Leetcode 3200. Maximum Height of a Triangle

Find the largest height h such that rows 1..h (row i has i balls) can be colored alternately with one color per row without exceeding the given red and blue counts; equivalently, for each h check whether the total T = h(h+1)/2 can be split into the alternating (odd/even index) row sums to fit red and blue (try both starting colors).