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Solution to problem 15 in Python

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David Doblas Jiménez 2023-10-30 17:16:30 +01:00
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# --- Day 15: Chiton ---
# You've almost reached the exit of the cave, but the walls are getting closer
# together. Your submarine can barely still fit, though; the main problem is
# that the walls of the cave are covered in chitons, and it would be best not to
# bump any of them.
# The cavern is large, but has a very low ceiling, restricting your motion to
# two dimensions. The shape of the cavern resembles a square; a quick scan of
# chiton density produces a map of risk level throughout the cave (your puzzle
# input). For example:
# 1163751742
# 1381373672
# 2136511328
# 3694931569
# 7463417111
# 1319128137
# 1359912421
# 3125421639
# 1293138521
# 2311944581
# You start in the top left position, your destination is the bottom right
# position, and you cannot move diagonally. The number at each position is its
# risk level; to determine the total risk of an entire path, add up the risk
# levels of each position you enter (that is, don't count the risk level of your
# starting position unless you enter it; leaving it adds no risk to your total).
# Your goal is to find a path with the lowest total risk. In this example, a
# path with the lowest total risk is highlighted here:
# 1163751742
# 1381373672
# 2136511328
# 3694931569
# 7463417111
# 1319128137
# 1359912421
# 3125421639
# 1293138521
# 2311944581
# The total risk of this path is 40 (the starting position is never entered, so
# its risk is not counted).
# What is the lowest total risk of any path from the top left to the bottom
# right?
import heapq
with open("files/P15.txt") as f:
grid = {
(x, y): int(n)
for y, row in enumerate(f.read().split("\n"))
for x, n in enumerate(row)
}
max_x, max_y = max(grid)
def get_value(pos, width, height):
# Calculate additional components for the value
x_component = pos[0] // width
y_component = pos[1] // height
current_value = grid[pos[0] % width, pos[1] % height]
combined_value = current_value + x_component + y_component
if combined_value < 10:
return combined_value
else:
return combined_value % 9
def bfs(width, height, scale):
queue, visited = [(0, 0, 0)], {(0, 0)}
while queue:
risk, x, y = heapq.heappop(queue)
# Check if we reached the target coordinates
if (x, y) == (width * scale - 1, height * scale - 1):
return risk
for neighb in ((x + 1, y), (x, y + 1), (x - 1, y), (x, y - 1)):
if neighb in visited:
continue
if (
0 <= neighb[0] < width * scale
and 0 <= neighb[1] < height * scale
):
new_risk = risk + get_value(neighb, width, height)
visited.add(neighb)
heapq.heappush(queue, (new_risk, *neighb))
def part1():
res = bfs(max_x + 1, max_y + 1, scale=1)
print(f"The lowest total risk is {res}")
# --- Part Two ---
# Now that you know how to find low-risk paths in the cave, you can try to find
# your way out.
# The entire cave is actually five times larger in both dimensions than you
# thought; the area you originally scanned is just one tile in a 5x5 tile area
# that forms the full map. Your original map tile repeats to the right and
# downward; each time the tile repeats to the right or downward, all of its risk
# levels are 1 higher than the tile immediately up or left of it. However, risk
# levels above 9 wrap back around to 1. So, if your original map had some
# position with a risk level of 8, then that same position on each of the 25
# total tiles would be as follows:
# 8 9 1 2 3
# 9 1 2 3 4
# 1 2 3 4 5
# 2 3 4 5 6
# 3 4 5 6 7
# Each single digit above corresponds to the example position with a value of 8
# on the top-left tile. Because the full map is actually five times larger in
# both dimensions, that position appears a total of 25 times, once in each
# duplicated tile, with the values shown above.
# Here is the full five-times-as-large version of the first example above, with
# the original map in the top left corner highlighted:
# 11637517422274862853338597396444961841755517295286
# 13813736722492484783351359589446246169155735727126
# 21365113283247622439435873354154698446526571955763
# 36949315694715142671582625378269373648937148475914
# 74634171118574528222968563933317967414442817852555
# 13191281372421239248353234135946434524615754563572
# 13599124212461123532357223464346833457545794456865
# 31254216394236532741534764385264587549637569865174
# 12931385212314249632342535174345364628545647573965
# 23119445813422155692453326671356443778246755488935
# 22748628533385973964449618417555172952866628316397
# 24924847833513595894462461691557357271266846838237
# 32476224394358733541546984465265719557637682166874
# 47151426715826253782693736489371484759148259586125
# 85745282229685639333179674144428178525553928963666
# 24212392483532341359464345246157545635726865674683
# 24611235323572234643468334575457944568656815567976
# 42365327415347643852645875496375698651748671976285
# 23142496323425351743453646285456475739656758684176
# 34221556924533266713564437782467554889357866599146
# 33859739644496184175551729528666283163977739427418
# 35135958944624616915573572712668468382377957949348
# 43587335415469844652657195576376821668748793277985
# 58262537826937364893714847591482595861259361697236
# 96856393331796741444281785255539289636664139174777
# 35323413594643452461575456357268656746837976785794
# 35722346434683345754579445686568155679767926678187
# 53476438526458754963756986517486719762859782187396
# 34253517434536462854564757396567586841767869795287
# 45332667135644377824675548893578665991468977611257
# 44961841755517295286662831639777394274188841538529
# 46246169155735727126684683823779579493488168151459
# 54698446526571955763768216687487932779859814388196
# 69373648937148475914825958612593616972361472718347
# 17967414442817852555392896366641391747775241285888
# 46434524615754563572686567468379767857948187896815
# 46833457545794456865681556797679266781878137789298
# 64587549637569865174867197628597821873961893298417
# 45364628545647573965675868417678697952878971816398
# 56443778246755488935786659914689776112579188722368
# 55172952866628316397773942741888415385299952649631
# 57357271266846838237795794934881681514599279262561
# 65719557637682166874879327798598143881961925499217
# 71484759148259586125936169723614727183472583829458
# 28178525553928963666413917477752412858886352396999
# 57545635726865674683797678579481878968159298917926
# 57944568656815567976792667818781377892989248891319
# 75698651748671976285978218739618932984172914319528
# 56475739656758684176786979528789718163989182927419
# 67554889357866599146897761125791887223681299833479
# Equipped with the full map, you can now find a path from the top left corner
# to the bottom right corner with the lowest total risk:
# 11637517422274862853338597396444961841755517295286
# 13813736722492484783351359589446246169155735727126
# 21365113283247622439435873354154698446526571955763
# 36949315694715142671582625378269373648937148475914
# 74634171118574528222968563933317967414442817852555
# 13191281372421239248353234135946434524615754563572
# 13599124212461123532357223464346833457545794456865
# 31254216394236532741534764385264587549637569865174
# 12931385212314249632342535174345364628545647573965
# 23119445813422155692453326671356443778246755488935
# 22748628533385973964449618417555172952866628316397
# 24924847833513595894462461691557357271266846838237
# 32476224394358733541546984465265719557637682166874
# 47151426715826253782693736489371484759148259586125
# 85745282229685639333179674144428178525553928963666
# 24212392483532341359464345246157545635726865674683
# 24611235323572234643468334575457944568656815567976
# 42365327415347643852645875496375698651748671976285
# 23142496323425351743453646285456475739656758684176
# 34221556924533266713564437782467554889357866599146
# 33859739644496184175551729528666283163977739427418
# 35135958944624616915573572712668468382377957949348
# 43587335415469844652657195576376821668748793277985
# 58262537826937364893714847591482595861259361697236
# 96856393331796741444281785255539289636664139174777
# 35323413594643452461575456357268656746837976785794
# 35722346434683345754579445686568155679767926678187
# 53476438526458754963756986517486719762859782187396
# 34253517434536462854564757396567586841767869795287
# 45332667135644377824675548893578665991468977611257
# 44961841755517295286662831639777394274188841538529
# 46246169155735727126684683823779579493488168151459
# 54698446526571955763768216687487932779859814388196
# 69373648937148475914825958612593616972361472718347
# 17967414442817852555392896366641391747775241285888
# 46434524615754563572686567468379767857948187896815
# 46833457545794456865681556797679266781878137789298
# 64587549637569865174867197628597821873961893298417
# 45364628545647573965675868417678697952878971816398
# 56443778246755488935786659914689776112579188722368
# 55172952866628316397773942741888415385299952649631
# 57357271266846838237795794934881681514599279262561
# 65719557637682166874879327798598143881961925499217
# 71484759148259586125936169723614727183472583829458
# 28178525553928963666413917477752412858886352396999
# 57545635726865674683797678579481878968159298917926
# 57944568656815567976792667818781377892989248891319
# 75698651748671976285978218739618932984172914319528
# 56475739656758684176786979528789718163989182927419
# 67554889357866599146897761125791887223681299833479
# The total risk of this path is 315 (the starting position is still never
# entered, so its risk is not counted).
# Using the full map, what is the lowest total risk of any path from the top
# left to the bottom right?
def part2():
res = bfs(max_x + 1, max_y + 1, 5)
print(f"The lowest total risk is {res}")
if __name__ == "__main__":
part1()
part2()