24 - Best travel

Don’t say so much, just coding…

Instruction

John and Mary want to travel between a few towns A, B, C … Mary has on a sheet of paper a list of distances between these towns. ls = [50, 55, 57, 58, 60]. John is tired of driving and he says to Mary that he doesn’t want to drive more than t = 174 miles and he will visit only 3 towns.

Which distances, hence which towns, they will choose so that the sum of the distances is the biggest possible to please Mary and John?

Example:

With list ls and 3 towns to visit they can make a choice between: [50,55,57],[50,55,58],[50,55,60],[50,57,58],[50,57,60],[50,58,60],[55,57,58],[55,57,60],[55,58,60],[57,58,60].

The sums of distances are then: 162, 163, 165, 165, 167, 168, 170, 172, 173, 175.

The biggest possible sum taking a limit of 174 into account is then 173 and the distances of the 3 corresponding towns is [55, 58, 60].

The function chooseBestSum (or choose_best_sum or … depending on the language) will take as parameters t (maximum sum of distances, integer >= 0), k (number of towns to visit, k >= 1) and ls (list of distances, all distances are positive or null integers and this list has at least one element). The function returns the “best” sum ie the biggest possible sum of k distances less than or equal to the given limit t, if that sum exists, or otherwise nil, null, None, Nothing, depending on the language. With C++, C, Rust, Swift, Go, Kotlin return -1.

Examples:

ts = [50, 55, 56, 57, 58] choose_best_sum(163, 3, ts) -> 163

xs = [50] choose_best_sum(163, 3, xs) -> nil (or null or ... or -1 (C++, C, Rust, Swift, Go)

ys = [91, 74, 73, 85, 73, 81, 87] choose_best_sum(230, 3, ys) -> 228

Ruby

Init

def choose_best_sum(t, k, ls)
    # your code
end

Sample Testing

Test.describe("choose_best_sum") do
  Test.it("Basic Tests") do
    ts = [50, 55, 56, 57, 58]
    Test.assert_equals(choose_best_sum(163, 3, ts), 163)
    ts = [50]
    Test.assert_equals(choose_best_sum(163, 3, ts), nil)
    ts = [91, 74, 73, 85, 73, 81, 87]
    Test.assert_equals(choose_best_sum(230, 3, ts), 228)
  end
end

Javascript

Init

function chooseBestSum(t, k, ls) {
  // your code
}

Sample Testing

Test.describe("chooseBestSum",function() {
  Test.it("Basic tests ",function() {        
    var ts = [50, 55, 56, 57, 58]
    Test.assertEquals(chooseBestSum(163, 3, ts), 163)
    ts = [50]
    Test.assertEquals(chooseBestSum(163, 3, ts), null)
    ts = [91, 74, 73, 85, 73, 81, 87]
    Test.assertEquals(chooseBestSum(230, 3, ts), 228)
})})

---

Thinking

想法(1): 以 k 個 towns 來作為陣列，並且加總然後選擇小於 t miles 的數字，並且找出最大值
想法(2): 這邊查到 combination 這個 ruby 的方法減少很多麻煩… 寫了好幾題覺得 ruby 真好 ·＿·

圖片來源：Unsplash Ergita Sela

Hint & Reference

• Ruby
  • Ruby - apidock combination
• JavaScript
  • JS - MDN Array.prototype.concat()

Solution

Ruby

# Solution 1
def choose_best_sum(t, k, ls)
  ls.combination(k)
    .map{ |array| array.reduce(:+) }
    .select{ |sum| sum <= t }
    .max
end

# Solution 2
def choose_best_sum(t, k, ls)
  ls.combination(k).map(&:sum).reject { |n| n > t }.max
end

Javascript

// Solution 1
function chooseBestSum(t, k, ls) {
  var biggestCount = 0;
  var recurseTowns = function(townsSoFar, lastIndex) {
    townsSoFar = townsSoFar || [];

    if (townsSoFar.length === k) {
      var sumDistance = townsSoFar.reduce((a,b)=>a+b);
      if (sumDistance <= t && sumDistance > biggestCount) {
        biggestCount = sumDistance;
      }      
      return;
    }

    for (var i = lastIndex + 1 || 0; i < ls.length; i++) {
      recurseTowns(townsSoFar.concat(ls[i]), i);
    }
  }
  recurseTowns();
  
  return biggestCount || null;
}