Swift Warmup climb stairs

Transcript

1. Swift ఔࣜখ೤਎ Climb Stairs John Lin
2. Climb Stairs • https://leetcode.com/problems/climbing-stairs/ • You are climbing a stair case. It takes n steps to reach to the top.
 Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
 Note: Given n will be a positive integer. • 㟬ࡏᗡఐࢠɼཁᗡ̣㑊࠽။౸௖ɻ
 㟬Ұ࣍ՄҎᗡҰ֨҃ၷ֨ɼ㟬༗زछՄೳతᗡ๏䏆ʁ
 PS. N ੋਖ਼੔Ꮠ
3. ൣྫ • n = 4 • 1,1,1,1
 1,1,2
 1,2,1
 2,1,1
 2,2 • ڞ༗ 5 छᗡ๏
4. ൣྫ • n = 5 • 1,1,1,1,1
 1,1,1,2
 1,1,2,1
 1,2,1,1
 2,1,1,1
 2,2,1
 2,1,2
 1,2,1 • ڞ༗ 8 छᗡ๏
5. ໰୊ࠎՍ class Solution { func climbStairs(_ n: Int) -> Int { } }
6. ԋࢉ๏ • Ҏޒ֊ᒭఐҝྫɼ༗Մೳੋኺୈ࢛֊૸Ұ㑊্ိɼ໵ ༗Մೳੋኺୈࡾ֊૸ၷ㑊্ိɻ • ࣕୈ࢛֊༗Մೳੋኺୈೋ֊҃ୈࡾ֊ᗡ্ိɻ • ୈࡾ֊༗ՄೳੋኺୈҰ֊҃ୈೋ֊ᗡ্ိɻ • ୈೋ֊༗Մೳੋኺୈྵ֊҃ୈҰ֊ᗡ্ိɻ • ୈҰ֊୞ೳኺୈྵ֊ᗡ্ိɻ
7. ԋࢉ๏ 5 4 3 3 2 2 2 1 1 1 1 0 0 0 0 0 0 1 0
8. ԋࢉ๏ • ୈN֊తՄೳ૸๏Ꮠ= ୈN - 1֊తՄೳ૸๏Ꮠ + 
 ୈN - 2֊తՄೳ૸๏Ꮠ
 ୈҰ֊࿨ୈྵ֊౎୞༗Ұछ૸๏ • F(n) = F(n-1) + F(n-2) • F(0) = 1 • F(1) = 1
9. class Solution { func climbStairs(_ n: Int) -> Int { guard n > 1 else { return 1} let ans = climbStairs(n-1) + climbStairs(n-2) return ans } }
10. class Solution { func climbStairs(_ n: Int) -> Int { guard n > 1 else { return 1} let ans = climbStairs(n-1) + climbStairs(n-2) return ans } } ࣌ؒෳᯑ౓: O(2^N)
 ۭؒෳᯑ౓: O(2^N) ࢉෆ׬ OTL
11. Ճ଎ • ࢖༻ memoization ٕ޼ɼل㑚༌ೖ࿨༌ग़ɼ೗Ռ༌ ೖग़ݱաब௚઀ճၚ೭લత݁Ռɻ
12. class Solution { var memo:[Int:Int] = [:] func climbStairs(_ n: Int) -> Int { guard n > 1 else { return 1} guard memo[n] == nil else { return memo[n]! } let ans = climbStairs(n-1) + climbStairs(n-2) memo[n] = ans return ans } } ࣌ؒෳᯑ౓: O(N)
 ۭؒෳᯑ౓: O(N) 32 ms
13. ࠶Ճ଎ • ଖመṜݸ໰୊తղ౴ੋఞఞେ໊తඅ೾ೲحᏐྻ
 1,1,2,3,5,8,13,21,34 • ՄҎኺୈҰ߲։࢝ࢉൺֱշɻ
14. class Solution { func climbStairs(_ n: Int) -> Int { guard n > 1 else { return 1} var big = 1 var small = 1 for i in 2...n { let sum = big + small small = big big = sum } return big } } ࣌ؒෳᯑ౓: O(N)
 ۭؒෳᯑ౓: O(N) 16 ms
15. ࠶Ճ଎Ճ଎ • අ೾ೲحᏐྻ ଖመ༗ެࣜղ
16. class Solution01 { func climbStairs(_ n: Int) -> Int { let nd : Double = Double(n+1) let sqrt5 = sqrt(5) let ans = ( pow((1+sqrt5)/2, nd) - pow((1- sqrt5)/2, nd) ) / sqrt5 return Int(ans.rounded()) } } ࣌ؒෳᯑ౓: O(1)
 ۭؒෳᯑ౓: O(1) 48 ms XDDᏓຫྃ
17. Q&A