Project Euler Problem 83 Solution

Question

NOTE: This problem is a significantly more challenging version of Problem 81.

In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by moving left, right, up, and down, is indicated in bold red and is equal to 2297.

 131 673 234 103 18 201 96 342 965 150 630 803 746 422 111 537 699 497 121 956 805 732 524 37 331

Find the minimal path sum, in matrix.txt (right click and ‘Save Link/Target As…’), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by moving left, right, up, and down.

JavaScript

const fs = require("fs")

function parseMatrix(matrix) {
return matrix.toString().trim().split("\n").map((line) => {
return line.split(",").map((c) => parseInt(c))
})
}

function bfs(graph, root, target) {
function neighbors([x, y]) {
const candidates = [
[x - 1, y],
[x + 1, y],
[x, y - 1],
[x, y + 1]
]
return candidates.filter(([x, y]) => {
return x >= 0 && x < graph[0].length && y >= 0 && y < graph.length
})
}

function evaluate(path) {
return path.reduce((acc, [x, y]) => acc + graph[y][x], 0)
}

const start = [root]
const frontier = [[evaluate(start), start]]
const explored = new Set()
while (frontier.length > 0) {
let path = null
let min = Infinity
let index = -1
frontier.forEach(([score, candidate], i) => {
if (score < min) {
min = score
path = candidate
index = i
}
})
frontier.splice(index, 1)
const node = path[path.length - 1]
if (node.toString() === target.toString()) {
return min
}
neighbors(node).forEach((neighbor) => {
if (!explored.has(neighbor.toString())) {
const newPath = path.slice()
newPath.push(neighbor)
frontier.push([evaluate(newPath), newPath])
}
})
}
}

const graph = parseMatrix(fs.readFileSync(__dirname + "/matrix.txt"))
console.log(bfs(graph, [0, 0], [graph[0].length - 1, graph.length - 1]))
$time node --use-strict path-sum.js real 0m6.001s user 0m6.004s sys 0m0.008s Python #!/usr/bin/env python2 import os import heapq def parse(matfile): return [[int(n) for n in row.split(',')] for row in matfile] def distance(a, b): return sum(abs(a[i] - b[i]) for i in range(len(a))) def astar(matrix, targets, sources): def neighbors(position): (x, y) = position candidates = [(x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1)] return [(x, y) for (x, y) in candidates if x >= 0 and x < len(matrix) and y >= 0 and y < len(matrix[0])] def evaluate(path): f = sum(matrix[y][x] for (x, y) in path) h = min(distance(path[-1], target) for target in targets) return f + h targets = set(targets) frontier = set(sources) explored = set() frontier_queue = [] for source in sources: path = [source] heapq.heappush(frontier_queue, (evaluate(path), path)) while frontier: (_, path) = heapq.heappop(frontier_queue) frontier.remove(path[-1]) explored.add(path[-1]) if path[-1] in targets: return path for neighbor in neighbors(path[-1]): if neighbor not in frontier | explored: frontier.add(neighbor) new_path = path + [neighbor] heapq.heappush(frontier_queue, (evaluate(new_path), new_path)) def main(): with open(os.path.join(os.path.dirname(__file__), "matrix.txt")) as matfile: matrix = parse(matfile) targets = [(len(matrix) - 1, len(matrix[0]) - 1)] sources = [(0, 0)] print(sum(matrix[y][x] for (x, y) in astar(matrix, targets, sources))) if __name__ == "__main__": main() $ time python3 path-sum.py
real   0m1.643s
user   0m1.640s
sys    0m0.000s