> For the complete documentation index, see [llms.txt](https://lochiwei.gitbook.io/web/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://lochiwei.gitbook.io/web/js/ex/exercises/pascals-triangle.md).

# Pascal's Triangle

{% tabs %}
{% tab title="demo" %}
{% embed url="<https://codesandbox.io/embed/pascal-triangle-94yoh?fontsize=14&hidenavigation=1&theme=dark>" %}
Pascal's Triangle
{% endembed %}
{% endtab %}

{% tab title="c(m,n)" %}

```javascript
import { caching } from '../decorator/caching.js';

// binomial combinations
function _c(m, n) {
  if (m - n < 0 || n < 0) return 0;
  if (m - n === 0 || n === 0) return 1;
  return _c(m - 1, n - 1) + _c(m - 1, n);
}

// give 'memory' to function '_c'
export const c = caching(_c);
```

{% endtab %}
{% endtabs %}

## caching decorator

{% tabs %}
{% tab title="caching(f)" %}

```javascript
// ⭐️ caching decorator
//    use a closure to ecapsulate 'f'
export function caching(f) {
  // make a new cache for this 'f'
  let cache = new Map();

  // returns a function that can remember
  return function (...args) {
    // if not in cache, cache it.
    const key = `${args}`;
    if (!cache.has(key)) {
      //          ╭- call a method -╮  ('f' could be a method)
      let value = f.apply(this, args); // ⭐️ with "this" context
      cache.set(key, value);
      // log(`(${key}, ${value}) cached ...`);
    }
    // get function value from cache
    return cache.get(key);
  };
}
```

{% endtab %}

{% tab title="📗 參考" %}

* JS.info ⟩ [Decorators and forwarding, call/apply](https://javascript.info/call-apply-decorators)
* PJCHENder ⟩ [\[演算法\] Fibonacci：善用 cache 和 Memoization 提升程式效能](https://pjchender.blogspot.com/2017/09/fibonacci-cache-memoization.html)
  {% endtab %}

{% tab title="💾 程式" %}

* codesandbox - [Pascal Triangle](https://codesandbox.io/s/pascal-triangle-94yoh?file=/decorator/caching.js)
* replit - [decorating methods](https://replit.com/@pegasusroe/decorating-methods#script.js)
  {% endtab %}
  {% endtabs %}


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