From 905723f6d079d785b6eef3055444137b624332aa Mon Sep 17 00:00:00 2001 From: Tibor Bizjak Date: Sun, 26 Mar 2023 22:59:33 +0200 Subject: [PATCH] Added solutions for N=80-100 --- 080_square_root_digital_expansion.py | 25 + 081_path_sum.py | 23 + 082_path_sum.py | 29 + 083_path_sum.py | 135 +++ 084_monopoly_odds.py | 79 ++ 085_counting_rectangles.c | 43 + 087_prime_power_triples.py | 38 + 088_product-sum_numbers.py | 70 ++ 089_roman_numerals.py | 41 + 090_cube_digit_pairs.py | 22 + ...ight_triangles_with_integer_coordinates.py | 18 + 093_arithmetic_expressions.py | 98 ++ 094_almost_equilateral_triangles.py | 21 + 099_largest_exponential.py | 23 + data/081_matrix.txt | 80 ++ data/082_matrix.txt | 80 ++ data/083_matrix.txt | 80 ++ data/089_roman_numerals.txt | 1000 +++++++++++++++++ data/098_words.txt | 1 + data/099_base_exp.txt | 1000 +++++++++++++++++ makefile | 6 + 21 files changed, 2912 insertions(+) create mode 100644 080_square_root_digital_expansion.py create mode 100644 081_path_sum.py create mode 100644 082_path_sum.py create mode 100644 083_path_sum.py create mode 100644 084_monopoly_odds.py create mode 100644 085_counting_rectangles.c create mode 100644 087_prime_power_triples.py create mode 100644 088_product-sum_numbers.py create mode 100644 089_roman_numerals.py create mode 100644 090_cube_digit_pairs.py create mode 100644 091_right_triangles_with_integer_coordinates.py create mode 100644 093_arithmetic_expressions.py create mode 100644 094_almost_equilateral_triangles.py create mode 100644 099_largest_exponential.py create mode 100644 data/081_matrix.txt create mode 100644 data/082_matrix.txt create mode 100644 data/083_matrix.txt create mode 100644 data/089_roman_numerals.txt create mode 100644 data/098_words.txt create mode 100644 data/099_base_exp.txt create mode 100644 makefile diff --git a/080_square_root_digital_expansion.py b/080_square_root_digital_expansion.py new file mode 100644 index 0000000..81b60a1 --- /dev/null +++ b/080_square_root_digital_expansion.py @@ -0,0 +1,25 @@ +#!/usr/bin/env python3 + +from decimal import * + +dn = 103 + +getcontext().prec = dn + +def sumdigs(x): + r = 0 + while x: + r, x = r + x % 10, x // 10 + return r + +def sumsquare(x): + sq = Decimal(x).sqrt() + return sumdigs(int((sq) * 10**(dn - 1)) // 1000) + +sm = 0 + +for i in range(2, 101): + x = sumsquare(i) + sm += x if x >10 else 0 + +print(sm) diff --git a/081_path_sum.py b/081_path_sum.py new file mode 100644 index 0000000..4a1ef2b --- /dev/null +++ b/081_path_sum.py @@ -0,0 +1,23 @@ +#!/usr/bin/env python3 + +def from_file(name): + m = [] + with open(name, 'r') as f: + for row in f.readlines(): + m.append([int(num) if num[-1] != '\n' else int(num[:-1]) for num in row.split(',')]) + return m + +def main(): + mx = from_file('data/081_matrix.txt') + rl = len(mx[0]) + cl = len(mx) + for i in range(rl - 2, -1, -1): mx[cl - 1][i] += mx[cl - 1][i + 1] + for i in range(cl - 2, -1, -1): mx[i][rl - 1] += mx[i + 1][rl - 1] + + for col in range(cl - 2, -1, -1): + for row in range(rl - 2, -1, -1): + mx[col][row] += mx[col][row + 1] if mx[col][row + 1] < mx[col + 1][row] else mx[col + 1][row] + return mx[0][0] + +if __name__ == '__main__': + print(main()) diff --git a/082_path_sum.py b/082_path_sum.py new file mode 100644 index 0000000..bfc548f --- /dev/null +++ b/082_path_sum.py @@ -0,0 +1,29 @@ +#!/usr/bin/env python3 + +def from_file(name): + mx = [] + with open(name, 'r') as f: + for row in f.readlines(): + mx.append([int(num) if num[-1] != '\n' else int(num[:-1]) for num in row.split(',')]) + return mx + +def main(): + mx = from_file('data/082_matrix.txt') + rl = len(mx) + cl = len(mx[0]) + for col in range(cl - 2, -1, -1): + cache = [None for i in range(rl)] + cache[rl - 1] = sum(mx[rl - 1][col : col + 2]) + + for row in range(rl - 2, -1, -1): + cache[row] = mx[row][col] + min(cache[row + 1], mx[row][col + 1]) + s = sum(mx[0][col : col + 2]) + mx[0][col] = min(s, cache[0]) + + for row in range(1, rl): + s = mx[row][col] + min(s, mx[row][col + 1]) + mx[row][col] = min(cache[row], s) + return min(list(zip(*mx))[0]) + +if __name__ == '__main__': + print(main()) diff --git a/083_path_sum.py b/083_path_sum.py new file mode 100644 index 0000000..70665d5 --- /dev/null +++ b/083_path_sum.py @@ -0,0 +1,135 @@ +#!/usr/bin/env python3 + +def deadeasy(matrix): + mx = len(matrix) + my = len(matrix[0]) + change = True + cache = [[9999999 for y in range(my+2)] for x in range(mx+2)] + cache[1][1] = matrix[0][0] + while change: + change = False + for x in range(1, mx+1): + for y in range(1, my+1): + new_val = matrix[x-1][y-1] + min(cache[x+1][y], cache[x][y+1], cache[x-1][y], cache[x][y-1]) + if new_val < cache[x][y]: + cache[x][y] = new_val + change = True + return cache[mx][my] + +class Matrix: + def __init__(self, matrix): + self.x = self.y = 0 + self.mx = len(matrix) - 1 + self.my = len(matrix[0]) - 1 + self.org = matrix + self.overlay = [[None for y in x] for x in matrix] + self.overlay[0][0] = self.org[0][0] + self.change = [[0 for y in x] for x in matrix] + def add(self, xshft, yshft): + x = self.x + y = self.y + xn = x + xshft + yn = y + yshft + chng_id = xshft + 2*yshft + #if chng_id == -self.change[x][y]: + #return False + new_val = self.overlay[x][y] + self.org[xn][yn] + if new_val < self.overlay[xn][yn] or self.overlay[xn][yn] == None: + self.overlay[xn][yn] = new_val + self.change[xn][yn] = chng_id + return True + return False + + def right(self): + return self.add(1, 0) + def left(self): + return self.add(-1, 0) + def up(self): + return self.add(0, -1) + def down(self): + return self.add(0, 1) + +def up(matrix): + matrix.y = matrix.my + while matrix.y > 0: + matrix.up() + matrix.y -= 1 + +def down(matrix): + matrix.y = 0 + while matrix.y < matrix.my: + matrix.down() + matrix.y += 1 + +def right(matrix): + matrix.y = 0 + while matrix.y <= matrix.my: + matrix.right() + matrix.y += 1 + matrix.x += 1 + +def alter_right(matrix): + matrix.x = 0 + while matrix.x < matrix.mx: + matrix.y = 0 + while matrix.y <= matrix.my: + matrix.right() + matrix.y += 1 + up(matrix) + down(matrix) + matrix.x += 1 + +def alter_left(matrix): + matrix.x = matrix.mx + while matrix.x > 0: + matrix.y = 0 + while matrix.y <= matrix.my: + matrix.left() + matrix.y += 1 + up(matrix) + down(matrix) + matrix.x -= 1 + +def left(matrix): + cont = True + matrix.x += 1 + while cont and matrix.x > 1: + matrix.x -= 1 + up(matrix) + down(matrix) + matrix.y = 0 + cont = False + while matrix.y <= matrix.my: + cont = cont or matrix.left() + matrix.y += 1 + +def get_matrix(path): + with open(path) as f: + matrix = [map(int, row.split(",")) for row in f.read().split("\n")[:-1]] + return list(zip(*matrix)) + +def alter_main(matrix): + down(matrix) + prevm = False + while prevm != matrix.overlay[matrix.mx][matrix.my]: + prevm = matrix.overlay[matrix.mx][matrix.my] + alter_right(matrix) + alter_left(matrix) + return matrix.overlay[matrix.mx][matrix.my] + +def main(matrix): + down(matrix) + while matrix.x < matrix.mx: + right(matrix) + left(matrix) + return matrix.overlay[matrix.mx][matrix.my] + +if __name__ == "__main__": + matrix = [[131, 201, 630, 537, 805], + [673, 96, 803, 699, 732], + [234, 342, 746, 497, 524], + [103, 965, 422, 121, 37 ], + [18, 150, 111, 956, 331] + ] + + print(deadeasy(get_matrix("data/083_matrix.txt"))) diff --git a/084_monopoly_odds.py b/084_monopoly_odds.py new file mode 100644 index 0000000..ca5c225 --- /dev/null +++ b/084_monopoly_odds.py @@ -0,0 +1,79 @@ +#!/usr/bin/env python3 + +from random import randint, choice + +def dice_roll(sides, num): + return sum(randint(1, sides) for i in range(num)) + +def dice_mask(sides): + mask = [0] * sides*2 + for a in range(1, sides+1): + for b in range(1, sides+1): + mask[a+b-1] += 1.0 / sides**2 + print(mask) + return mask + +def monopoly(n, sides, itrs): + board = [0] * n + board[0] = 1 + mask = dice_mask(sides) + for i in range(itrs): + for p in range(n): + for mv in range(len(mask)): + if p+mv+1 < n: + board[p + mv + 1] += board[p] * mask[mv] + else: + board[p + mv - n + 1] += board[p] * mask[mv] + return [sq/sum(board) for sq in board] + +def move(board, p, sides, dicenum): + roll = dice_roll(sides, dicenum) + move.rolls.pop(0) + move.rolls.append(roll) + p += roll + if p >= len(board): + p -= len(board) + return p + +def simulation(sqnum, sides, dnum, itrs): + cc = (2, 17, 33) + ch = (7, 22, 36) + jail = 10 + goto_jail = 30 + railways = (5, 15, 25, 35) + utilities = (12, 28) + cards_chance = [0, jail, 11, 24, 39, 5, railways, railways, utilities, -3] + [None]*6 + cards_chest = [0, jail] + [None]*14 + + board = [0] * sqnum + board[0] = 1 + p = 0 + move.rolls = [0]*3 + for i in range(itrs): + p = move(board, p, sides, dnum) + if set(move.rolls) == {2} or p == goto_jail: + p = jail + elif p in cc + ch: + card = choice(cards_chest if p in cc else cards_chance) + if card is None: + pass + elif type(card) is tuple: + if p > max(card): + p = min(card) + else: + p = [sq for sq in card if sq >= p][0] + elif card < 0: + p += card + if p in cc: + card = choice(cards_chest) + if card is not None: + p = card + else: + p = card + board[p] += 1 + return [float(sq)/sum(board) for sq in board] + +sides = 4 +board = simulation(40, sides, 2, 1000000) +squares = [board.index(sq) for sq in sorted(board, reverse = True)] +print(''.join(map(str, squares[:3]))) diff --git a/085_counting_rectangles.c b/085_counting_rectangles.c new file mode 100644 index 0000000..fc7f5ec --- /dev/null +++ b/085_counting_rectangles.c @@ -0,0 +1,43 @@ +#include +#include +#include + +int dev(int a, int b, int p); +int calcb(int a, int p); + +int main(int argc, char *argv[]) +{ + int p = 2000000; + int a, b; + int d1, d2; //dev of b, dev of b+1 + int cd, td; //current dev, min dev + int tb, ta; //best a and b + + ta = tb = td = -1; + for(a = 1; (b = calcb(a, p)) + 1 >= a; ++a){ + d1 = dev(a, b, p); + d2 = dev(a, b + 1, p); + cd = d1 > d2 ? d2 : d1; + b += (d2 == cd); + if(cd < td || td == -1){ + //smaller deviation + td = cd; + tb = b; + ta = a; + } + } + //printf("a = %d\nb = %d\ndev = %d\narea = %d\n", ta, tb, td, ta*tb); + printf("%d\n", ta*tb); +} + +//calculate b +int calcb(int a, int p) +{ + return (sqrt(1 + ((float) 16*p)/(a*a + a)) - 1)/2; +} + +//eval deviation +int dev(int a, int b, int p) +{ + return abs(a*b*(a + 1)*(b + 1)/4 - p); +} diff --git a/087_prime_power_triples.py b/087_prime_power_triples.py new file mode 100644 index 0000000..951b43b --- /dev/null +++ b/087_prime_power_triples.py @@ -0,0 +1,38 @@ +#!/usr/bin/env python3 + +def main(lim): #exclusive lim + primes = get_primes(bound(lim, 2)) + nums = [True] * lim + c = 0 + fb = bound(lim, 4) + for frth in primes: + if frth > fb: + break + cb = bound(lim-frth**4, 3) + for cube in primes: + if cube > cb: + break + sb = bound(lim - frth**4 - cube**3, 2) + for sq in primes: + if sq > sb: + break + n = frth**4 + cube**3 + sq**2 + c += nums[n] + nums[n] = False + return c + +def bound(lim, pw): + return int(lim**(1.0/pw)) + +def get_primes(lim): #inclusive lim + sieve = [False]*2 + [True] * (lim-1) + p = [] + for i in range(2, len(sieve)): + if sieve[i]: + p.append(i) + for j in range(2*i, len(sieve), i): + sieve[j] = False + return p + +#print(main(50)) +print(main(50*10**6)) diff --git a/088_product-sum_numbers.py b/088_product-sum_numbers.py new file mode 100644 index 0000000..7a29980 --- /dev/null +++ b/088_product-sum_numbers.py @@ -0,0 +1,70 @@ +#!/usr/bin/env python3 + +# Two solutions, recursive order of magniture faster + +def base(k): + lim = 2*k + cache = [False for i in range(k+1)] + for n in range(2, lim+1): + recursive(n, n, n, lim, 2, cache) + return sum(set(cache[2:])) + +def recursive(s, p, n, lim, d, cache): #sum, product, last digit, limit, depth + m = p*n #number + x = n + while m <= lim: + ns = s+x + k = m - ns + d + if k <= lim//2 and (not cache[k] or cache[k] > m): + cache[k] = m + recursive(ns, m, x, lim, d+1, cache) + x += 1 + m += p + + + +def main(k): + return sum(set([minnum(i) for i in range(2, k+1)])) + +def minnum(k): + s = [2, 2] + s[0], mod = findn(k, s) + r = num(k, s) + while set(s[1:]) != {2} or s[0] > 2: + count(s) + s[0], mod = findn(k, s) + if mod == 0 and s[0] >= s[1] and num(k, s) < r: + r = num(k, s) + return r + +def count(s): + i = 0 + while i < len(s)-2 and s[i] <= s[i+1]: + s[i+2] += 1 + i += 1 + if s[i] <= s[i+1]: + s.append(2) + i += 1 + if i == 0: + s[1] += 1 + else: + for j in range(i+1): + s[j] = s[i+1] + +def num(k, s): + return k-len(s) + sum(s) + +def findn(k, s): + a = k-len(s) + sum(s[1:]) + b = pro(s[1:]) - 1 + return a//b, a%b + +def pro(s): + r = 1 + for i in s: + r *= i + return r + +#print(base(6)) +#print(base(12)) +print(base(12000)) diff --git a/089_roman_numerals.py b/089_roman_numerals.py new file mode 100644 index 0000000..4484dfe --- /dev/null +++ b/089_roman_numerals.py @@ -0,0 +1,41 @@ +#!/usr/bin/env python3 + +#oneoffs = set(["D", "CD", "L", "XL", "V", "IV"]) +roman_numerals = {"M" : 1000, "CM" : 900, + "D" : 500, "CD" : 400, + "C" : 100, "XC" : 90, + "L" : 50, "XL" : 40, + "X" : 10, "IX" : 9, + "V" : 5, "IV" : 4, + "I" : 1} + +def parse(path): + with open(path) as f: + return f.read().split("\n") + +def roman2int(num): + rn = roman_numerals + r = 0 + for dig, i in zip(num, num[1:]+"I"): + r += rn[dig] * (-1 if rn[dig] < rn[i] else 1) + return r + +def int2roman(num): + rnum = str() + pairs = list(roman_numerals.items()) + pairs.sort(key = lambda x: -x[1]) + for dig, val in pairs: + while val <= num: + rnum += dig + num -= val + #if rnum in oneoffs: + #break + return rnum + +def main(path): + nums = parse(path) + min_nums = map(int2roman, map(roman2int, nums)) + return sum(map(len, nums)) - sum(map(len, min_nums)) + +if __name__ == '__main__': + print(main("data/089_roman_numerals.txt")) diff --git a/090_cube_digit_pairs.py b/090_cube_digit_pairs.py new file mode 100644 index 0000000..f9353b2 --- /dev/null +++ b/090_cube_digit_pairs.py @@ -0,0 +1,22 @@ +#!/usr/bin/env python3 + +# Enumerate all possible combinations of faces and check if valid + +from itertools import combinations + +combs = [(0, 1), (0, 4), (0, 6), (1, 6), (1, 8), (2, 5), (3, 6), (4, 6)] + +def main(): + c = 0 + cubes = list(combinations(list(range(7))+list(range(6,9)), 6)) + for i,a in enumerate(cubes): + for b in cubes[i+1:]: + c += conds(a, b) + return c + +def conds(a, b): + def sym(x, y): + return (x in a and y in b) or (x in b and y in a) + return all(sym(x, y) for x,y in combs) + +print(main()) diff --git a/091_right_triangles_with_integer_coordinates.py b/091_right_triangles_with_integer_coordinates.py new file mode 100644 index 0000000..dc68e5e --- /dev/null +++ b/091_right_triangles_with_integer_coordinates.py @@ -0,0 +1,18 @@ +#!/usr/bin/env python3 + +from math import gcd + +def main(n): + c = 3 * n**2 + for x in range(1, n+1): + for y in range(1, n+1): + g = gcd(x, y) + a, b = x//g, y//g + c += min((n-x)//b, y//a) * 2 + return c + +#print(main(2)) + +print(main(50)) + +#print(main(500)) diff --git a/093_arithmetic_expressions.py b/093_arithmetic_expressions.py new file mode 100644 index 0000000..2ca278f --- /dev/null +++ b/093_arithmetic_expressions.py @@ -0,0 +1,98 @@ +#!/usr/bin/env python3 + +#Naive and buggy +#check 2 + 8 + 6 + 12 + 48 = 76 per quad + +from fractions import Fraction +from itertools import permutations, combinations, starmap + +def new_count(c, x): + while x[c] == c+1: + c+=1 + return c-1 + +def test(): + c = 27 + best = (1,2,3,4) + best_r = [] + for i in combinations(range(1, 10), 4): + r = sorted(list(main(i))) + if r[c] == c+1: + best_r = r + best = i + c = new_count(c, r) + return best, c + + +def naive(s): + r = [] + for perm in permutations(s, 4): + r += alt_prod(perm) + return r + +def alt_prod(s): + a = add(s[0], mlt(s[1], add(s[2], set([s[3]]) ))) + b = mlt(s[0], add(s[1], mlt(s[2], set([s[3]]) ))) + return [a, b] + +def main(s): + r = [] + prods = tree(s, mlt) + sums = tree(s, add) + r += fold(s[::-1], sums[1], mlt) + r += fold(s[::-1], prods[1], add) + r += fold(sums[0][:3], sums[0][3:], mlt_sets) + r += fold(prods[0][:3], prods[0][3:], add_sets) + r += fold(sums[0], prods[0][::-1], add_sets) + r += fold(sums[0], prods[0][::-1], mlt_sets) + r += [add(s[-1], sums[1][0]), mlt(s[-1], prods[1][0])] + r += naive(s) + return set([int(x) for x in set.union(*r) if x == int(x)]) + +def fold(a, b, f): + return starmap(f, zip(a, b)) + +def tree(s, f): + sc = [] + tr = [] + for i in range(4): + for j in range(i+1, 4): + sc.append(f(s[i], set([s[j]]) )) + for k in range(j+1, 4): + tr.append(f(s[k], sc[-1])) + return sc, tr + +def add_sets(a, b): + r = set() + for i in a: + r.update(add(i, b)) + return r + +def mlt_sets(a, b): + r = set() + for i in a: + for j in b: + r.add(i*j) + return r +def add(e, x): + r = set() + for i in x: + r.add(e+i) + if e != i: + r.add(abs(e-i)) + return r + +def mlt(e, x): + r = set() + for i in x: + r.add(e*i) + r.add(Fraction(1, e) * i) + r.add(Fraction(1, i) * e) + return r + +a = set([2, 3, 45, 8]) +b = set([4, 6,7]) + +r = test() +s = ''.join(map(str, r[0])) +print(s) diff --git a/094_almost_equilateral_triangles.py b/094_almost_equilateral_triangles.py new file mode 100644 index 0000000..dda5fbd --- /dev/null +++ b/094_almost_equilateral_triangles.py @@ -0,0 +1,21 @@ +#!/usr/bin/env python3 + +def pell3(): + x, y = 2, 1 + while True: + yield x, y + x, y = 2*x + 3*y, 2*y + x + +max_perimiter = 10**9 +s = 0 + +for x, y in pell3(): + p = 12*(2*y**2 + x*y) + 2 + if p <= max_perimiter: + s += p + p = 6*(x**2 - y**2) - 2 + if p > max_perimiter: + break + s += p + +print(s) diff --git a/099_largest_exponential.py b/099_largest_exponential.py new file mode 100644 index 0000000..dd3ab5a --- /dev/null +++ b/099_largest_exponential.py @@ -0,0 +1,23 @@ +#!/usr/bin/env python3 + +from math import log + +def parse(path): + with open(path) as f: + return (tuple(map(int, line.split(","))) for line in f.read().split("\n")) + +def main(path): + exps = [exp * log(base) for base, exp in parse(path)] + return exps.index(max(exps)) + 1 + +def alter(path): + exps = list(parse(path)) + copy = exps[:] + while len(exps) > 1: + if exps[0][0] > exps[1][0]**(float(exps[1][1]) // exps[0][1]): + del exps[1] + else: + del exps[0] + return copy.index(exps[0]) + 1 + +print(main("data/099_base_exp.txt")) diff --git a/data/081_matrix.txt b/data/081_matrix.txt new file mode 100644 index 0000000..f65322a --- /dev/null +++ b/data/081_matrix.txt @@ -0,0 +1,80 @@ +4445,2697,5115,718,2209,2212,654,4348,3079,6821,7668,3276,8874,4190,3785,2752,9473,7817,9137,496,7338,3434,7152,4355,4552,7917,7827,2460,2350,691,3514,5880,3145,7633,7199,3783,5066,7487,3285,1084,8985,760,872,8609,8051,1134,9536,5750,9716,9371,7619,5617,275,9721,2997,2698,1887,8825,6372,3014,2113,7122,7050,6775,5948,2758,1219,3539,348,7989,2735,9862,1263,8089,6401,9462,3168,2758,3748,5870 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+137410,584913 +217615,563034 +556887,523038 +667229,515991 +672276,515708 +325361,545187 +172115,573985 +13846,725685 \ No newline at end of file diff --git a/makefile b/makefile new file mode 100644 index 0000000..6424554 --- /dev/null +++ b/makefile @@ -0,0 +1,6 @@ + +85 : 085_counting_rectangles.c + gcc 085_counting_rectangles.c -lm -o 085_counting_rectangles.exe + +clean : + rm -f *.exe *.out