4 Sum
19% Accepted
Given an array S of n integers, are there elements a, b, c, and d in S such that a + b + c + d = target?
Find all unique quadruplets in the array which gives the sum of target.
Have you met this question in a real interview? Yes
Example
For example, given array S = {1 0 -1 0 -2 2}, and target = 0. A solution set is:
(-1, 0, 0, 1)
(-2, -1, 1, 2)
(-2, 0, 0, 2)
Note
Elements in a quadruplet (a,b,c,d) must be in non-descending order. (ie, a ≤ b ≤ c ≤ d)
The solution set must not contain duplicate quadruplets.
Tags Expand
- Two Pointers
- Sort
- Hash Table
- Array
思路
- O(n3)的话，就按照3 sum的思路就行
- 也有使用hashmap把一对数的和存起来的，变成two sum,时间复杂度变成O(n2) 最坏情况的是o(n3)
O(n3)
public class Solution {
/**
* @param numbers : Give an array numbersbers of n integer
* @param target : you need to find four elements that's sum of target
* @return : Find all unique quadruplets in the array which gives the sum of
* zero.
*/
public ArrayList<ArrayList<Integer>> fourSum(int[] numbers, int target) {
ArrayList<ArrayList<Integer>> res = new ArrayList<ArrayList<Integer>>();
if (numbers == null || numbers.length < 3 ) {
return res;
}
Arrays.sort(numbers);
for (int i = 0; i < numbers.length - 3; i++) {
if (i != 0 && numbers[i] == numbers[i - 1]) {
continue;
}
for (int j = i + 1; j < numbers.length - 2; j++) {
// if (j != 1 && numbers[j] == numbers[j - 1]) {
// continue;
// }
int find = target - numbers[i] - numbers[j];
int start = j + 1;
int end = numbers.length - 1;
while (start < end) {
ArrayList set = new ArrayList();
if (numbers[start] + numbers[end] > find) {
end--;
} else if (numbers[start] + numbers[end] < find) {
start++;
} else {
set.add(numbers[i]);
set.add(numbers[j]);
set.add(numbers[start]);
set.add(numbers[end]);
if(!res.contains(set)){
res.add(set);
}
start++;
end--;
while (start < end && numbers[start] == numbers[start - 1]){
start++;
}
while (start < end && numbers[end] == numbers[end + 1]) {
end--;
}
}
}
}
}
return res;
}
}
O(n2) 做法
- 测试结果与 答案一模一样,就是在Lintcode上未能通过 不知原因
- 尾部还添加了ArrayList
public class Solution {
/**
* @param numbers : Give an array numbersbers of n integer
* @param target : you need to find four elements that's sum of target
* @return : Find all unique quadruplets in the array which gives the sum of
* zero.
*/
private class Pair {
Integer x;
Integer y;
Pair(int x, int y) {
this.x = x;
this.y = y;
}
// @Override
// public int hashCode(){
// return this.x.hashCode() + this.y.hashCode();
// }
// @Override
// public boolean equals(Object d) {
// if (!(d instanceof Pair)) {
// return false;
// }
// Pair p = (Pair)d;
// return (this.x == p.x) && (this.y == p.y);
// }
}
public ArrayList<ArrayList<Integer>> fourSum(int[] numbers, int target) {
/* your code */
if (numbers == null || numbers.length < 3) {
return new ArrayList<ArrayList<Integer>>();
}
ArrayList<ArrayList<Integer>> result = new ArrayList<ArrayList<Integer>>();
HashMap<Pair, Integer> map = new HashMap<Pair, Integer>();
int size = numbers.length;
Arrays.sort(numbers);
for (int i = 1; i < size; i++) {
for (int j = 0; j < i; j++) {
Pair pair = new Pair(i, j);
map.put(pair, numbers[i] + numbers[j]);
}
}
for (Map.Entry<Pair, Integer> entry : map.entrySet()) {
Pair pair = entry.getKey();
int sum = entry.getValue();
int index1 = pair.x;
int index2 = pair.y;
int newTarget = target - sum;
int start = 0;
int end = size - 1;
while (start < end) {
ArrayList<Integer> list = new ArrayList<Integer>();
if (start == index1 || start == index2) {
start++;
continue;
}
if (end == index1 || end == index2) {
end--;
continue;
}
if (numbers[start] + numbers[end] > newTarget) {
end--;
} else if (numbers[start] + numbers[end] < newTarget) {
start++;
} else {
list.add(numbers[index1]);
list.add(numbers[index2]);
list.add(numbers[start]);
list.add(numbers[end]);
Collections.sort(list);
if (!result.contains(list)) {
result.add(list);
}
start++;
end--;
}
}
}
Collections.sort(result, new Comparator<ArrayList<Integer>>() {
public int compare(ArrayList<Integer> o1, ArrayList<Integer> o2) {
int size = o1.size() > o2.size() ? o2.size() : o1.size();
for (int i = 0; i < size; i++) {
if (o1.get(i) != o2.get(i)) {
return o1.get(i).compareTo(o2.get(i));
} else {
continue;
}
}
return o1.get(0).compareTo(o2.get(0));
}
});
return result;
}
}
eclipse测试 与 答案一模一样,就是在Lintcode上未能通过 不知原因
import java.security.KeyStore.Entry;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map;
public class Solution {
/**
* @param str a string
* @return all permutations
*/
static class Pair {
Integer x;
Integer y;
public Pair(int x, int y) {
this.x = x;
this.y = y;
}
// @Override
// public int hashCode(){
// return this.x.hashCode() + this.y.hashCode();
// }
// @Override
// public boolean equals(Object d) {
// if (!(d instanceof Pair)) {
// return false;
// }
// Pair p = (Pair)d;
// return (this.x == p.x) && (this.y == p.y);
// }
}
public static ArrayList<ArrayList<Integer>> fourSum(int[] numbers, int target) {
/* your code */
if (numbers == null || numbers.length < 3) {
return new ArrayList<ArrayList<Integer>>();
}
ArrayList<ArrayList<Integer>> result = new ArrayList<ArrayList<Integer>>();
HashMap<Pair, Integer> map = new HashMap<Pair, Integer>();
int size = numbers.length;
Arrays.sort(numbers);
for (int i = 1; i < size; i++) {
for (int j = 0; j < i; j++) {
Pair pair = new Pair(i, j);
map.put(pair, numbers[i] + numbers[j]);
}
}
for (Map.Entry<Pair, Integer> entry : map.entrySet()) {
Pair pair = entry.getKey();
int sum = entry.getValue();
int index1 = pair.x;
int index2 = pair.y;
int newTarget = target - sum;
int start = 0;
int end = size - 1;
while (start < end) {
ArrayList<Integer> list = new ArrayList<Integer>();
if (start == index1 || start == index2) {
start++;
continue;
}
if (end == index1 || end == index2) {
end--;
continue;
}
if (numbers[start] + numbers[end] > newTarget) {
end--;
} else if (numbers[start] + numbers[end] < newTarget) {
start++;
} else {
list.add(numbers[index1]);
list.add(numbers[index2]);
list.add(numbers[start]);
list.add(numbers[end]);
Collections.sort(list);
if (!result.contains(list)) {
result.add(list);
}
start++;
end--;
}
}
}
Collections.sort(result, new Comparator<ArrayList<Integer>>() {
public int compare(ArrayList<Integer> o1, ArrayList<Integer> o2) {
int size = o1.size() > o2.size() ? o2.size() : o1.size();
for (int i = 0; i < size; i++) {
if (o1.get(i) != o2.get(i)) {
return o1.get(i).compareTo(o2.get(i));
} else {
continue;
}
}
return o1.get(0).compareTo(o2.get(0));
}
});
return result;
}
public static void main(String[] input) {
int[] nums = new int[]{0,0,-1012,0,0,0,-3002,0,0,0,-10,-19,0,0,90,0,92,0,1,1,1,9,9,9,10,11,1001,2001,-404,201,203,201,999,345,1,1,1,1,1,1,1,-2,1,1,1,1,1,-1,1,1,-2,1,1,1,1,3,1,1,1,1,1,-1200,1,1,1,1,1,2,1202,2,2,-4,2,2,2,2,4,5,6,1,1,-11,1,1,1,1,1,1,1,1,101,1,1,1,1,1,-1,1,-6};
ArrayList<ArrayList<Integer>> result = new ArrayList<ArrayList<Integer>>();
result = fourSum(nums, 92);
for (int i = 0; i < result.size(); i++) {
ArrayList<Integer> list = result.get(i);
for (int j = 0; j < list.size(); j++) {
int cur = list.get(j);
System.out.print(cur);
System.out.print(", ");
}
System.out.println("");
}
}
}
测试结果 与 答案一模一样,就是在Lintcode上未能通过 不知原因
[[-3002,92,1001,2001],
[-1200,-11,101,1202],
[-1200,-2,92,1202],
[-1200,0,90,1202],
[-1200,90,201,1001],
[-1200,90,203,999],
[-1200,92,201,999],
[-1012,2,101,1001],
[-1012,4,101,999],
[-1012,11,92,1001],
[-404,92,201,203],
[-19,-1,11,101],
[-19,0,10,101],
[-19,1,9,101],
[-19,4,6,101],
[-19,9,10,92],
[-19,10,11,90],
[-11,-4,6,101],
[-11,-2,4,101],
[-11,-1,3,101],
[-11,0,2,101],
[-11,0,11,92],
[-11,1,1,101],
[-11,1,10,92],
[-11,2,9,92],
[-11,2,11,90],
[-11,3,10,90],
[-11,4,9,90],
[-11,5,6,92],
[-10,-4,5,101],
[-10,-2,3,101],
[-10,-1,2,101],
[-10,-1,11,92],
[-10,0,1,101],
[-10,0,10,92],
[-10,1,9,92],
[-10,1,11,90],
[-10,2,10,90],
[-10,3,9,90],
[-10,4,6,92],
[-6,-4,1,101],
[-6,-4,10,92],
[-6,-2,-1,101],
[-6,-2,10,90],
[-6,-1,9,90],
[-6,0,6,92],
[-6,1,5,92],
[-6,2,4,92],
[-6,2,6,90],
[-6,3,5,90],
[-4,-2,6,92],
[-4,-1,5,92],
[-4,0,4,92],
[-4,0,6,90],
[-4,1,3,92],
[-4,1,5,90],
[-4,2,2,92],
[-4,2,4,90],
[-2,-2,4,92],
[-2,-2,6,90],
[-2,-1,3,92],
[-2,-1,5,90],
[-2,0,2,92],
[-2,0,4,90],
[-2,1,1,92],
[-2,1,3,90],
[-2,2,2,90],
[-1,-1,2,92],
[-1,-1,4,90],
[-1,0,1,92],
[-1,0,3,90],
[-1,1,2,90],
[0,0,0,92],
[0,0,2,90],
[0,1,1,90]]