// 837. New 21 Game #include #include /* * 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 }