Final answer:
The Qin dynasty was the key supporter of Legalism, a philosophy that emphasized strict laws and centralized control, which greatly influenced the unification of China under Qin Shi Huang but also led to the dynasty's quick downfall.
Step-by-step explanation:
The dynasty that supported the growth of Legalism was the Qin dynasty. Legalism was a strict philosophical school of thought that emphasized the rule of law as the key to running a state, which contrasted highly with the moralistic nature of Confucianism. This philosophy was instrumental during the Qin state's meteoric rise to power and the founding of the Qin Empire under Qin Shi Huang.
Legalism was propelled by influential advisers such as Shang Yang and later Han Feizi. It promoted the idea that a ruler must govern with a strong, unyielding hand, using clear and harsh laws to maintain order and control. During the Qin dynasty, legalist policies were implemented that favored centralization, bureaucracy, and militarization, contributing to the Qin's rapid expansion and the consolidation of the warring states into an empire.
However, these same policies also led to the dynasty's downfall. After the death of Qin Shi Huang in 210 BCE, the heavy-handed Legalist approach incited rebellion among the populace and dissent within the royal court. This resulted in the swift collapse of the Qin dynasty, but the foundation had been set for the imperial structure that would be adopted by successive Chinese dynasties.