1240 5343

6. (20 marks) Merge sort implementation. (12 out of 20 marks) Please implement the merge sort algorithm and sort all data stored in the file sort.txt. Print the sorted items to show that your program can work correctly. You may use the following code to read values from the file sort.txt #include a. ifstream input("sort.txt") int number; while (input >> number) v.push_back (number); input.close) b. (4 out of 20 marks) Please prove the time complexity of the merge sort algorithm is O(Nlog2N). (4 out of20 marks) Please indicate if the merge sort you implement is stable. How many auxiliary memory spaces are required during the merge sort algorithm? c