Number of Subsequences That Satisfy the Given Sum Condition

arraytwo pointersbinary search

Problem Statement

You are given an array of integers nums and an integer target .

Return the number of non-empty subsequences of nums such that the sum of the minimum and maximum element on it is less or equal to target . Since the answer may be too large, return it modulo 10 ^9 + 7 .

Examples

Example 1

Input: nums = [3,5,6,7], target = 9
Output: 4
There are 4 subsequences that satisfy the condition.
[3] -> Min value + max value <= target (3 + 3 <= 9)
[3,5] -> (3 + 5 <= 9)
[3,5,6] -> (3 + 6 <= 9)
[3,6] -> (3 + 6 <= 9)

Example 2

Input: nums = [3,3,6,8], target = 10
Output: 6
There are 6 subsequences that satisfy the condition. (nums can have repeated numbers).
[3] , [3] , [3,3], [3,6] , [3,6] , [3,3,6]

Example 3

Input: nums = [2,3,3,4,6,7], target = 12
Output: 61
There are 63 non-empty subsequences, two of them do not satisfy the condition ([6,7], [7]).
Number of valid subsequences (63 - 2 = 61).

Constraints

1 <= nums.length <= 10 ^5

1 <= nums[i] <= 10 ^6

1 <= target <= 10 ^6

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicTwo Pointers