// 808. Soup Servings #include #include /* * there are two types of soup: type a, and type b. initially, we have 'n' ml of * each type of soup. there are four kinds of operations: * 1. serve 100 ml of soup a and 0ml of soup b * 2. serve 75ml of soup a and 25ml of soup b * 3. serve 50ml of soup a and 50ml of soup b * 4. serve 25ml of soup a and 75ml of soup b * when we serve some soup, we give it to someone, and we no longer have it. * each turn, we will choose from the four operations with an equal probability * of '0.25'. if the remaining volume of soup is not enough to complete the * operation, we will serve as much as possible. we stop once we no longer have * some quantity of both types of soup. note that we do not have an operation * where all 100 ml's of soup b are used first. return the probability that soup * a will be empty first, plus half the probability that a and b become empty at * the same time. answers within '10^-5' of the actual answer will be accepted. */ double process(int a, int b, double **record) { if (a <= 0 && b <= 0) return 0.5; if (a <= 0) return 1.0; if (b <= 0) return 0; if (record[a][b]) return record[a][b]; record[a][b] = 0.25 * (process(a - 4, b, record) + process(a - 3, b - 1, record) + process(a - 2, b - 2, record) + process(a - 1, b - 3, record)); return record[a][b]; } double soupServings(int n) { double **record = malloc(150 * sizeof(double *)); for (int i = 0; i < 150; i++) record[i] = calloc(150, sizeof(double)); double ans = n >= 3600 ? 1.0 : process((n + 24) / 25, (n + 24) / 25, record); for (int i = 0; i < 150; i++) free(record[i]); free(record); return ans; } int main() { printf("%f\n", soupServings(50)); // expect: 0.625000 printf("%f\n", soupServings(100)); // expect: 0.71875 }