Given various ways to score points, represented by an arbitrary array w, count how many ways you can add up to a score s.

dynamic_programming_permutations.js

function waysToScore(awards, score, sorted = false) {
  // Ensure the ways to score points are sorted.
  if(!sorted) { awards.sort((a, b)=>( a - b )); }

  var ways = new Array(score + 1).fill(0);

  // There's one way to score 0 points
  ways[0] = 1;

  // Loop through each integer from 1 up to the score
  for (var s = 1; s <= score; s++){
    // Loop through the awards that are not greater than this score
    for (var a = 0; a < awards.length && awards[a] <= s; a++){
      // Calculate what the score must have been prior to award
      let previousScore = ways[s - awards[a]];
      // Add each of the ways of getting previousScore to current ways
      ways[s] += previousScore;
    }
  }
  // return the score (or 0 if it is still undefined)
  return ways[score];
}

waysToScore([2, 3, 7, 8], 0, true);  // 1
waysToScore([2, 3, 7, 8], 1, true);  // 0
waysToScore([2, 3, 7, 8], 2, true);  // 1
waysToScore([2, 3, 7, 8], 3, true);  // 1
waysToScore([2, 3, 7, 8], 4, true);  // 1
waysToScore([2, 3, 7, 8], 5, true);  // 2
waysToScore([2, 3, 7, 8], 6, true);  // 2
waysToScore([2, 3, 7, 8], 7, true);  // 4
waysToScore([2, 3, 7, 8], 8, true);  // 5
waysToScore([2, 3, 7, 8], 9, true);  // 7
waysToScore([2, 3, 7, 8], 26, true); // 2687