********************************************************************** BRONZE PROBLEMS ********************************************************************** Three problems numbered 11 through 13 ********************************************************************** Problem 11: Bookshelf [Neal Wu, 2007] Farmer John recently bought a bookshelf for cow library, but the shelf is getting filled up quite quickly, and now the only available space is at the top. Each of the N cows (1 <= N <= 20,000) has some height of H_i (1 <= H_i <= 10,000) and a total height summed across all N cows of S. The bookshelf has a height of B (1 <= B <= S < 2,000,000,007). To reach the top of the bookshelf taller than the tallest cow, one or more of the cows can stand on top of each other in a stack, so that their total height is the sum of each of their individual heights. This total height must be no less than the height of the bookshelf. Since more cows than necessary in the stack can be dangerous, your job is to find the set of cows that produces a stack of the smallest number of cows possible such that the stack can reach the bookshelf. PROBLEM NAME: shelf INPUT FORMAT: * Line 1: Two space-separated integers: N and B * Lines 2..N+1: Line i+1 contains a single integer: H_i SAMPLE INPUT (file shelf.in): 6 40 6 18 11 13 19 11 INPUT DETAILS: Six cows; bookshelf height 40. Cow heights fall in the range 6..19. OUTPUT FORMAT: * Line 1: A single integer representing the size of the smallest set of cows that can reach the bookshelf. SAMPLE OUTPUT (file shelf.out): 3 OUTPUT DETAILS: One way to reach 40 with 3 cows is 18+11+13; many others exist ********************************************************************** Problem 12: Bookshelf 2 [Neal Wu, 2007] Farmer John recently bought another bookshelf for the cow library, but the shelf is getting filled up quite quickly, and now the only available space is at the top. FJ has N cows (1 <= N <= 20) each with some height of H_i (1 <= H_i <= 1,000,000 - these are very tall cows). The bookshelf has a height of B (1 <= B <= S, where S is the sum of the heights of all cows). To reach the top of the bookshelf, one or more of the cows can stand on top of each other in a stack, so that their total height is the sum of each of their individual heights. This total height must be no less than the height of the bookshelf in order for the cows to reach the top. Since a taller stack of cows than necessary can be dangerous, your job is to find the set of cows that produces a stack of the smallest height possible such that the stack can reach the bookshelf. Your program should print the minimal 'excess' height between the optimal stack of cows and the bookshelf. PROBLEM NAME: shelf2 INPUT FORMAT: * Line 1: Two space-separated integers: N and B * Lines 2..N+1: Line i+1 contains a single integer: H_i SAMPLE INPUT (file shelf2.in): 5 16 3 1 3 5 6 OUTPUT FORMAT: * Line 1: A single integer representing the (non-negative) difference between the total height of the optimal set of cows and the height of the shelf. SAMPLE OUTPUT (file shelf2.out): 1 OUTPUT DETAILS: Here we use cows 1, 3, 4, and 5, for a total height of 3 + 3 + 5 + 6 = 17. It is not possible to obtain a total height of 16, so the answer is 1. ********************************************************************** Problem 13: Card Stacking [Jeffrey Wang, 2007] Bessie is playing a card game with her N-1 (2 <= N <= 100) cow friends using a deck with K (N <= K <= 100,000; K is a multiple of N) cards. The deck contains M = K/N "good" cards and K-M "bad" cards. Bessie is the dealer and, naturally, wants to deal herself all of the "good" cards. She loves winning. Her friends suspect that she will cheat, though, so they devise a dealing system in an attempt to prevent Bessie from cheating. They tell her to deal as follows: 1. Start by dealing the card on the top of the deck to the cow to her right 2. Every time she deals a card, she must place the next P (1 <= P <= 10) cards on the bottom of the deck; and 3. Continue dealing in this manner to each player sequentially in a counterclockwise manner Bessie, desperate to win, asks you to help her figure out where she should put the "good" cards so that she gets all of them. Notationally, the top card is card #1, next card is #2, and so on. PROBLEM NAME: cheat INPUT FORMAT: * Line 1: Three space-separated integers: N, K, and P SAMPLE INPUT (file cheat.in): 3 9 2 INPUT DETAILS: Bessie is playing cards with two cow friends and a deck of 9 cards. She must place two cards on the bottom of the deck each time she deals one. OUTPUT FORMAT: * Lines 1..M: Positions from top in ascending order in which Bessie should place "good" cards, such that when dealt, Bessie will obtain all good cards. SAMPLE OUTPUT (file cheat.out): 3 7 8 OUTPUT DETAILS: Bessie should put the "good" cards in positions 3, 7, and 8. The cards will be dealt as follows; the card numbers are "position in original deck": Card Deck P1 P2 Bessie Initial configuration 1 2 3 4 5 6 7 8 9 - - - - - - - - - Deal top card [1] to Player 1 2 3 4 5 6 7 8 9 1 - - - - - - - - Top card to bottom (#1 of 2) 3 4 5 6 7 8 9 2 1 - - - - - - - - Top card to bottom (#2 of 2) 4 5 6 7 8 9 2 3 1 - - - - - - - - Deal top card [4] to Player 2 5 6 7 8 9 2 3 1 - - 4 - - - - - Top card to bottom (#1 of 2) 6 7 8 9 2 3 5 1 - - 4 - - - - - Top card to bottom (#2 of 2) 7 8 9 2 3 5 6 1 - - 4 - - - - - Deal top card [7] to Bessie 8 9 2 3 5 6 1 - - 4 - - 7 - - Top card to bottom (#1 of 2) 9 2 3 5 6 8 1 - - 4 - - 7 - - Top card to bottom (#2 of 2) 2 3 5 6 8 9 1 - - 4 - - 7 - - Deal top card [2] to Player 1 3 5 6 8 9 1 2 - 4 - - 7 - - Top card to bottom (#1 of 2) 5 6 8 9 3 1 2 - 4 - - 7 - - Top card to bottom (#2 of 2) 6 8 9 3 5 1 2 - 4 - - 7 - - Deal top card [6] to Player 2 8 9 3 5 1 2 - 4 6 - 7 - - Top card to bottom (#1 of 2) 9 3 5 8 1 2 - 4 6 - 7 - - Top card to bottom (#2 of 2) 3 5 8 9 1 2 - 4 6 - 7 - - Deal top card [3] to Bessie 5 8 9 1 2 - 4 6 - 7 3 - Top card to bottom (#1 of 2) 8 9 5 1 2 - 4 6 - 7 3 - Top card to bottom (#2 of 2) 9 5 8 1 2 - 4 6 - 7 3 - Deal top card [9] to Player 1 5 8 1 2 9 4 6 - 7 3 - Top card to bottom (#1 of 2) 8 5 1 2 9 4 6 - 7 3 - Top card to bottom (#2 of 2) 5 8 1 2 9 4 6 - 7 3 - Deal top card [5] to Player 2 8 1 2 9 4 6 5 7 3 - Top card to bottom (#1 of 2) 8 1 2 9 4 6 5 7 3 - Top card to bottom (#1 of 2) 8 1 2 9 4 6 5 7 3 - Deal top card [8] to Bessie - 1 2 9 4 6 5 7 3 8 Bessie will end up with the "good cards" that have been placed in positions 3, 7, and 8 in the original deck. **********************************************************************