Implement four coding challenges

You are asked to solve the following four independent coding problems. --- ## 1) Block Placement Simulator (Tetris-like) You have an empty `n x m` grid (rows indexed top-to-bottom, columns left-to-right). You will place a sequence of pieces, each piece being one of five types `A/B/C/D/E`. Each piece type is defined by a fixed set of occupied cells in its own local coordinate system (e.g., a small boolean matrix or a list of `(dr, dc)` offsets). Pieces: - cannot be rotated or flipped, - must be placed fully within the grid, - cannot overlap already-occupied cells. **Placement rule (scan order):** For each incoming piece, find the first valid placement position by scanning candidate top-left anchors in priority order: 1) smallest row index (top to bottom), 2) within the same row, smallest column index (left to right). Place the piece at that first valid position. If no valid position exists, stop and return the grid/state according to the output requirement. **Task:** Implement the simulator that processes the piece sequence and produces the final grid (or alternatively the number of pieces placed), following the scan-order placement rule. --- ## 2) Longest Continuous Houses After Each Build On an integer number line, you build houses one by one at positions given by an array `queries`, in order. After each build, you must output the current length of the longest contiguous segment of built houses, where “contiguous” means consecutive integer positions. Example: if houses exist at `{2,3,4,10}`, the longest contiguous segment length is `3` (for `2-4`). Notes: - Coordinates can be very large (e.g., up to billions), - The number of builds is manageable, - Duplicate builds (building again at an already-built coordinate) should be handled (either ignored or specified by the problem). **Task:** Return an array `ans` where `ans[i]` is the longest contiguous segment length after processing `queries[0..i]`. --- ## 3) Rating Calculator (Max and Final Rating) You start with rating `1500`. You are given an integer array `diffs`, where `diffs[i]` is the rating change applied after the `i`-th event. Let `rating_0 = 1500` and `rating_{i+1} = rating_i + diffs[i]`. **Task:** Compute: 1) the maximum rating ever reached across the whole process (including the initial rating), and 2) the final rating after all changes. Return `(max_rating, final_rating)`. --- ## 4) Array Reduction Game Given an array of non-negative integers `a`: Repeat until all elements become `0`: 1) Find the leftmost index `i` such that `a[i] > 0`. Let `x = a[i]`. 2) Starting from index `i` and moving right, subtract `x` from each element while it is legal to do so (i.e., continue for indices `j = i, i+1, ...` as long as `a[j] >= x` at the moment you are about to subtract). Stop at the first position where the current value is `< x`. 3) Add `x` to an accumulator `result`. **Task:** Return `result`. (You may assume inputs are such that the process terminates; implement according to the exact step rules above.)