---
id: 5900f3b01000cf542c50fec2
title: 'Problema 67: somma massima del percorso II'
challengeType: 1
forumTopicId: 302179
dashedName: problem-67-maximum-path-sum-ii
---

# --description--

Cominciando dalla parte superiore del triangolo sottostante e spostandosi verso i numeri adiacenti sulla riga sottostante, il totale massimo dall'alto al basso è 23.

<div style='text-align: center;'>
  <strong style='color: red;'>3</strong><br>
  <strong style='color: red;'>7</strong> 4<br>
  2 <strong style='color: red;'>4</strong> 6<br>
  8 5 <strong style='color: red;'>9</strong> 3
</div>

Cioè, 3 + 7 + 4 + 9 = 23.

Trova il totale massimo da cima a fondo in `numTriangle`, un array 2D definito dietro le quinte contenente un triangolo con cento righe.

**Nota:** questa è una versione molto più difficile del problema 18. Non è possibile provare ogni percorso per risolvere questo problema, ce ne sono 2<sup>99</sup> in tutto! Se tu potessi controllare mille miliardi (10<sup>12</sup>) di percorsi ogni secondo ci vorrebbero dieci milioni di anni per controllarli tutti. C'è un algoritmo efficiente per risolverlo. ;o)

# --hints--

`maximumPathSumII([[3, 0, 0, 0],[7, 4, 0, 0],[2, 4, 6, 0],[8, 5, 9, 3]])` dovrebbe restituire un numero.

```js
assert(typeof maximumPathSumII(_testTriangle) === 'number');
```

`maximumPathSumII([[3, 0, 0, 0],[7, 4, 0, 0],[2, 4, 6, 0],[8, 5, 9, 3]])` dovrebbe restituire 23.

```js
assert.strictEqual(maximumPathSumII(_testTriangle), 23);
```

`maximumPathSumII(numTriangle)` dovrebbe restituire 7273.

```js
assert.strictEqual(maximumPathSumII(_numTriangle), 7273);
```

# --seed--

## --before-user-code--

```js
const _testTriangle = [[3, 0, 0, 0],
                      [7, 4, 0, 0],
                      [2, 4, 6, 0],
                      [8, 5, 9, 3]];
const _numTriangle = 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```

## --seed-contents--

```js
function maximumPathSumII(triangle) {

  return true;
}
```

# --solutions--

```js
function maximumPathSumII(triangle) {
  const newTriangle = [];
  for (let i = 0; i < triangle.length; i++) {
    newTriangle.push(triangle[i].slice());
  }

  for (let i = newTriangle.length - 2; i >= 0; i--) {
    for (let j = i; j >= 0; j--) {
      let higherOption = 0;
      if (newTriangle[i + 1][j + 1] > newTriangle[i + 1][j]) {
        higherOption = newTriangle[i + 1][j + 1];
      } else {
        higherOption = newTriangle[i + 1][j];
      }
      newTriangle[i][j] += higherOption;
    }
  }
  return newTriangle[0][0];
}
```
