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1991 | Pinely Round 4 (Div. 1 + Div. 2) | FINISHED | False | 10800 | 15002663 | July 28, 2024, 2:35 p.m. |
Solved$ |
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( 514 ) | H | Prime Split Game | PROGRAMMING | fft games math number theory |
B'Alice and Bob are playing a game with n piles of stones, where the i -th pile has a_i stones. Players take turns making moves, with Alice going first. On each move, the player does the following three-step process: The player who is unable to make a move loses. Determine who will win if both players play optimally. Each test contains multiple test cases. The first line contains a single integer t ( 1 <= t <= 10^4 ) -- the number of test cases. The description of test cases follows. The first line of each test case contains a single integer n ( 2 <= n <= 2 cdot 10^5 ) -- the number of piles of stones. The second line of each test case contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 2 cdot 10^5 ) -- the number of stones in the piles. It is guaranteed that the sum of n over all test cases does not exceed 2 cdot 10^5 . For each test case, output "Alice" (without quotes) if Alice wins and "Bob" (without quotes) otherwise. You can output each letter in any case (upper or lower). For example, the strings "alIcE", "Alice", and "alice" will all be considered identical. In the first test case, there are 2 piles of stones with 2 and 1 stones respectively. Since neither 1 nor 2 can be split into two prime numbers, Alice cannot make a move, so Bob wins. In the second test case, there are 3 piles of stones with 3 , 5 , and 7 stones respectively. Alice can choose k = 1 , remove the pile of 7 stones, and then split the pile of 5 stones into two piles of prime numbers of stones, 2 and 3 . Then, the piles consist of 3 piles of stones with 3 , 2 , and 3 stones respectively, leaving Bob with no valid moves, so Alice wins. In the third test case, there are 4 piles of stones with 4 , 6 , 8 , and 10 stones respectively. Alice can choose k = 2 , removing two pil'... |
Video Tutorial |
Submission Id |
Author(s) |
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Language |
Test Set |
Tests Passed |
Time taken (ms) |
Memory Consumed (bytes) |
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Rating |
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273237872 | jdurie | H | July 28, 2024, 7:16 p.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 124 | 2048000 | ||
273220804 | Szoboszlai10 | H | July 28, 2024, 5:15 p.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 202 | 3993600 | ||
273281579 | K_M_offical | H | July 29, 2024, 5:42 a.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 265 | 819200 | ||
273237245 | shilpabanerjee50 | H | July 28, 2024, 7:11 p.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 296 | 819200 | ||
273248170 | Noobish_Monk | H | July 28, 2024, 9:35 p.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 327 | 12492800 | ||
273226512 | hank55663 | H | July 28, 2024, 5:30 p.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 374 | 12902400 | ||
273270670 | Hanghang007 | H | July 29, 2024, 3:36 a.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 406 | 307200 | ||
273273613 | wzc_IOI_czw | H | July 29, 2024, 4:10 a.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 843 | 15360000 | ||
273263599 | Sparkle_Twilight | H | July 29, 2024, 2:14 a.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 1187 | 51507200 | ||
273229115 | dreamoon_love_AA | H | July 28, 2024, 5:34 p.m. | OK | C++17 (GCC 7-32) | TESTS | 12 | 1484 | 2457600 | ||
273240528 | Agreb | H | July 28, 2024, 7:43 p.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 93 | 3276800 | ||
273278298 | zwh2008 | H | July 29, 2024, 5:06 a.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 108 | 1945600 | ||
273272275 | xvzhiming | H | July 29, 2024, 3:55 a.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 109 | 3379200 | ||
273241197 | orz | H | July 28, 2024, 7:51 p.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 124 | 2560000 | ||
273250616 | maxplus | H | July 28, 2024, 10:21 p.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 139 | 614400 | ||
273249423 | Mangooste | H | July 28, 2024, 9:58 p.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 186 | 7577600 | ||
273257689 | Richard1211 | H | July 29, 2024, 12:57 a.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 187 | 33075200 | ||
273252915 | jiangbowen_ | H | July 28, 2024, 11:09 p.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 202 | 3993600 | ||
273226666 | Ormlis | H | July 28, 2024, 5:30 p.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 202 | 20070400 | ||
273251605 | skittles1412 | H | July 28, 2024, 10:41 p.m. | OK | C++20 (GCC 13-64) | TESTS | 12 | 234 | 0 |
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