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Diffstat (limited to 'other/soup_servings.cpp')
-rw-r--r-- | other/soup_servings.cpp | 54 |
1 files changed, 54 insertions, 0 deletions
diff --git a/other/soup_servings.cpp b/other/soup_servings.cpp new file mode 100644 index 0000000..1733c21 --- /dev/null +++ b/other/soup_servings.cpp @@ -0,0 +1,54 @@ +// 808. Soup Servings +#include "leetcode.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. + */ + +class Solution { + unordered_map<int, unordered_map<int, double>> store; + double helper(int a, int b) { + if (!a && b) + return 1; + else if (!a && !b) + return 0.5; + else if (a && !b) + return 0; + if (store[a][b]) + return store[a][b]; + double prob = 0; + prob += 0.25 * helper(a - min(a, 100), b); + prob += 0.25 * helper(a - min(a, 75), b - min(b, 25)); + prob += 0.25 * helper(a - min(a, 50), b - min(b, 50)); + prob += 0.25 * helper(a - min(a, 25), b - min(b, 75)); + store[a][b] = prob; + return prob; + } + +public: + double soupServings(int n) { + if (n >= 5000) + return 1.0; + else + return helper(n, n); + } +}; + +int main() { + Solution obj; + printf("%f\n", obj.soupServings(50)); // expect: 0.62500 + printf("%f\n", obj.soupServings(100)); // expect: 0.71875 +} |