Three Sum with duplicated values

1. Link

三数之和_牛客题霸_牛客网

2. 描述

给出一个有n个元素的数组S，S中是否有元素a,b,c满足a+b+c=0？找出数组S中所有满足条件的三元组。注意：

1. 三元组（a、b、c）中的元素必须按非降序排列。（即a≤b≤c）

2. 解集中不能包含重复的三元组。

例如，给定的数组 S = {-10 0 10 20 -10 -40},解集为(-10, -10, 20),(-10, 0, 10) 
0 <= S.length <= 1000

示例1

输入：

[0]

复制返回值：

[]

复制

示例2

输入：

[-2,0,1,1,2]

复制返回值：

[[-2,0,2],[-2,1,1]]

3. 思路

1. sort array

2. iterate every element num[i]

3. binary search for the remaining element to check if two sum to target = 0- num[i] exist

4. skip all duplicated values once the first element found to avoid duplicated results

5. Time: O(nlogn) for sorting O(n ) for the first loop, O(n) for binary search in worst case, so O(n^2 + nlogn) = O(n^2)

6. Space O(1)

4. Coding

#
# 
# @param num int整型一维数组 
# @return int整型二维数组
#
class Solution:
    def threeSum(self , num ):
        # write code here
        if not num or len(num) <3:
            return []
        res = []
        num.sort()
        i = 0
        while i < len(num):
            target = 0 - num[i]
            sol = [num[i]]
            # two sum with binary search
            left, right = i+1, len(num)-1
            while left < right:
                tmp = num[left] + num[right]
                if tmp < target:
                    left += 1
                elif tmp > target:
                    right -= 1
                else:
                    sol.append(num[left])
                    sol.append(num[right])
                    sol.sort()
                    res.append(sol[:])
                    sol =[num[i]]
                    left_idx = left+1
                    # skip all duplicated value to avoid duplicated result
                    while left_idx <right and num[left] == num[left_idx]:
                        left_idx += 1
                    left = left_idx
                    right_idx = right-1
                    while right_idx >left and num[right] == num[right_idx]:
                        right_idx -= 1
                    right = right_idx
                    
                
            # skip all duplicated element 
            idx = i + 1
            while idx<len(num) and num[idx] == num[i]:
                idx += 1
            i = idx

        return res