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金色童年故事:著名数学猜想 Collatz Conjecture

(2019-10-16 19:45:39) 下一个

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Collatz Conjecture

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Oct 16 · 4 min read

Andy started with 9, 3 and 100 manually after I showed him the rules with sample initial value 5. He is strong in mental calculation since he made not a single mistake when writing down the following.

Collatz Conjecturelet's start from an integer 5  5, ?, ?, ?, ?,  if the previous one is  even, then the new number = previous one divided by 2  odd, then the new number = 3 * "previous one" + 1  5, 16, 8, 4, 2, 1  9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1  3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1  100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34,

Collatz Conjecture is one of the hardest math problems in front of our human being. No one can prove it (any number will stop at 1 eventually) even today.

This is the first time we met while loop.

func testCollatz() { // 13 % 5 = 3, 13 % 2 = 1, 42 % 2 = 0    var c = 1000000    while c != 1 {        print("(c), ", terminator: "")        if c % 2 == 1 {            c = 3 * c + 1        } else {            c = c / 2        }    }}

And at the end of class our program generated the long series for 1000000:

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