add dp

budd-common/src/main/java/io/github/ehlxr/algorithm/DynamicProgramming.java

@@ -0,0 +1,65 @@
+/*
+ * The MIT License (MIT)
+ *
+ * Copyright © 2020 xrv <xrg@live.com>
+ *
+ * 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;
+
+/**
+ * 在一个数组 arr 中，找出一组不相邻的数字，使得最后的和最大
+ *
+ * 图解 https://cdn.jsdelivr.net/gh/0vo/oss/images/dp.jpg
+ *
+ * @author ehlxr
+ * @since 2021-10-31 22:46.
+ */
+public class DynamicProgramming {
+    public static int recOpt(int[] arr, int i) {
+        if (i == 0) {
+            return arr[0];
+        } else if (i == 1) {
+            return Math.max(arr[0], arr[1]);
+        } else {
+            int a = recOpt(arr, i - 2) + arr[i];
+            int b = recOpt(arr, i - 1);
+            return Math.max(a, b);
+        }
+    }
+
+    public static int dpOpt(int[] arr) {
+        int[] opt = new int[arr.length];
+        opt[0] = arr[0];
+        opt[1] = Math.max(arr[0], arr[1]);
+        for (int i = 2; i < opt.length; i++) {
+            int a = opt[i - 2] + arr[i];
+            int b = opt[i - 1];
+            opt[i] = Math.max(a, b);
+        }
+        return opt[arr.length - 1];
+    }
+
+    public static void main(String[] args) {
+        int[] arr = {4, 1, 1, 9, 1};
+        System.out.println(dpOpt(arr));
+        System.out.println(recOpt(arr, arr.length - 1));
+    }
+}