Find where to cut cake into equal areas

### Cut a cake so both sides have equal area A cake is made of **N** rectangular blocks arranged left-to-right in a straight line (no gaps, no overlap). Block `i` has: - width `w_i` - height `h_i` All blocks share the same baseline; the cake’s top edge forms a step-like profile. You want to make **one vertical cut** at position `x` (measured from the cake’s left edge) so that the **area to the left of the cut equals the area to the right**. #### Input - An integer `N`. - Arrays `w[0..N-1]`, `h[0..N-1]`. #### Output - Return the cut position `x` as a real number such that: - `0 <= x <= sum(w_i)` - area(left of `x`) = total_area / 2 #### Notes - If the cut falls inside a block, that block is split proportionally by width. - Assume `total_area` is even in the sense that an exact cut position exists. #### Complexity discussion Explain your approach and its time/space complexity. (A common approach is to search which block contains the half-area point, then locate the exact offset inside that block.)