66 lines
2.2 KiB
Java
66 lines
2.2 KiB
Java
/*
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* The MIT License (MIT)
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*
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* Copyright © 2020 xrv <xrv@live.com>
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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package io.github.ehlxr.algorithm.dp;
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/**
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* 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
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* <p>
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* 图解 https://cdn.jsdelivr.net/gh/0vo/oss/images/dp.jpg
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*
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* @author ehlxr
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* @since 2021-10-31 22:46.
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*/
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public class FindMaxSum {
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public static int recOpt(int[] arr, int i) {
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if (i == 0) {
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return arr[0];
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} else if (i == 1) {
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return Math.max(arr[0], arr[1]);
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} else {
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int a = recOpt(arr, i - 2) + arr[i];
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int b = recOpt(arr, i - 1);
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return Math.max(a, b);
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}
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}
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public static int dpOpt(int[] arr) {
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int[] opt = new int[arr.length];
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opt[0] = arr[0];
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opt[1] = Math.max(arr[0], arr[1]);
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for (int i = 2; i < opt.length; i++) {
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int a = opt[i - 2] + arr[i];
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int b = opt[i - 1];
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opt[i] = Math.max(a, b);
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}
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return opt[arr.length - 1];
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}
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public static void main(String[] args) {
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int[] arr = {4, 1, 1, 9, 1};
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System.out.println(dpOpt(arr));
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System.out.println(recOpt(arr, arr.length - 1));
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}
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}
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