diff --git a/100_arranged_probability.py b/100_arranged_probability.py new file mode 100644 index 0000000..39eda9b --- /dev/null +++ b/100_arranged_probability.py @@ -0,0 +1,13 @@ +#!/usr/bin/env python3 + +lim = 10**12 +x, y = 3, 1 +blue = 3 +total = 4 + +while total <= lim: + x, y = 3*x + 8*y, 3*y + x + blue = (2*y + x + 1) // 2 + total = (4*y + x + 1) // 2 + +print(blue) diff --git a/101_optimum_polynomials.py b/101_optimum_polynomials.py new file mode 100644 index 0000000..3c270d6 --- /dev/null +++ b/101_optimum_polynomials.py @@ -0,0 +1,27 @@ +#!/usr/bin/env python3 + +CFS = [1, -1]*5 + [1] + +def main(cfs): + seq = getseq(cfs) + py = pyramid(seq) + return sum(op(n, py) for n in range(1, len(cfs))) + +def getseq(cfs): + return [sum(c*n**pw for pw, c in enumerate(cfs)) + for n in range(1, len(cfs))] + +def pyramid(seq): + r = [seq] + for i in range(len(seq)-1): + lvl = [] + for j in range(len(r[i])-1): + lvl.append(r[i][j+1] - r[i][j]) + r.append(lvl) + return r + +def op(n, py): + return sum(py[i][n-i-1] for i in range(n)) + +#print(main([0,0,0,1])) +print(main(CFS)) diff --git a/102_triangle_containment.py b/102_triangle_containment.py new file mode 100644 index 0000000..fe73595 --- /dev/null +++ b/102_triangle_containment.py @@ -0,0 +1,23 @@ +#!/usr/bin/env python3 + +# Calculate area of triangle and compare to areas +# of triangles with one vertex = origin +# better solution -> check sign of cross products + +def main(): + tr = parse("data/102_triangles.txt") + return len([0 for p in tr if areaTR(p) == areaOG(0,2,p) + areaOG(0,4,p) + areaOG(2,4,p)]) + +def areaTR(p): #triangle area + return abs(p[0]*p[3] - p[0]*p[5] + + p[2]*p[5] - p[2]*p[1] + + p[4]*p[1] - p[4]*p[3]) + +def areaOG(a, b, p): #triangle with with a=0,0 + return abs(p[a]*p[b+1] - p[b]*p[a+1]) + +def parse(path): + with open(path) as f: + return [list(map(int, row.split(","))) for row in f.read()[:-1].split("\n")] + +print(main()) diff --git a/103_special_subset_sums_optimum.py b/103_special_subset_sums_optimum.py new file mode 100644 index 0000000..256eba0 --- /dev/null +++ b/103_special_subset_sums_optimum.py @@ -0,0 +1,46 @@ +#!/usr/bin/env python3 + +def test(n, setsums): + newsums = [s+n for s in setsums] + setsums + [n] + if len(newsums) != len(set(newsums)): + return False + return newsums + +def search(left, right, length, best, setsums, lor, w): #left to right + if len(left + right) >= length: + if sum(left + right) < best: + #print left+right, sum(left+right) + for i, n in enumerate(left+right): + w[i] = n + return sum(left + right) + return best + hole = length - len(left + right) - 1 + minsum = sum(left + right) + (hole*(hole+1))//2 + left[-1]*hole + if lor: + n = max(left[-1]+1, sum(right)-sum(left) + 1) + bound = right[0] - hole + else: + n = left[-1] + hole + 1 + bound = best - minsum + if len(right) > 0 and right[0] < bound: + bound = right[0] + while n < bound and n < best - minsum - (n-left[-1])*hole*lor: + newsums = test(n, setsums) + if newsums: + best = search(left + [n]*lor, + [n]*(not lor) + right, + length, best, newsums, not lor, w) + n += 1 + return best + +def base(length, best): + x = length//2 + length % 2 + n = (x + 1 - length%2) * (x-1) + 1 + n = 20 + w = [0]*length + while n < best - (length-1)*length - n*(length-1): + best = search([n], [], length, best, [n], False, w) + n += 1 + return "".join(map(str, w)), best + +print(base(7, 500)[0]) diff --git a/104_pandigital_fibonacci_ends.py b/104_pandigital_fibonacci_ends.py new file mode 100644 index 0000000..2e771bb --- /dev/null +++ b/104_pandigital_fibonacci_ends.py @@ -0,0 +1,25 @@ +#!/usr/bin/env python3 + +from math import sqrt, log10 + +def main(): + k = 1 + m = 0 + last = 1 + gr = (1 + sqrt(5)) / 2 + first = gr*(1/sqrt(5)) + while cond(str(int(first))[:9], str(last)): + last, m = (last+m)%10**9, last + first = gr*first + if first >= 10**9: + first /= 10 + k += 1 + return k, int(log10(gr)*k - log10(1/sqrt(5)) + 1/2.0) + +def cond(first, last): + a = len(set(last)) != 9 + b = len(set(first)) != 9 + c = '0' in first+last + return a or b or c + +print(main()[0]) diff --git a/105_special_subset_sums_testing.py b/105_special_subset_sums_testing.py new file mode 100644 index 0000000..b405a59 --- /dev/null +++ b/105_special_subset_sums_testing.py @@ -0,0 +1,21 @@ +#!/usr/bin/env python3 + +def test(s): + if len(s) != len(set(s)): + return False + s.sort() + if sum(s[:len(s)//2 + len(s)%2]) <= sum(s[len(s)//2+1:]): + return False + setsums = [] + for n in s: + setsums += [m+n for m in setsums] + [n] + if len(setsums) != len(set(setsums)): + return False + return True + +with open("data/105_sets.txt") as f: + r = f.read() + +sets = [list(map(int, line.split(','))) for line in r.split('\n')[:-1]] + +print(sum(sum(s) for s in sets if test(s))) diff --git a/106_special_subset_sums_meta.py b/106_special_subset_sums_meta.py new file mode 100644 index 0000000..c5174cb --- /dev/null +++ b/106_special_subset_sums_meta.py @@ -0,0 +1,17 @@ +#!/usr/bin/env python3 + +from math import factorial + +def bin(n, k): + if n < 0: + return 0 + if n < k: + return 0 + return factorial(n) // (factorial(n-k) * factorial(k)) + +n = 12 +ms = 0 +for k in range(0, n//2 +1): + ms += bin(n, 2*k) * bin(2*k-1, k+1) + +print(ms) diff --git a/107_minimal_network.py b/107_minimal_network.py new file mode 100644 index 0000000..a27de4d --- /dev/null +++ b/107_minimal_network.py @@ -0,0 +1,30 @@ +#!/usr/bin/env python3 + +def parse(fname): + with open(fname) as f: + r = f.read() + r = [line.split(',') for line in r.split('\n')[:-1]] + weights = {a : [(b, int(w)) for b, w in enumerate(line) + if w!='-' + ] + for a, line in enumerate(r) + } + return weights + +def search(network, visited={0}): + if len(visited) == len(network): + return 0 + edges = [(n2, w) for node in visited + for n2, w in network[node] + if n2 not in visited + ] + next, w = min(edges, key = lambda x: x[1]) + return w + search(network, visited | {next}) + +network = parse("data/107_network.txt") +total_weight = sum(w for node in network + for _, w in network[node]) +total_weight //= 2 +min_weight = search(network) + +print(total_weight - min_weight) diff --git a/108_diophantine_reciprocals_I.py b/108_diophantine_reciprocals_I.py new file mode 100644 index 0000000..1eb8b6d --- /dev/null +++ b/108_diophantine_reciprocals_I.py @@ -0,0 +1,54 @@ +#!/usr/bin/env python3 + +from lib import primegen +from math import log +from operator import mul +from functools import reduce + +def calc(pows): + return (reduce(mul, (2*p + 1 for p in pows)) + 1) // 2 + +def increment(i, pows): + n = 0 + if i < len(pows): + n = pows[i] + return [n + 1] * (i+1) + pows[i+1:] + +def val(pows): + return sum(p*v for p, v in zip(pows, vals)) + +def fpwof2(pows, n): + if len(pows) == 1: + return n-1 + r = (2*n - 1) // reduce(mul, (2*p + 1 for p in pows[1:])) + r = (r - 1) // 2 + while calc([r] + pows[1:]) < n: + r += 1 + return r + +N = 10 ** 3 + +primes = list(primegen(100)) +vals = [log(p) / log(2) for p in primes] + +i = 0 +pows = [0] +best = fpwof2(pows, N) +best_pows = None + +while not (val(pows) >= best and sum(pows) == len(pows)): + if not i: + pows[0] = fpwof2(pows, N) + if len(pows) > 1 and pows[0] < pows[1]: + pows[0] = pows[1] + if val(pows) < best: + best = val(pows) + best_pows = pows + i = 1 + pows = increment(i, pows) + if val(pows) >= best: + i += 1 + else: + i = 0 + +print(reduce(mul, (n**pw for n, pw in zip(primes, best_pows)))) diff --git a/109_darts.py b/109_darts.py new file mode 100644 index 0000000..1bdcb1c --- /dev/null +++ b/109_darts.py @@ -0,0 +1,24 @@ +#!/usr/bin/env python3 + +bull = [25] +miss = [0] +fields = list(range(1, 21)) +single = fields + bull +double = [2*i for i in single] +treble =[3*i for i in fields] + +regs = miss + single + double + treble +regs.sort() + +count = 0 +score = 100 + +for fst in double: + for i, sec in enumerate(regs): + if fst + 2*sec >= score: + break + for thd in regs[i:]: + if fst + sec + thd >= score: + break + count += 1 +print(count) diff --git a/data/102_triangles.txt b/data/102_triangles.txt new file mode 100644 index 0000000..3f01a1a --- /dev/null +++ b/data/102_triangles.txt @@ -0,0 +1,1000 @@ +-340,495,-153,-910,835,-947 +-175,41,-421,-714,574,-645 +-547,712,-352,579,951,-786 +419,-864,-83,650,-399,171 +-429,-89,-357,-930,296,-29 +-734,-702,823,-745,-684,-62 +-971,762,925,-776,-663,-157 +162,570,628,485,-807,-896 +641,91,-65,700,887,759 +215,-496,46,-931,422,-30 +-119,359,668,-609,-358,-494 +440,929,968,214,760,-857 +-700,785,838,29,-216,411 +-770,-458,-325,-53,-505,633 +-752,-805,349,776,-799,687 +323,5,561,-36,919,-560 +-907,358,264,320,204,274 +-728,-466,350,969,292,-345 +940,836,272,-533,748,185 +411,998,813,520,316,-949 +-152,326,658,-762,148,-651 +330,507,-9,-628,101,174 +551,-496,772,-541,-702,-45 +-164,-489,-90,322,631,-59 +673,366,-4,-143,-606,-704 +428,-609,801,-449,740,-269 +453,-924,-785,-346,-853,111 +-738,555,-181,467,-426,-20 +958,-692,784,-343,505,-569 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