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]
    explored.add(node.toString())
    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 --harmony-destructuring path-sum.js
real   0m6.366s
user   0m6.148s
sys    0m0.104s

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   0m3.258s
user   0m3.220s
sys    0m0.000s