DSAAGP1098

editorial
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Problem Link - Aggressive Cows in Binary Search

Problem Statement:

Farmer John has built a barn with N stalls located at positions x_1, x_2, …, x_N along a straight line. He wants to place C cows in these stalls such that the minimum distance between any two cows is as large as possible. Your task is to determine this largest possible minimum distance.

In this problem we have to check if keeping a certain distance d he can assign a stall to each cow.

Approach:

The check function is a key part of solving this problem. Its purpose is to determine if it’s possible to place C cows in the stalls such that the minimum distance between any two cows is at least a given distance d.

  • Place the First Cow: Start by placing the first cow in the first stall (position arr[0]). This ensures we leave the largest possible space for the remaining cows.
  • Track Remaining Cows:
    • We initialize a count for the remaining cows (cows = c - 1) since we’ve already placed the first cow.
    • We also keep track of the position of the last placed cow (prev = arr[0]).
  • Place the Rest of the Cows:
    • Iterate through the stalls, starting from the second one.
    • For each stall, check if it’s at least d distance away from the last placed cow.
    • If it is, place a cow there and update prev to the current stall’s position.
    • Decrease the cows count after placing a cow.
  • Check if All Cows Are Placed:
    • If all cows are placed successfully (i.e., cows == 0), return true, meaning it’s possible to place the cows with at least d distance between them.
  • If Not All Cows Are Placed:
    • If the loop finishes and we haven’t placed all cows, return false, meaning it’s not possible to place the cows with that distance.

Complexity:

  • Time Complexity: O(N) We are iterating through the array once.
  • Space Complexity: O(1) We have not used extra space.