Apply Operations to an Array

Use two logical phases because merging and moving zeros have different invariants. First scan i from 0 through n minus 2. When nums[i] equals nums[i plus one], double nums[i] and assign zero to nums[i plus one]. Continue to the next i normally; this matters because a value created by a merge must not immediately merge backward. Next compact the array. Keep write at zero and scan every value; whenever the value is nonzero, write it at nums[write] and increment write. Finally overwrite positions write through n minus 1 with zero. For [1, 2, 2, 1, 1, 0], the merge phase creates [1, 4, 0, 2, 0, 0], then compaction produces [1, 4, 2, 0, 0, 0]. Check adjacent equal runs, zeros between values, and length one. This is O(n) time and O(1) extra space.