是动态编程还是分而治之？

Question

I'm in the middle of studying algorithms. There is an article I read indirectly discussing the knapsack problem. In the end it is said to be solved with dynamic programming but to me it looks like just divide and conquer with minor optimizations. Can someone have a look? I have pasted the code into a bin http://jsbin.com/sulipipole/edit?js,console .

const ACTIVITIES = [
  {name: 'side-project', time: 10, xp: 12},
  {name: 'algorithms', time: 3, xp: 7},
  {name: 'networking', time: 1, xp: 0.5},
  {name: 'exercise', time: 2, xp: 1.5},
  {name: 'systems design', time: 4, xp: 4},
  {name: 'making CSS codepens', time: 3, xp: 4}
];


const findJob = function(time, activities) {

    const optimalSolution = function(items, n = items.length, timeLeft = time) {

    if (n === 0 || timeLeft === 0) {
      return [];
    }

    if (items[n - 1].time > timeLeft) {
      return optimalSolution(items, n - 1, timeLeft);
    }

     const lastItem = items[n - 1];

    const withLastItem = [
      lastItem,
      ...optimalSolution(items, n - 1, timeLeft - lastItem.time)
    ];
    const withoutLastItem = optimalSolution(items, n - 1, timeLeft);

    if (totalXp(withLastItem) > totalXp(withoutLastItem)) {
      return withLastItem;
    } else {
      return withoutLastItem;
    }
    };

    const totalXp = arr => arr.reduce((total, ea) => total + ea.xp, 0);

    const sortedByTime = activities
      .slice()
      .sort((a, b) => a.time - b.time);

    return optimalSolution(sortedByTime)
      .map(act => act.name);
    };

Dynamic programming requires some memoization or tabling scheme correct?

Answer 1

I really like the way Skiena described dynamic programming in his book "the algorithm design manual". "Dynamic programming is a technique for efficiently implementing a recursive algorithm by storing partial results".

You have a recursive algorithm here but no storing of partial results. So it is not dynamic programming. But it can probably be turned into a dynamic programming algorithm by storing and reusing the partial results.