I read many people's solutions and I realized the technique that helps me count effectively. This technique is:
If i want to increase all elements in range $$$[l;r]$$$ in array $$$cnt$$$, i will set $$$cnt[l]++$$$ and $$$cnt[r+1]--$$$, after that i will calculate cumulative sum from left to right, $$$cnt[i]+= cnt[i-1], \forall i \in [1:n]$$$.
The same approach is applied for 2d counting arrray. If i want to increase every cell in rectangle with top-left $$$(x_1, y_1)$$$ and bottom-right $$$(x_2, y_2)$$$. I will set
cnt[x1][y1]++; cnt[x1][y2+1]--; cnt[x2+1][y1]--; cnt[x2+1][y2+1]++; and then calculate the partial sum of this 2d counting array.
I want to get more information for this technique. Could you help me the name of it or any link that is relevant. Thanks in advance.