Question

这里的间隔与Line相同。尽管我为两个目的找到了正确的解决方案：

1）排序间隔；

2）在添加与现有间隔重叠的间隔时拒绝。

struct Line {
    int down;
    int up;

    Line(int down, int up) {
        this->down = down;
        this->up = up;
    }
};

int main() {
    auto cmp = [] (const Line& a, const Line& b) {//NOTE: this can even detect the intersection, as well as sort the interval!!
        if (a.up <= b.down) return true;
        else return false;
    };

    set<Line, decltype(cmp)> s(cmp);
    Line l1{2, 3};
    Line l2{3, 5};
    Line l3{1, 2}; //success for insertion
    Line l4{4, 6}; //fail for insertion b/c of insersection


    auto ret = s.insert(l2);
    cout << "insert 3->5 ";
    if (ret.second) cout << "success " << endl;
    else cout << "fail " << endl;

    ret = s.insert(l3);
    cout << "insert 1->2 ";
    if (ret.second) cout << "success " << endl;
    else cout << "fail " << endl;

    ret = s.insert(l1);
    cout << "insert 2->3 ";
    if (ret.second) cout << "success " << endl;
    else cout << "fail " << endl;

    ret = s.insert(l4);
    cout << "insert 4->6 ";
    if (ret.second) cout << "success " << endl;
    else cout << "fail " << endl;

    return 0;
}

Output:
insert 3->5 success
insert 1->2 success
insert 2->3 success
insert 4->6 fail
set finally contains: 1->2, 2->3, 3->5,

还有一些令人困惑的事情：

1）为什么简单地比较a.up <= b.down就足以检测重叠间隔了？

我们不应该做类似检测间隔重叠的标准方法吗？

max(a.down, b.down) < min(a.up, b.up)

2）第三步对我来说还不清楚

insert 3->5 success
insert 1->2 success //OK, b/c 2 <= 3, a.up <= b.down return true
insert 2->3 success //Why success? 3 > 1, i.e., a.up > b.down, return false; does it only compare with interval 3->5?

3）为什么下面的代码对于删除重叠间隔无效？

    auto cmp_set = [](const Line& a, const Line& b) {
        if (max(a.down, b.down) < min(a.up, b.up)) return 0; //standard way to detect overlapping of intervals
        else { //sort the two intervals 
            if(a.up <= b.down) return -1;
            else return 1;
        }
    };

Answer 1

1）为什么仅比较a.up <= b.down足以检测重叠间隔？

当[a.down, a.up[时

[b.down, b.up[与max(a.down, b.down) < min(a.up, b.up)重叠等效于a.down < b.up && b.down < a.up（请记住，区间定义中也有a.down <= a.up && b.down <= b.up）。

我们还可以列出可能性：

a.down < a.up < b.down < b.up (a < b)
a.down < b.down < a.up < b.up交叉点
a.down < b.down < b.up < a.up交叉路口（全部包含）
b.down < a.down < a.up < b.up交叉路口（全部包含）
b.down < a.down < b.up < a.up交叉点
b.down < b.up < a.down < a.up (b < a)

我不清楚第三步

insert 3->5 success insert 1->2 success //OK, b/c 2 <= 3, a.up <= b.down return true insert 2->3 success //Why success? 3 > 1, i.e., a.up > b.down, return false; does it only compare with interval 3->5?

Line l1{2, 3};
Line l2{3, 5};
Line l3{1, 2};
Line l4{4, 6};

要在l1中插入{l3, l2}

l1 < l2，所以l1在l2之前
!(l1 < l3)，所以l1不在l3之前
l3 < l1，所以l1在l3之后 -> {l3, l1, l2}

对于l4中的{l3, l1, l2}，我们有：

!(l4 < l2)（类似于l3和l1），因此l4不在l2之前
!(l2 < l4)，因此l4不在l2之后

我们都有!(l2 < l4) && !(l4 < l2)，所以有等价，我们不插入l4。

3）为什么下面的代码对于删除重叠间隔无效？

我不知道您在哪里使用它。

C ++排序间隔结构以及删除重叠间隔

1 个答案: