Sliding window and two pointers

Sliding Window and two pointers:

We declare l and r depending on question. One of this variable will increment by default or on success of our condition and other will change when condition fails. We implement it such a way that we can perform operations in O(n) .

Let x be variable which is incremented when condition fulfills or by default;

x->[R,L]

let y be the variable which is incremented when condition doesn’t fulfill;

y->[R,L] x!=y;

basic condition for Sliding window or two pointer is for current value of x if y is failing then we are sure that previous value of y will also fail for x and we need to increment further. If we just arrived at x and y is passing for this value of x then we need to be sure previous values of y would have failed for this x and y is at the first position which satisfies for x.

this ensures that we do need to run additional loop to check all values of y, to check for each possible pairs because we know that the previous values of y which we have checked already wouldn’t satisfy for current value  of x. 

example question

Number of Subsequences That Satisfy the Given Sum Condition

ou 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 109 + 7.

 

Example 1:

Input: nums = [3,5,6,7], target = 9
Output: 4
Explanation: 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
Explanation: 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
Explanation: 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 <= 105
  • 1 <= nums[i] <= 106
  • 1 <= target <= 106

    Solution:

 

 

 

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