From 3c8752be704a369a19846c3c1bf21369193f6e6c Mon Sep 17 00:00:00 2001 From: ehlxr Date: Sat, 5 Mar 2022 17:05:21 +0800 Subject: [PATCH] update at 2022-03-05 17:05:21 by ehlxr --- .../github/ehlxr/algorithm/dp/KnapSack3.java | 108 ++++++++++++++++++ .../io/github/ehlxr/algorithm/dp/MinDist.java | 107 +++++++++++++++++ 2 files changed, 215 insertions(+) create mode 100644 budd-common/src/main/java/io/github/ehlxr/algorithm/dp/KnapSack3.java create mode 100644 budd-common/src/main/java/io/github/ehlxr/algorithm/dp/MinDist.java diff --git a/budd-common/src/main/java/io/github/ehlxr/algorithm/dp/KnapSack3.java b/budd-common/src/main/java/io/github/ehlxr/algorithm/dp/KnapSack3.java new file mode 100644 index 0000000..45b85d2 --- /dev/null +++ b/budd-common/src/main/java/io/github/ehlxr/algorithm/dp/KnapSack3.java @@ -0,0 +1,108 @@ +/* + * The MIT License (MIT) + * + * Copyright © 2022 xrv + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in + * all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + * THE SOFTWARE. + */ + +package io.github.ehlxr.algorithm.dp; + +/** + * 对于一组不同重量、不同价值、不可分割的物品，我们选择将某些物品装入背包，在满足背包最大重量限制的前提下，背包中可装入物品的总价值最大是多少呢？ + * + * @author ehlxr + * @since 2022-03-05 14:31. + */ +public class KnapSack3 { + private final int[] weight = {2, 2, 4, 6, 3}; // 物品的重量 + private final int[] value = {3, 4, 8, 9, 6}; // 物品的价值 + private final int n = 5; // 物品个数 + private final int w = 9; // 背包承受的最大重量 + private int maxV = Integer.MIN_VALUE; // 结果放到 maxV 中 + + /** + * 动态规划方式 + * + * @param weight 物品重量 + * @param value 物品的价值 + * @param n: 物品个数 + * @param w: 背包可承载重量 + * @return 最大价值 + */ + public static int knapsack3(int[] weight, int[] value, int n, int w) { + int[][] states = new int[n][w + 1]; + for (int i = 0; i < n; ++i) { // 初始化 states,默认 -1 + for (int j = 0; j < w + 1; ++j) { + states[i][j] = -1; + } + } + states[0][0] = 0; + if (weight[0] <= w) { + states[0][weight[0]] = value[0]; + } + for (int i = 1; i < n; ++i) { // 动态规划,状态转移 + for (int j = 0; j <= w; ++j) { // 不选择第 i 个物品 + if (states[i - 1][j] >= 0) { + // 复制上一层状态 + states[i][j] = states[i - 1][j]; + } + } + // 下面的 j 表示重量 + for (int j = 0; j <= w - weight[i]; ++j) { // 选择第 i 个物品 + if (states[i - 1][j] >= 0) { // 表示上一层存在重量为 j 的状态 + int v = states[i - 1][j] + value[i]; // 上一层重量为 j 的价值 + i 物品的价值 + if (v > states[i][j + weight[i]]) { // states[i][j + weight[i]]：存储当前重量 j + 物品 i 的重量所在位置的价值 + states[i][j + weight[i]] = v; + } + } + } + } + // 找出最大值 + int maxvalue = -1; + for (int j = 0; j <= w; ++j) { + if (states[n - 1][j] > maxvalue) { + maxvalue = states[n - 1][j]; + } + } + return maxvalue; + } + + /** + * 回溯方式 + * + * @param i 第几个物品 + * @param cw 物品的重量 + * @param cv 物品的价值 + */ + public void f(int i, int cw, int cv) { // 调用 f (0, 0, 0) + if (cw == w || i == n) { //cw==w 表示装满了,i==n 表示物品都考察完了 + if (cv > maxV) { + maxV = cv; + } + return; + } + f(i + 1, cw, cv); // 选择不装第 i 个物品 + if (cw + weight[i] <= w) { + f(i + 1, cw + weight[i], cv + value[i]); // 选择装第 i 个物品 + } + } + + +} diff --git a/budd-common/src/main/java/io/github/ehlxr/algorithm/dp/MinDist.java b/budd-common/src/main/java/io/github/ehlxr/algorithm/dp/MinDist.java new file mode 100644 index 0000000..8ebeda9 --- /dev/null +++ b/budd-common/src/main/java/io/github/ehlxr/algorithm/dp/MinDist.java @@ -0,0 +1,107 @@ +/* + * The MIT License (MIT) + * + * Copyright © 2022 xrv + * + * Permission is hereby granted, free of charge, to any person obtaining a copy + * of this software and associated documentation files (the "Software"), to deal + * in the Software without restriction, including without limitation the rights + * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the Software is + * furnished to do so, subject to the following conditions: + * + * The above copyright notice and this permission notice shall be included in + * all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + * THE SOFTWARE. + */ + +package io.github.ehlxr.algorithm.dp; + +/** + * 假设我们有一个 n 乘以 n 的矩阵 w [n][n]。矩阵存储的都是正整数。棋子起始位置在左上角，终止位置在右下角。 + * 我们将棋子从左上角移动到右下角。每次只能向右或者向下移动一位。从左上角到右下角，会有很多不同的路径可以走。 + * 我们把每条路径经过的数字加起来看作路径的长度。那从左上角移动到右下角的最短路径长度是多少呢？ + * + * @author ehlxr + * @since 2022-03-05 16:46. + */ +public class MinDist { + + private final int[][] matrix = {{1, 3, 5, 9}, {2, 1, 3, 4}, {5, 2, 6, 7}, {6, 8, 4, 3}}; + private final int[][] mem = new int[4][4]; + private int minDist = Integer.MAX_VALUE; // 全局变量或者成员变量 + + /** + * 状态转移表法 + */ + public int minDistDP(int[][] matrix, int n) { + int[][] states = new int[n][n]; + int sum = 0; + for (int j = 0; j < n; ++j) { // 初始化states的第一行数据 + sum += matrix[0][j]; + states[0][j] = sum; + } + sum = 0; + for (int i = 0; i < n; ++i) { // 初始化states的第一列数据 + sum += matrix[i][0]; + states[i][0] = sum; + } + for (int i = 1; i < n; ++i) { + for (int j = 1; j < n; ++j) { + states[i][j] = matrix[i][j] + Math.min(states[i][j - 1], states[i - 1][j]); + } + } + return states[n - 1][n - 1]; + } + + /** + * 状态转移方程法 + */ + public int minDist(int i, int j) { // 调用minDist(n-1, n-1); + if (i == 0 && j == 0) { + return matrix[0][0]; + } + // 备忘录，如果计算过，即有数字存在，则直接返回 + if (mem[i][j] > 0) { + return mem[i][j]; + } + int minLeft = Integer.MAX_VALUE; + if (j - 1 >= 0) { + minLeft = minDist(i, j - 1); + } + int minUp = Integer.MAX_VALUE; + if (i - 1 >= 0) { + minUp = minDist(i - 1, j); + } + + int currMinDist = matrix[i][j] + Math.min(minLeft, minUp); + mem[i][j] = currMinDist; + return currMinDist; + } + + /** + * 回溯方式 + */ + public void minDistBacktracing(int i, int j, int dist, int[][] w, int n) { + // 到达了n-1, n-1这个位置了，这里看着有点奇怪哈，你自己举个例子看下 + if (i == n && j == n) { + if (dist < minDist) { + minDist = dist; + } + return; + } + if (i < n) { // 往下走，更新i=i+1, j=j + minDistBacktracing(i + 1, j, dist + w[i][j], w, n); + } + if (j < n) { // 往右走，更新i=i, j=j+1 + minDistBacktracing(i, j + 1, dist + w[i][j], w, n); + } + } +}