Suppose we have an array of n = 10^5 elements . 1 index based.

now , we build a segment tree with lazy propogation .

there are large queries , in each query you have to update elements in the range from 1 to n every time . by +x.

will the time complexity be O(n*m*logn) ? ? since everytime our numbers are from minn index to maxxindex.

that's incorrect. we can always re-write the arithmetic operation on a segment to (r — l + 1) * x where the segment is represented by [l, r]. Also, it doesn't matter how large your update range is. Only O(logn) segments are processed on each update. This makes your time complexity become O(q * logn) where q is number of queries and n is number of elements in your array.