diff --git a/problems/背包理论基础01背包-1.md b/problems/背包理论基础01背包-1.md index ee19e53d..8f4ca2d4 100644 --- a/problems/背包理论基础01背包-1.md +++ b/problems/背包理论基础01背包-1.md @@ -271,39 +271,64 @@ int main() { ### java ```java +public class BagProblem { public static void main(String[] args) { - int[] weight = {1, 3, 4}; - int[] value = {15, 20, 30}; - int bagsize = 4; - testweightbagproblem(weight, value, bagsize); + int[] weight = {1,3,4}; + int[] value = {15,20,30}; + int bagSize = 4; + testWeightBagProblem(weight,value,bagSize); } - public static void testweightbagproblem(int[] weight, int[] value, int bagsize){ - int wlen = weight.length, value0 = 0; - //定义dp数组:dp[i][j]表示背包容量为j时,前i个物品能获得的最大价值 - int[][] dp = new int[wlen + 1][bagsize + 1]; - //初始化:背包容量为0时,能获得的价值都为0 - for (int i = 0; i <= wlen; i++){ - dp[i][0] = value0; + /** + * 动态规划获得结果 + * @param weight 物品的重量 + * @param value 物品的价值 + * @param bagSize 背包的容量 + */ + public static void testWeightBagProblem(int[] weight, int[] value, int bagSize){ + + // 创建dp数组 + int goods = weight.length; // 获取物品的数量 + int[][] dp = new int[goods][bagSize + 1]; + + // 初始化dp数组 + // 创建数组后,其中默认的值就是0 + for (int j = weight[0]; j <= bagSize; j++) { + dp[0][j] = value[0]; } - //遍历顺序:先遍历物品,再遍历背包容量 - for (int i = 1; i <= wlen; i++){ - for (int j = 1; j <= bagsize; j++){ - if (j < weight[i - 1]){ - dp[i][j] = dp[i - 1][j]; - }else{ - dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - weight[i - 1]] + value[i - 1]); + + // 填充dp数组 + for (int i = 1; i < weight.length; i++) { + for (int j = 1; j <= bagSize; j++) { + if (j < weight[i]) { + /** + * 当前背包的容量都没有当前物品i大的时候,是不放物品i的 + * 那么前i-1个物品能放下的最大价值就是当前情况的最大价值 + */ + dp[i][j] = dp[i-1][j]; + } else { + /** + * 当前背包的容量可以放下物品i + * 那么此时分两种情况: + * 1、不放物品i + * 2、放物品i + * 比较这两种情况下,哪种背包中物品的最大价值最大 + */ + dp[i][j] = Math.max(dp[i-1][j] , dp[i-1][j-weight[i]] + value[i]); } } } - //打印dp数组 - for (int i = 0; i <= wlen; i++){ - for (int j = 0; j <= bagsize; j++){ - System.out.print(dp[i][j] + " "); + + // 打印dp数组 + for (int i = 0; i < goods; i++) { + for (int j = 0; j <= bagSize; j++) { + System.out.print(dp[i][j] + "\t"); } - System.out.print("\n"); + System.out.println("\n"); } } +} + ``` ### python