原题链接：

1262. 可被三整除的最大和

https://leetcode.cn/problems/greatest-sum-divisible-by-three/description/

完成情况：

解题思路：

方法一：贪心 + 正向思维

方法二：贪心 + 逆向思维

参考代码：

方法一：贪心 + 正向思维

package LeetCode中等题;import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;public class __1262可被三整除的最大和__贪心_余数分组配对 {public static void main(String[] args) {int nums[] = {3,6,5,1,8};maxSumDivThree(nums);}/**** @param nums* @return*/public static int maxSumDivThree(int[] nums) {//用v_remind[i]来表示余数List<Integer> v_remind [] = new List[3];for (int i=0;i<3;i++){v_remind[i] = new ArrayList<Integer>();}//按余数值进行分组for (int num : nums){v_remind[num % 3].add(num);}Collections.sort(v_remind[1],(a,b)-> b-a);  //自定义Collecctions类的v_remind[1]排序规则Collections.sort(v_remind[2],(a,b)-> b-a);  //自定义Collecctions类的v_remind[2]排序规则int ans = 0;int lb = v_remind[1].size(),lc = v_remind[2].size();//每一个v_remind[1]和一个v_remind[2]，都可以进行匹配为一组//因此，我应该是放任所有的v_remind[0]不去管//然后大小排序好1,2.。。。。。。。//然后每一组1,2就从大到小区合并//同时不能让他们某一组多余值大于%3的余数，因为任何数得余数都一个除以3for(int countB = lb-2;countB <= lb;countB++){if (countB >= 0){for (int countC = lc-2;countC<= lc;countC++){if (countC >=0 && (countB - countC)%3 == 0){ans = Math.max(ans,getSum(v_remind[1],0,countB)+getSum(v_remind[2],0,countC));}}}}return ans+getSum(v_remind[0],0,v_remind[0].size());}/**** @param listRemind* @param start* @param end* @return*/private static int getSum(List<Integer> listRemind, int start, int end) {int sum = 0;for (int i = start;i<end;i++){sum += listRemind.get(i);}return sum;}
}

方法二：贪心 + 逆向思维

package LeetCode中等题;import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;public class __1262可被三整除的最大和__贪心_先取所有的数再按余数对应去除 {/**** @param nums* @return*/public int maxSumDivThree(int[] nums) {//用v_remind[i]来表示余数// 使用 v[0], v[1], v[2] 分别表示 a, b, cList<Integer> v_remind[] = new List[3];for (int i=0;i<3;i++){v_remind[i] = new ArrayList<Integer>();}//按余数值进行分组for (int num : nums){v_remind[num % 3].add(num);}Collections.sort(v_remind[1],(a, b)-> b-a);  //自定义Collecctions类的v_remind[1]排序规则Collections.sort(v_remind[2],(a,b)-> b-a);  //自定义Collecctions类的v_remind[2]排序规则int total = Arrays.stream(nums).sum();int remove = Integer.MAX_VALUE;if (total % 3 == 0){remove = 0;} else if (total % 3 == 1) {if (v_remind[1].size() >= 1){remove = Math.min(remove,v_remind[1].get(v_remind[1].size() - 1));}if (v_remind[2].size() >= 2){remove = Math.min(remove,v_remind[2].get(v_remind[2].size() - 2) + v_remind[2].get(v_remind[2].size() - 1) );}}else {if (v_remind[1].size() >= 2){remove = Math.min(remove,v_remind[1].get(v_remind[1].size() - 2)+v_remind[1].get(v_remind[1].size() - 1));}if (v_remind[2].size() >= 1){remove = Math.min(remove,v_remind[2].get(v_remind[2].size() - 1));}}return total - remove;}
}