From 88b71415830ddc0a7019411919959d3b10b37ed3 Mon Sep 17 00:00:00 2001 From: Ivan Solomatin Date: Mon, 2 Dec 2024 20:58:37 +0300 Subject: [PATCH] Added W09 materials --- README.md | 2 +- week09_rsq_rmq/MSAI.2024.Algo.W09.slides.pdf | Bin 0 -> 1323271 bytes week09_rsq_rmq/fenwick.py | 30 ++++++++++++ week09_rsq_rmq/prefix_sum.py | 16 +++++++ week09_rsq_rmq/rsq_segmenttree.py | 47 +++++++++++++++++++ week09_rsq_rmq/sparcetable.py | 37 +++++++++++++++ week09_rsq_rmq/sqrt_decomposition.py | 39 +++++++++++++++ 7 files changed, 170 insertions(+), 1 deletion(-) create mode 100644 week09_rsq_rmq/MSAI.2024.Algo.W09.slides.pdf create mode 100644 week09_rsq_rmq/fenwick.py create mode 100644 week09_rsq_rmq/prefix_sum.py create mode 100644 week09_rsq_rmq/rsq_segmenttree.py create mode 100644 week09_rsq_rmq/sparcetable.py create mode 100644 week09_rsq_rmq/sqrt_decomposition.py diff --git a/README.md b/README.md index d65d24a..d8b49aa 100644 --- a/README.md +++ b/README.md @@ -47,8 +47,8 @@ | 06 | KMP & Heap | [Slides][Slides_W06] | [Test][WarmUp_test_W06] | [Contest][ContestID_W06] | 18.11.2024 19:00 UTC+3 | | 07 | DFS & BFS | [Slides][Slides_W07] | [Test][WarmUp_test_W07] | [Contest][ContestID_W07] | 25.11.2024 19:00 UTC+3 | | 08 | Shortest paths | [Slides][Slides_W08] | [Test][WarmUp_test_W08] | [Contest][ContestID_W08] | 02.12.2024 19:00 UTC+3 | +| 09 | RSQ & RMQ | [Slides][Slides_W09] | [Test][WarmUp_test_W09] | [Contest][ContestID_W09] | 09.12.2024 19:00 UTC+3 | diff --git a/week09_rsq_rmq/MSAI.2024.Algo.W09.slides.pdf b/week09_rsq_rmq/MSAI.2024.Algo.W09.slides.pdf new file mode 100644 index 0000000000000000000000000000000000000000..28302dd4291a184b796d38aaea0be130b5ae6b7b GIT binary patch literal 1323271 zcmce;bwF0l);>&^bR%`sT{qp`-5?;{(kUg{eGA>BxaARW?(gmg+sh~Eu79`!uW zdCz&j_c=fQVDEeHH8X2w)~vZ^t~HxNNlb!)g^?WzfuaudhlIcaUM=HHFP$7W@pZ%WN2>c1OS3wt1!tK+L}|F+A^rC(g2uLogH0_oz)yoO;zmdoB=G% zocA*FhK|dO#mP{QvuK)5`w9%$$c4jx&2nyeIZPub}qKg09IBeSxXZq 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delta + i += ~i & (i + 1) + + def rsq(self, left, right): + return self.query(right - 1) - self.query(left - 1) + + +if __name__ == '__main__': + N = int(input()) + s = RSQFenwick(N) + while True: + a, b, c = input().split() + if a == '+': + s.update(int(b), int(c)) + elif a == '?': + print(s.rsq(int(b), int(c))) diff --git a/week09_rsq_rmq/prefix_sum.py b/week09_rsq_rmq/prefix_sum.py new file mode 100644 index 0000000..b7cc1c2 --- /dev/null +++ b/week09_rsq_rmq/prefix_sum.py @@ -0,0 +1,16 @@ +class RSQPrefixSum: + def __init__(self, a): + self.s = [0] + for v in a: + self.s.append(self.s[-1] + v) + + def rsq(self, l, r): + return self.s[r] - self.s[l] + + +if __name__ == '__main__': + a = list(map(int, input().split())) + s = RSQPrefixSum(a) + while True: + l, r = map(int, input().split()) + print(s.rsq(l, r)) diff --git a/week09_rsq_rmq/rsq_segmenttree.py b/week09_rsq_rmq/rsq_segmenttree.py new file mode 100644 index 0000000..5180e2c --- /dev/null +++ b/week09_rsq_rmq/rsq_segmenttree.py @@ -0,0 +1,47 @@ +from math import log2, floor, ceil + + +class RSQSegmentTree: + neutral_value = 0 + + def __init__(self, a): + self.N = 2 ** int(ceil(log2(len(a)))) + self.s = [None] * (self.N - 1) + list(a) + ([self.neutral_value] * (self.N - len(a))) + for i in range(self.N - 2, -1, -1): + self.refresh_s(i) + + def refresh_s(self, i): + self.s[i] = self.s[2 * i + 1] + self.s[2 * i + 2] + + def rsq_i(self, l, r, i, li, ri): + if (r <= li) or (ri <= l): + return self.neutral_value + if (l <= li) and (ri <= r): + return self.s[i] + middle = li + (ri - li) // 2 + return (self.rsq_i(l, r, i * 2 + 1, li, middle) + + self.rsq_i(l, r, i * 2 + 2, middle, ri)) + + def update(self, i, v): + i += self.N - 1 + self.s[i] = v + while i > 0: + i = (i - 1) // 2 + self.refresh_s(i) + + def rsq(self, l, r): + return self.rsq_i(l, r, 0, 0, self.N) + + +if __name__ == '__main__': + a = list(map(int, input().split())) + #N = int(input()) + s = RSQSegmentTree(a) + while True: + a, b, c = input().split() + if a == '+': + s.update(int(b), int(c)) + elif a == '?': + print(s.rsq(int(b), int(c))) + elif a == '!': + print(' '.join(map(str, s.a))) diff --git a/week09_rsq_rmq/sparcetable.py b/week09_rsq_rmq/sparcetable.py new file mode 100644 index 0000000..fdf4d3e --- /dev/null +++ b/week09_rsq_rmq/sparcetable.py @@ -0,0 +1,37 @@ +from math import log2, floor, ceil + +inf = 10**9 + + +class RMQSparseTable: + def __init__(self, a): + N = len(a) + K = ceil(log2(N)) + 1 + + self.ST = [[None] * N for k in range(K)] + self.ST[0] = list(a) + + for k in range(1, K): + for i in range(N): + if i + 2 ** (k - 1) < N: + self.ST[k][i] = min(self.ST[k - 1][i], + self.ST[k - 1][i + 2 ** (k - 1)]) + else: + self.ST[k][i] = self.ST[k - 1][i] + for k in range(K): + print(' '.join(map(str, self.ST[k]))) + + def rmq(self, l, r): + if l == r: + return inf + k = floor(log2(r - l)) + return min(self.ST[k][l], + self.ST[k][r - 2 ** k]) + + +if __name__ == '__main__': + a = list(map(int, input().split())) + s = RMQSparseTable(a) + while True: + l, r = map(int, input().split()) + print(s.rmq(l, r)) diff --git a/week09_rsq_rmq/sqrt_decomposition.py b/week09_rsq_rmq/sqrt_decomposition.py new file mode 100644 index 0000000..caf7ac0 --- /dev/null +++ b/week09_rsq_rmq/sqrt_decomposition.py @@ -0,0 +1,39 @@ +from math import sqrt, floor, ceil + + +class RSQSqrtDecomposition: + def __init__(self, a): + N = len(a) + self.k = max(int(ceil(sqrt(N))), 1) + self.a = a + self.b = [0] * (self.k + 1) + + for i, v in enumerate(a): + self.b[i // self.k] += v + + def rsq(self, l, r): + l_block = self.k * int(ceil(l / self.k)) + r_block = self.k * int(floor(r / self.k)) + if l_block > r_block: + return sum(self.a[l:r]) + return (sum(self.a[l:l_block]) + + sum(self.b[l_block // self.k:r_block // self.k]) + + sum(self.a[r_block:r])) + + def update(self, i, v): + delta = v - self.a[i] + self.a[i] = v + self.b[i // self.k] += delta + + +if __name__ == '__main__': + a = list(map(int, input().split())) + s = RSQSqrtDecomposition(a) + while True: + a, b, c = input().split() + if a == '+': + s.update(int(b), int(c)) + elif a == '?': + print(s.rsq(int(b), int(c))) + elif a == '!': + print(' '.join(map(str, s.a)))