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author | jack <[email protected]> | 2024-06-14 13:13:15 -0600 |
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committer | jack <[email protected]> | 2024-06-14 13:13:15 -0600 |
commit | d343a3b18dbaca9297d4f7b2280c4a16f0a5c8aa (patch) | |
tree | 96df922dae2a5073d9a50ea70c7aae6aa37e3ebe /new_21_game.c | |
download | leetcode-d343a3b18dbaca9297d4f7b2280c4a16f0a5c8aa.tar.gz leetcode-d343a3b18dbaca9297d4f7b2280c4a16f0a5c8aa.zip |
initial
Diffstat (limited to 'new_21_game.c')
-rw-r--r-- | new_21_game.c | 38 |
1 files changed, 38 insertions, 0 deletions
diff --git a/new_21_game.c b/new_21_game.c new file mode 100644 index 0000000..4076f33 --- /dev/null +++ b/new_21_game.c @@ -0,0 +1,38 @@ +// 837. New 21 Game +#include <stdio.h> +#include <stdlib.h> + +/* + * alice plays the following game, loosely based on the card game "21". alice + * starts with 0 points and draws numbers while she has less than 'k' points. + * during each draw, she gains an integer number of points randomly from range + * '[1, max_pts]', where 'max_pts' is an integer. each draw is independent and + * the outcomes have equal posibilities. alice stops drawing numbers when she + * gets 'k' or more points. return the probability that alice has 'n' or fewer + * points. answers within 10^-5 of the actual answer are considered accepted + */ + +double new21Game(int n, int k, int max_pts) { + if (!k || n >= k + max_pts) + return 1.0; + double *dp = malloc((n + 1) * sizeof(double)); + dp[0] = 1.0; + double sum = 1.0, ans = 0.0; + for (int i = 1; i <= n; ++i) { + dp[i] = sum / max_pts; + if (i < k) + sum += dp[i]; + else + ans += dp[i]; + if (i - max_pts >= 0) + sum -= dp[i - max_pts]; + } + return ans; +} + +int main() { + // new21Game(21,17,10); + printf("%f\n", new21Game(10, 1, 10)); // expect: 1.00000 + printf("%f\n", new21Game(6, 1, 10)); // expect: 0.60000 + printf("%f\n", new21Game(21, 17, 10)); // expect: 0.73278 +} |