Maximize minimum sweetness in cake cutting

Given that cake consists of N chunks, whose individual sweetness is represented by the sweetness[] array, the task is to cut the cake into K + 1 pieces to maximize the minimum sweetness.

Examples:

Input: N  = 6, K = 2, sweetness[] = {6, 3, 2, 8, 7, 5}
Output: 9
Explanation: Divide the cake into [6, 3], [2, 8], [7, 5] with sweetness levels 9, 10, and 12 respectively.

Input: N  = 7, K = 3, sweetness[] = {1, 2, 4, 7, 3, 6, 9}
Output: 7
Explanation: Divide the cake into [1, 2, 4], [7], [3, 6], [9]  with sweetness levels 7, 7, 9, and 9 respectively.

Approach: This can be solved with the following idea:

The approach used is the binary search to find the maximum sweetness value that can be achieved after dividing the given array of sweetness values into k + 1 groups, where each group has a minimum sweetness value of mn_value.

Steps involved in the implementation of code:

• First, we initialize the variables "sum" and "mn_value" to calculate the sum of all sweetness levels and the minimum sweetness level in the array respectively.
• We set the low and high values of binary search as 1 and sum respectively.
• We perform a binary search on the range [low, high] until low > high. In each iteration, we calculate the mid-value and call the "canSplit" function to check if the array can be split into k+1 subarrays where the minimum sweetness level of each subarray is at least mid.
• If "canSplit" returns true, we store the current mid value as the answer and update the low value to mid+1 to search for larger mid values.
• Otherwise, if "canSplit" returns false, we set the high value to mid-1 to search for smaller mid-values.
• Finally, we return the answer.

Below is the implementation of the above approach:

9

Time Complexity: O(n * log(sum))
Auxiliary Space:  O(1)