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// 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
}
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