檢查給定的兩個集合是否是 disjoint 集合?


當兩個集合沒有公共元素時,它們是 disjoint 集合。換句話說,如果我們得到兩個集合的交集,那麼我們將會得到空集。

該方法很簡單,在這個演算法中,給定了兩個集合。我們假設這兩個集合已經被排序,在兩個集合之間比較項。當匹配時,它不是一個 disjoint 集合,當沒有項匹配時,它們是 disjoint 集合。

輸入和輸出

Input:
Two sets:
set1: {15, 12, 36, 21, 14}
set2: {7, 89, 56, 32}
Output:
Both sets are disjoint

演算法

isDisjoint(set1, set2)

輸入:兩個集合。

輸出:當兩個集合都是 disjoint 集合時為 True。

Begin
   i1 := start of first set
   i2 := start of second set
   while i1 in set1 and i2 in set 2, do
      if set1[i1] < set2[i2], then
         i1 := i1 + 1
      else if set2[i2] < set1[i1], then
         i2 := i2 + 1
      else
         return false
   done
   return true
End

示例

#include<iostream>
#include<set>
using namespace std;

bool isDisjoint(set<int> set1, set<int> set2) {
   set<int>::iterator i1, i2;
   i1 = set1.begin(); i2 = set2.begin();            //initialize iterators with first element
   while(i1 != set1.end() && i2 != set2.end()) {         //when both set have some elements to check
      if(*i1 < *i2)
         i1++;                   //when item of first set is less than second set
      else if(*i2 < *i1)
         i2++;               //when item of second set is less than first set
      else
         return false;            //if items are matched, sets are not disjoint
   }
   return true;

}

int main() {
   set<int> set1, set2;
   int n1, n2;
   cout << "Enter number of elements in set 1: "; cin >>n1;

   while(n1 != set1.size()) {       //duplicate items will be discarded
      int item;
      cout << "Enter element: "; cin >> item;
      set1.insert(item);
   }

   cout << "Enter number of elements in set 2: "; cin >>n2;
   while(n2 != set2.size()) {
      int item;
      cout << "Enter element: "; cin >> item;
      set2.insert(item);
   }

   if(isDisjoint(set1, set2))
      cout << "Both sets are disjoint";
   else
      cout << "Sets are not disjoint";
}

輸出

Enter number of elements in set 1: 5
Enter element: 15
Enter element: 12
Enter element: 36
Enter element: 21
Enter element: 14
Enter number of elements in set 2: 4
Enter element: 7
Enter element: 89
Enter element: 56
Enter element: 32
Both sets are disjoint

更新於: 2020 年 6 月 17 日

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