Given a dynamic array ( A ) of size ( N ) and an update operation that modifies a specified segment of the array, the task is to design algorithms to efficiently find the minimum element in the array after each update operation, and to calculate the frequency of occurrence of the identified minimum value. Formally, let ( A=left[a_{1}, a_{2}, ldots, a_{N} ight] ) be the dynamic array, and let ( U(i, j, Delta) ) represent the update operation that increments each element in the segment ( a_{i}, a_{i+1}, ldots, a_{j} ) by ( Delta ). After each update operation, the task is to compute: (a) The minimum element in the updated array. (b) The frequency of occurrence of the identified minimum value in the updated array.

The goal is to devise an efficient algorithm to handle a sequence of such update operations and maintain the required information about the minimum

element along with its frequency.

Given a dynamic array A of size N and an update operation that modifies a specified segment of the array, the task is to design algorithms to efficiently find the minimum element in the array after each update operation, and to calculate the frequency of occurrence of the identified minimum value. Formally, let A=[a1,a2,,aN] be the dynamic array, and let U(i,j,) represent the update operation that increments each element in the segment ai,ai+1,,aj by . After each update operation, the task is to compute: (a) The minimum element in the updated array. (b) The frequency of occurrence of the identified minimum value in the updated array