一种选择是对两个数组进行排序,然后遍历两者,比较元素。如果在超级包中没有找到子包候选中的元素,则前者不是子包。排序一般为 O(n*log(n)),比较为 O(max(s,t)),其中s和t是数组大小,总时间复杂度为 O(m*log(m)) , 其中 m=max(s,t)。
function superbag(sup, sub) {
sup.sort();
sub.sort();
var i, j;
for (i=0,j=0; i<sup.length && j<sub.length;) {
if (sup[i] < sub[j]) {
++i;
} else if (sup[i] == sub[j]) {
++i; ++j;
} else {
// sub[j] not in sup, so sub not subbag
return false;
}
}
// make sure there are no elements left in sub
return j == sub.length;
}
如果实际代码中的元素是整数,则可以使用特殊用途的整数排序算法(例如radix sort)来实现整体 O(max(s,t)) 时间复杂度,但如果包很小,则构建的-inArray.sort
可能比自定义整数排序运行得更快。
时间复杂度可能较低的解决方案是创建包类型。整数袋特别容易。翻转包的现有数组:创建一个对象或数组,以整数为键,重复计数值。使用数组不会浪费空间,因为数组在 Javascript 中是稀疏的。您可以使用包操作进行子包或超级包检查。例如,从子候选中减去 super 并测试结果是否为非空。或者,contains
操作应该是 O(1)(或可能是 O(log(n))),因此循环遍历候选子袋并测试超级袋的容纳量是否超过每个子袋元素的子袋的容纳量应该是 O(n) 或 O(n*log(n))。
以下内容未经测试。isInt
左的实施作为练习。
function IntBag(from) {
if (from instanceof IntBag) {
return from.clone();
} else if (from instanceof Array) {
for (var i=0; i < from.length) {
this.add(from[i]);
}
} else if (from) {
for (p in from) {
/* don't test from.hasOwnProperty(p); all that matters
is that p and from[p] are ints
*/
if (isInt(p) && isInt(from[p])) {
this.add(p, from[p]);
}
}
}
}
IntBag.prototype=[];
IntBag.prototype.size=0;
IntBag.prototype.clone = function() {
var clone = new IntBag();
this.each(function(i, count) {
clone.add(i, count);
});
return clone;
};
IntBag.prototype.contains = function(i) {
if (i in this) {
return this[i];
}
return 0;
};
IntBag.prototype.add = function(i, count) {
if (!count) {
count = 1;
}
if (i in this) {
this[i] += count;
} else {
this[i] = count;
}
this.size += count;
};
IntBag.prototype.remove = function(i, count) {
if (! i in this) {
return;
}
if (!count) {
count = 1;
}
this[i] -= count;
if (this[i] > 0) {
// element is still in bag
this.size -= count;
} else {
// remove element entirely
this.size -= count + this[i];
delete this[i];
}
};
IntBag.prototype.each = function(f) {
var i;
foreach (i in this) {
f(i, this[i]);
}
};
IntBag.prototype.find = function(p) {
var result = [];
var i;
foreach (i in this.elements) {
if (p(i, this[i])) {
return i;
}
}
return null;
};
IntBag.prototype.sub = function(other) {
other.each(function(i, count) {
this.remove(i, count);
});
return this;
};
IntBag.prototype.union = function(other) {
var union = this.clone();
other.each(function(i, count) {
if (union.contains(i) < count) {
union.add(i, count - union.contains(i));
}
});
return union;
};
IntBag.prototype.intersect = function(other) {
var intersection = new IntBag();
this.each(function (i, count) {
if (other.contains(i)) {
intersection.add(i, Math.min(count, other.contains(i)));
}
});
return intersection;
};
IntBag.prototype.diff = function(other) {
var mine = this.clone();
mine.sub(other);
var others = other.clone();
others.sub(this);
mine.union(others);
return mine;
};
IntBag.prototype.subbag = function(super) {
return this.size <= super.size
&& null !== this.find(
function (i, count) {
return super.contains(i) < this.contains(i);
}));
};
如果您希望禁止重复元素,请参阅“比较 javascript 数组”以获取一组对象的示例实现。