ACM程序设计竞赛备战资料：0-1背包问题详解

The ACM programming contest example questions include problems related to the 0-1 knapsack problem. In the 0/1 knapsack problem, the goal is to pack a knapsack of capacity c with selected items from n items, each with a weight wi and a value pi. The total weight of the items in the knapsack cannot exceed the knapsack's capacity, and the objective is to maximize the total value of the items packed. The program for this problem could be structured as follows: ```python def knapsack_01(c, n, weights, values): dp = [[0 for _ in range(c+1)] for _ in range(n+1)] for i in range(1, n+1): for w in range(1, c+1): if weights[i-1] <= w: dp[i][w] = max(dp[i-1][w], dp[i-1][w-weights[i-1]] + values[i-1]) else: dp[i][w] = dp[i-1][w] return dp[n][c] # Example usage capacity = 10 n_items = 4 item_weights = [2, 3, 4, 5] item_values = [3, 4, 5, 6] result = knapsack_01(capacity, n_items, item_weights, item_values) print("Maximum value that can be achieved:", result) ``` This program uses a dynamic programming approach to solve the 0-1 knapsack problem by building a 2D table `dp` where `dp[i][w]` represents the maximum value that can be achieved with the first `i` items and a knapsack of capacity `w`. The solution can then be found at `dp[n][c]`, where `n` is the number of items and `c` is the knapsack's capacity. By using this program, one can efficiently solve the 0-1 knapsack problem and find the optimal solution to packing a knapsack with a given set of items, weights, and values. This type of problem is commonly encountered in ACM programming contests and requires a solid understanding of dynamic programming and algorithmic optimization techniques.