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authorjack <[email protected]>2024-06-14 13:13:15 -0600
committerjack <[email protected]>2024-06-14 13:13:15 -0600
commitd343a3b18dbaca9297d4f7b2280c4a16f0a5c8aa (patch)
tree96df922dae2a5073d9a50ea70c7aae6aa37e3ebe /soup_servings.c
downloadleetcode-d343a3b18dbaca9297d4f7b2280c4a16f0a5c8aa.tar.gz
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+// 808. Soup Servings
+#include <stdio.h>
+#include <stdlib.h>
+
+/*
+ * 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
+}