Multi-agent code-generation systems often use one communication topology for every problem. Across five topologies and 614 problems from APPS, HumanEval+ and LiveCodeBench, the advantage of hierarchical collaboration over a single agent grows from 2.4 points of pass@1 on the easiest third to 21.1 points on the hardest third, at about ten times the token cost. We propose the Difficulty-Aware Topology Selector (DATS), which predicts each topology's success probability and maximises predicted success minus cost. Its graph predictor treats topologies as nodes of a connectivity order. The complete graph-head comparison reports a 1.7-point advantage over a flat multi-label head while changing several mechanisms; capacity-matched adjacency controls show smaller descriptive differences. A scalar cost penalty can be recalibrated without retraining for approximately matched-spend comparisons when targets are attained. With a shared penalty, six methods span 21.6 percentage points of spend; two leading baselines fall behind DATS after method-specific calibration near the common target. At 40% of always-hierarchical cost, DATS reaches 77.7% pass@1 versus 73.6% for always-hierarchical and 74.3% for the strongest learned competitor. The main comparison includes Holm--Bonferroni-adjusted McNemar tests; unequal-cost differences do not imply matched-budget superiority. Backbone-specific gains are 4.07--4.23 points across four backbones. Alternatives to the 39 interpretable features, including a hybrid encoder, yield a largest observed gain of 1.3 points, with no significant pairwise improvement; this establishes neither equivalence nor an upper bound. A study on 400 mathematical reasoning problems reproduces difficulty-dependent collaboration gains, widening from 2.5 to 20.9 points.

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