一种 Select 是对两个数组进行排序,然后遍历这两个数组,比较元素.如果在超级包中找不到子包候选元素,则前者不是子包.排序通常为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)来计算总体O(最大(s,t))时间复杂度,不过如果行李很小,内置Array.sort
可能会比自定义整数排序运行得更快.
一个可能时间复杂度较低的解决方案是创建一个包类型.整型包特别容易.翻转行李的现有数组:创建一个对象或一个数组,将整数作为键,并对值进行重复计数.使用数组不会因为创建arrays are sparse in Javascript而浪费空间.您可以使用行李操作进行子行李或超级行李判断.例如,从子候选项中减go super,然后测试结果是否为非空.或者,contains
操作应为O(1)(或可能为O(log(n)),因此,在子袋候选者上循环,并测试每个子袋元件的超级袋安全壳是否超过子袋安全壳应为O(n)或O(n*log(n)).
以下内容未经测试.实施isInt
个左作为练习.
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);
}));
};
如果您希望禁止元素重复,请参见"comparing javascript arrays"以获取一组对象的示例实现.