From 29a6bff45594367375a6bc2f413a90c2229b69b8 Mon Sep 17 00:00:00 2001 From: "i.solomatin" Date: Mon, 6 May 2024 17:31:14 +0700 Subject: [PATCH] Added W04 materials --- README.md | 2 +- .../HS.BKK.2024.Algo.Class04.pdf | Bin 0 -> 1307648 bytes week04_dynamic_programming/fibonacci.py | 54 ++++++++++++++++++ week04_dynamic_programming/lis_N2.py | 19 ++++++ week04_dynamic_programming/stairs.py | 33 +++++++++++ 5 files changed, 107 insertions(+), 1 deletion(-) create mode 100644 week04_dynamic_programming/HS.BKK.2024.Algo.Class04.pdf create mode 100644 week04_dynamic_programming/fibonacci.py create mode 100644 week04_dynamic_programming/lis_N2.py create mode 100644 week04_dynamic_programming/stairs.py diff --git a/README.md b/README.md index 46f8b24..c9f04c6 100644 --- a/README.md +++ b/README.md @@ -42,8 +42,8 @@ | 01 | Sorting algorithms | [Slides][Slides_W01] | [Test][WarmUp_test_W01] | [Contest][ContestID_W01] | 07.05.2024 09:00 UTC+7 | | 02 | Binary search | [Slides][Slides_W02] | [Test][WarmUp_test_W02] | [Contest][ContestID_W02] | 08.05.2024 09:00 UTC+7 | | 03 | Basic Data sturctures | [Slides][Slides_W03] | [Test][WarmUp_test_W03] | [Contest][ContestID_W03] | 09.05.2024 09:00 UTC+7 | -ZCE(S}1kn^1wG_jl=vES)-ieJaCi;>!h)WVmj*Aj6&-qz94&5>PpXGcBfI= z|IJu?tWju}8TErBJJ`+gj&oBdr52VBFguMV;&t|aIo6y^Oit2@0WK$LR2kyf3ioLM|F&LaH zULD0?@Me3hsi_=&fub&WowBWqytUp2(nE@}Krt35z5=2v98VeEDMVK|Y__|LQ**o? zCqK2qyX;*{HF&+gHV{q0FZ4&*$0>$_UoJW+f`VTyHcyLtN`imFD5WR~{&|0{e#XD(U-7R8iqRAp?)bpzkB-2R5jZYF zP!&w|I|fHYplAreGKz!{tO?d5{=wE@2gN_|G86$JI7U$qtkLr7v-)MkJUGlT4=CCJ z$2xGz!(sig4#J7yq;N`D6V`D=1H>~p6t;y+#LjSexYFqkJHxf%hH!JZE!-LI3HOJG z!Xx4F@Kkul%Y^5`9`~eNjnCh3-}g}e&Vq3sb!=bv z&3*Jpe4*$AbYFE^-%=@WQ)S7qA8J1M!7KV|Xs=ECO0@;|U8shXljJLCDcFkjg=|Abgbp|9Z)C+z}>_b z?E5K=Cbe2C1TvF@nwLYKCm+P*L+FQ}qIDPGg@I--6lRj&jBz{}cGa=67-YQOHvHHs9|lJ`tKZ z9qIgSw?}Y{U4QZ}l>ZR1b!7_m-iQ0P(JY|a%5&7BM)XNb;t@h!piyPeiqgafrQCoX z7|}ODA=LM7j4a8K=)LE0?dOqFfU71!mrmmNLvklTUev!+DE0}JbAR6_Xx8BDH*wX2 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+from time import time +from matplotlib import pyplot as plt + + +def fib_recursive(n): + if n < 2: + return n + return (fib_recursive(n - 1) + fib_recursive(n - 2)) % 10**9 + + +fibonacci_mem = {} + + +def fib_mem(n): + if n < 2: + return n + if n not in fibonacci_mem: + fibonacci_mem[n] = (fib_mem(n - 1) + fib_mem(n - 2)) % 10 ** 9 + return fibonacci_mem[n] + + +def fib_tab(n): + res = [0] * max((n + 1), 2) + res[0] = 0 + res[1] = 1 + for i in range(2, n + 1): + res[i] = (res[i - 1] + res[i - 2]) % 10**9 + return res[n] + + +if __name__ == '__main__': + times = [] + N_max = 35 + step = 1 + for i in range(1, N_max, step): + t = time() + + # naive solution: + x = fib_recursive(i) + + # memoization: + # cache is resettet to calculate correct time for each i + # otherwise it will take old values from cache: + # fibonacci_mem = {} + # x = fib_mem(i) + + # tabulation: + # x = fib_tab(i) + + times.append(time() - t) + print(f'N={i}: {times[-1]:.8f} sec.') + + plt.plot(times) + plt.show() diff --git a/week04_dynamic_programming/lis_N2.py b/week04_dynamic_programming/lis_N2.py new file mode 100644 index 0000000..c63443f --- /dev/null +++ b/week04_dynamic_programming/lis_N2.py @@ -0,0 +1,19 @@ +def lis_n2(x): + N = len(x) + d = [0] * N + d[0] = 1 + for i in range(1, N): + # don't need to find j + # Need just to calculate maxd: + max_d = 0 + for j in range(i): + if x[j] < x[i] and d[j] > max_d: + max_d = d[j] + d[i] = max_d + 1 + return max(d) + + +if __name__ == '__main__': + N = int(input()) + x = list(map(int, input().split())) + print(lis_n2(x)) diff --git a/week04_dynamic_programming/stairs.py b/week04_dynamic_programming/stairs.py new file mode 100644 index 0000000..10d3c6f --- /dev/null +++ b/week04_dynamic_programming/stairs.py @@ -0,0 +1,33 @@ +from time import time + + +def stairs_dp(s): + N = len(s) + d = [None] * N + d[0] = s[0] + d[1] = s[1] + for i in range(2, N): + d[i] = min(d[i - 1], d[i - 2]) + s[i] + return d[N - 1] + + +def stairs_rec(s): + if len(s) <= 2: + return s[-1] + d1 = stairs_rec(s[1:]) + s[0] + d2 = stairs_rec(s[2:]) + s[1] + return min(d1, d2) + + +if __name__ == '__main__': + N = int(input()) + s = list(map(int, input().split())) + t1 = time() + print(stairs_dp(s)) + t2 = time() + print(stairs_rec(s)) + t3 = time() + dp_time = t2 - t1 + rec_time = t3 - t2 + print(f'Naive: {rec_time:.8f} sec') + print(f'DP: {dp_time:.8f} sec')