Checking properties

Many problems can be formulated where one needs to verify if the elements of a vector satisfy various properties, but all can ultimately be reduced to one of the following:

• checking if all elements of a given vector satisfy a certain rule;
• checking if in a given vector there exist elements that satisfy a certain rule.

A solution could be to count the elements that satisfy the rule. Finally:

• if the number of elements satisfying the rule equals the total number of elements in the vector, then all elements satisfy the rule
• if the number of elements satisfying the rule is non-zero, then there exist elements that satisfy the rule.

Another, more efficient solution allows us to stop traversing when we are certain whether the vector satisfies the desired property or not. We'll use a boolean variable (with values true or false, 1 or 0, ...):

• if at the end the variable has the value true, then the vector satisfies the rule
• if at the end the variable has the value false, then the vector does not satisfy the rule

All elements satisfy the rule

          bool OK = true;
  for(int i = 0 ; i < n ; i ++)
      if(X[i] - does not satisfy the rule)
      {
          OK = false;
          break;
      }
        

There exist elements that satisfy the rule

bool OK = false;
  for(int i = 0 ; i < n ; i ++)
      if(X[i] - satisfies the rule)
      {
          OK = true;
          break;
      }