# Sum of Three Numbers Less than Target - Google Top Interview Questions

### Problem Statement :

Given a list of integers nums and an integer target, return the number of triples i < j < k that exist such that nums[i] + nums[j] + nums[k] < target.

Constraints

n ≤ 1,000 where n is the length of nums

Example 1

Input

nums = [-3, 5, 3, 2, 7]

target = 9

Output

5

Explanation

Here are the different triples' values:

-3 + 5 + 3 = 5
-3 + 5 + 2 = 4
-3 + 3 + 2 = 2
-3 + 3 + 7 = 7
-3 + 2 + 7 = 6

### Solution :

Solution in C++ :

int solve(vector<int>& nums, int target) {
sort(nums.begin(), nums.end());
int ans = 0;
for (int i = 0; i < nums.size(); i++) {
for (int j = i + 1, k = nums.size() - 1; j < k;) {
if (nums[i] + nums[j] + nums[k] < target) {
ans += k - j;
j++;
} else {
k--;
}
}
}
return ans;
}

Solution in Java :

import java.util.*;

class Solution {
public int solve(int[] nums, int target) {
int res = 0;
Arrays.sort(nums);
for (int i = 0; i < nums.length; i++) res += twoSum(nums, target, i);
return res;
}

// Two pointer function to find all triplets less than target
public int twoSum(int[] nums, int target, int i) {
int j = i + 1, k = nums.length - 1, res = 0;

// Do not do i <= j because the same index cannot be used twice
while (j < k) {
int total = nums[i] + nums[j] + nums[k];
if (total >= target)
k--;

// The array is sorted so all triplets using a smaller k can be added
else {
res += k - j;
j++;
}
}
return res;
}
}

Solution in Python :

class Solution:
def two_sum(self, nums, start, val, target):
a, b = start, len(nums) - 1

ans = 0

while a < b:
if nums[a] + nums[b] + val < target:
a += 1
ans += b - a + 1
else:
b -= 1

return ans

def solve(self, nums, target):
nums.sort()

return sum(self.two_sum(nums, i + 1, nums[i], target) for i in range(len(nums)))

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