Problem Link - Chopsticks in Greedy Algorithms
Problem Statement:
Actually, the two sticks in a pair of chopsticks need not be of the same length. A pair of sticks can be used to eat as long as the difference in their length is at most D. The Chef has N sticks in which the ith stick is L[i] units long. A stick can’t be part of more than one pair of chopsticks. Help the Chef in pairing up the sticks to form the maximum number of usable pairs of chopsticks.
Approach:
- Sort the list of chopstick lengths. This allows us to easily compare adjacent lengths to determine if they can be paired.
- Initialize a counter to keep track of the number of pairs formed.
- Iterate through the sorted list:
- For each chopstick, check if it can form a pair with the next chopstick (i.e., the difference between the lengths is less than or equal to D).
- If a pair is formed, skip the next chopstick (since a chopstick can’t be part of more than one pair), and move to another pair.
- Continue this process until all chopsticks are evaluated.
Complexity:
- Time Complexity:
O(N logN)due to sorting, andO(N)for the pairing process, leading to an overall complexity ofO(N logN). - Space Complexity:
O(1).