# Project Euler Problem 81 Solution

## Question

In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated in bold red and is equal to 2427.

 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 only moving right 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, 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 0m4.147s user 0m4.120s sys 0m0.036s ## Python #!/usr/bin/env python import os import sys from collections import defaultdict def dijkstra(matrix): def neighbors(node): (x, y) = node n = [] if x < len(matrix[0]) - 1: n.append((x + 1, y)) if y < len(matrix) - 1: n.append((x, y + 1)) return n def value(node): (x, y) = node return matrix[y][x] current = (0, 0) dest = (len(matrix[0]) - 1, len(matrix) - 1) unvisited = set((x, y) for x in range(dest[0] + 1) for y in range(dest[1] + 1)) nodes = {} for node in unvisited: nodes[node] = sys.maxsize nodes[current] = value(current) while 1: for node in [n for n in neighbors(current) if n in unvisited]: distance = nodes[current] + value(node) if distance < nodes[node]: nodes[node] = distance unvisited.remove(current) if current == dest: break else: current = min((nodes[node], node) for node in unvisited)[1] return nodes[dest] def main(): matrix = [] with open(os.path.join(os.path.dirname(__file__), "matrix.txt")) as matfile: for row in matfile: matrix.append([int(n) for n in row.split(',')]) print(dijkstra(matrix)) if __name__ == "__main__": main() $ time python3 minimal_path.py
real   0m3.090s
user   0m3.080s
sys    0m0.008s