Rhombus sums — prefix-sum optimization
A fresh walkthrough of LeetCode 1878 contrasts brute-force rhombus enumeration with a prefix-sum border technique that cuts runtime dramatically and handles deduplication for 'three largest distinct sums'. The tutorial focuses on edge detection and geometry-aware prefix sums — common interview follow-ups for grid problems explained.
Naive border-summing that walks every rhombus edge and its cells results in worst-case O(n^4) time on an n×n grid, which is the complexity shown in common walkthroughs and solution posts. (walkccc.me) Precomputing two diagonal prefix arrays yields an overall runtime of O(m × n × min(m,n)) and space O(m × n) for an m×n grid, a complexity breakdown used in official community solutions. (github.com) The standard implementation builds two diagonal accumulators — one for "/"-direction diagonals and one for "\"-direction — then computes any diagonal segment by subtracting two prefix entries instead of iterating each cell, an approach emphasized in multiple problem analyses. (algo.monster) Typical code-level deduplication stores every rhombus total in a set (or a bounded min-heap) and returns the top three distinct values; several reference implementations explicitly use set insertion with a size check to keep only the largest three. (walkccc.me) Valid rhombus radii are clipped by the distance to the grid edges using max_len = min(i, m-1-i, j, n-1-j) (or equivalent corner-based checks), which both bounds the inner loop and prevents out-of-bounds corner access in published solutions. (algomap.io) Multiple recent video walkthroughs demonstrate the geometry-aware prefix approach and live-code the diagonal prefixes, including the codestorywithMIK explainers and Developer Coder walkthroughs that show the step-by-step prefix construction and corner-case handling. (youtube.com)
