Option 1: Devaraya I

Devaraya I, the ruler of the Vijayanagara Empire, was known for his vision and administrative acumen. He was aware of the water scarcity issue hampering the growth of the royal capital. To address this, he constructed a large dam across the Tungabhadra River around 1410. Additionally, he commissioned a 24-kilometer long aqueduct from the river to the capital city. This massive project not only alleviated the water shortage but also allowed for better irrigation, leading to the growth of the city to become one of the largest in the 15th century.

Option 2: Mallikarjuna

Although Mallikarjuna was a significant ruler in the Vijayanagara Empire, there are no specific historical records suggesting that he undertook substantial irrigation or infrastructure projects similar to the construction of a dam and a long aqueduct.

Option 3: Vira Vijaya

Vira Vijaya is a lesser-known ruler of the Vijayanagara Empire, and no significant records suggest his involvement in significant water management projects like the specified dam and canal-cum-aqueduct construction.

Option 4: Virupaksha

Virupaksha's reign was marked by remarkable contributions to art and religion. However, historical evidence linked to his involvement in large-scale infrastructural projects such as constructing a dam and a long aqueduct is lacking.

In conclusion, the correct answer to this question, in light of the available information, is Option 1: Devaraya I. He was the Vijayanagara ruler who constructed a large dam across the Tungabhadra River and a canal-cum-aqueduct several kilometers long from the river to the capital city, effectively addressing the issue of water scarcity and boosting the city's growth.