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All of that was somewhat miraculous given the situation when Mr. Bloomberg took office.

“After the attack, people thought New York had no future,” said Mitchell Moss, a professor of urban policy and planning at N.Y.U. “There was a genuine sense that, ‘Who would want to live in New York, who would want to work in New York, who would want to visit New York?’”

In the years that followed, Mr. Bloomberg introduced an ambitious plan to preserve or build 165,000 units of affordable housing, and he oversaw the most extensive rezoning in modern city history. His administration rezoned about 40 percent of the city, paving the way for increased density and development in old industrial waterfront neighborhoods like Williamsburg and Greenpoint in Brooklyn.

“There’s this sense that the Bloomberg administration was about mega projects,” said Rafael Cestero, who led the Department of Housing Preservation and Development during part of the Bloomberg years. Mr. Cestero countered that many of those units of affordable housing were less visible but formed a more fundamental legacy. “We talk in these vagueries of units and developments and dollars and money. And the reality is that 500,000 people in our city are living more affordably because of the work that Mayor Bloomberg did over 12 years.”

As those homes were built or saved, the cost of housing in the city kept climbing. Median rents rose in New York by 19 percent, in real dollars, between 2002 and 2011, as the real median income of renter households declined slightly, according to a report by the Furman Center at N.Y.U. The number of residents in homeless shelters grew to 50,000 a night from less than 30,000.

New York’s growth and prosperity — seen at Atlantic Yards-Barclays Center; in Greenpoint; in Long Island City — appeared inseparable from the rising affordability crisis.