/** Find the Missing Number
*
* @reference https://www.geeksforgeeks.org/find-the-missing-number/
*
* You are given a list of n-1 integers and these integers are in the range of 1 to n.
* There are no duplicates in list. One of the integers is missing in the list.
* Write an efficient code to find the missing integer.
*
* @complexity O(n)
*/
auto FindTheMissingNumberSum(const ArrayType &integers) {
assert(not integers.empty());
const auto N = integers.size() + 1u;
const auto sum = N * (N + 1) / 2;
return std::accumulate(integers.cbegin(), integers.cend(), sum, std::minus<ArrayType::value_type> {});
}
auto FindTheMissingNumberXor(const ArrayType &integers) {
assert(not integers.empty());
const auto N = integers.size() + 1u;
auto xor_of_all = integers[0];
for (ArrayType::size_type i = 1ul; i < integers.size(); ++i) {
xor_of_all ^= (i ^ integers[i]);
}
return xor_of_all ^ N ^ integers.size();
}
std::pair<int, int> FindSubarrayWithGivenSum(const ArrayType &integers,
const ArrayType::value_type SUM) {
assert(not integers.empty());
auto start = integers.cbegin();
auto current_sum = *start;
for (auto i = start + 1; i != integers.cend(); ++i) {
while (current_sum > SUM and start < i - 1) {
current_sum -= *start++;
}
if (current_sum == SUM) {
return std::make_pair(start - integers.cbegin(), i - integers.cbegin() - 1);
}
current_sum += *i;
}
return NOT_FOUND;
}