In August 1942 US troops landed on Guadalcanal (an island covered by dense, malaria-ridden jungle) and the battle for the Pacific islands began in earnest. Hundreds of thousands of men were killed (24,000 died in the taking of Iwo Jima alone including the reporter, Ernie Pyle) before in June 1945 the Allies took Okinawa, an island within striking distance of the mainland of Japan.
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David W. Johnson (2003) studied this question.