3Sum

Given an array S of n integers, are there elements a, b, c in S such that a + b + c = 0? Find all unique triplets in the array which gives the sum of zero.

Note:
Elements in a triplet (a,b,c) must be in non-descending order. (ie, a ≤ b ≤ c)
The solution set must not contain duplicate triplets.
For example, given array S = {-1 0 1 2 -1 -4},

A solution set is:
(-1, 0, 1)
(-1, -1, 2)

典型的回溯法

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;


public class Demo1 {
    //保存最终结果
    List<List<Integer>> result ;
    //保存每一个解
    List<Integer> solu ;
    //传入的数据
    int[] data ;
    //目标值
    int target ;

    public Demo1(int[] data,int target){
        this.data = data ;
        this.target = target ;
    }
    public List<List<Integer>> combinationSum(int[] a,int n){
        result = new ArrayList() ;
        Arrays.sort(data) ;
        getCombination(a,0,n) ;
        return result ;
    }

    public void getCombination(int[] a , int k , int n){
        List<Integer> candidates = new ArrayList() ;
        if(is_a_solution(a,k,n)){
            process_solution(a,k,n) ;
        }else{
            if(k<n){
                k = k + 1 ;
                construct_candidates(a,k,n,candidates) ;
                for(int i=0;i<candidates.size();i++){
                    a[k] = candidates.get(i) ;
                    getCombination(a,k,n) ;
                }

            }
        }
    }

    //a是解向量空间从1下标开始
    //candidates是候选解空间从0开始
    //k从1开始
    //n为3
    void construct_candidates(int a[],int k,int n,List<Integer> candidates){
        int index ;
        if(k==1){
            index = 0 ;
        }else{
            index = a[k-1] ;
        }
        for(int j=index+1;j<=data.length;j++){
            int number = 0 ;
            while(j+1<=data.length&&data[j-1]==data[j]){
                j++ ;
                number ++ ;
            }
            candidates.add(j-number) ;
        }

    }

    boolean is_a_solution(int[] a,int k,int n){
        int sum = 0 ;
        if(k==n){
            for(int i=1;i<=k;i++){
                sum = sum + data[a[i]-1] ;
            }
            if(sum == target){
                return true ;
            }
        }

        return false ;
    }

    void process_solution(int[] a,int k,int target){
        solu = new ArrayList() ;
        for(int i=1;i<=k;i++){
            solu.add(data[a[i]-1]) ;
        }
        result.add(solu) ;
    }

    public static void main(String args[]){

        int[] candidates = {-1,0,1,2,-1,-4};

        int n = 3 ;

        int[] a = new int[n+1] ;

        Demo1 s = new Demo1(candidates,0) ;

        List<List<Integer>> list = s.combinationSum(a,n) ;

        for(List<Integer> l : list){
            for(Integer i : l){
                System.out.print(i+" ");
            }
            System.out.println();
        }
    }
}

但是代码不是很优美，所以改进如下。

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Solution {
    List<List<Integer>> result;
    List<Integer> solu;

    public List<List<Integer>> combinationSum(int[] candidates, int target) {
        result = new ArrayList();
        solu = new ArrayList();
        Arrays.sort(candidates);
        getCombination(candidates, target, 0, 0);
        return result;
    }

    public void getCombination(int[] candidates, int target, int sum, int level) {
        if(sum>target||solu.size()>3)
            return ;
        if (solu.size()==3&&sum == target) {
            result.add(new ArrayList(solu));
            return;
        }
        for (int i = level; i < candidates.length; i++) {
            sum += candidates[i];
            solu.add(candidates[i]);
            getCombination(candidates, target, sum, i + 1);
            solu.remove(solu.size() - 1);
            sum -= candidates[i];
            while(i+1 < candidates.length&&candidates[i]==candidates[i+1]){
                i++;
            }

        }
    }

    public static void main(String args[]){
        Solution s = new Solution() ;
        int[] candidates = {-1,0,1,2,-1,-4};
        List<List<Integer>> list = s.combinationSum(candidates, 0) ;
        for(List<Integer> l : list){
            for(Integer i : l){
                System.out.print(i+" ");
            }
            System.out.println();
        }
    }
}