HBC24722致两千年后的你,gcd与exgcd,数学,快速傅里叶变换（FFT）/快速数论变换（NTT）/快速沃尔什变换（FWT）,数论[USACO 2010 Feb S]Chocolate Buying题解 （bessieandtheherdlove）

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Bessie and the herd love chocolate so Farmer John is buying them some.

Bessie and the herd love chocolate so Farmer John is buying them some. The Bovine Chocolate Store features N (1 <= N <= 100,000) kinds of chocolate in essentially unlimited quantities. Each type i of chocolate has price P_i P i ​ (1 <= P_i P i ​ <= 10^{18} 10 18 ) per piece and there are C_i C i ​ (1 <= C_i C i ​ <= 10^{18} 10 18 ) cows that want that type of chocolate. Farmer John has a budget of B (1 <= B <= 10^{18} 10 18 ) that he can spend on chocolates for the cows. What is the maximum number of cows that he can satisfy? All cows only want one type of chocolate, and will be satisfied only by that type. Consider an example where FJ has 50 to spend on 5 different types of chocolate. A total of eleven cows have various chocolate preferences: Consider an example where FJ has 50 to spend on 5 different types of chocolate. A total of eleven cows have various chocolate preferences: Chocolate_Type Per_Chocolate_Cost Cows_preferring_this_type 1 5 3 2 1 1 3 10 4 4 7 2 5 60 1 Obviously, FJ can't purchase chocolate type 5, since he doesn't have enough money. Even if it cost only 50, it's a counterproductive purchase since only one cow would be satisfied. Looking at the chocolates start at the less expensive ones, he can * purchase 1 chocolate of type #2 for 1 x 1 leaving 50- 1=49, then * purchase 3 chocolate of type #1 for 3 x 5 leaving 49-15=34, then * purchase 2 chocolate of type #4 for 2 x 7 leaving 34-14=20, then * purchase 2 chocolate of type #3 for 2 x 10 leaving 20-20= 0. He would thus satisfy 1 + 3 + 2 + 2 = 8 cows.

标签： HBC24722致两千年后的你 gcd与exgcd 数学 快速傅里叶变换（FFT）/快速数论变换（NTT）/快速沃尔什变换（FWT） 数论[USACO 2010 Feb S]Chocolate Buying题解