#include <iostream>

// Consider a range of consecutive integers beginning at
// 'a' and containing 'b' integers:
//
//     a, a + 1, a + 2, ..., a + b - 1.
//
// We can describe this using the half-open interval
//
//     [a, a + b).
//
// The left endpoint is included, while the right endpoint
// is not included.
//
// For example, if
//
//     a = 5
//     b = 10,
//
// then the range is
//
//     5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
//
// Similarly, 'c' and 'd' define the range
//
//     [c, c + d).
//
// Two ranges overlap if there is at least one integer
// contained in both ranges.
//
// Notice that if b == 0, the first range is empty:
//
//     [a, a).
//
// Similarly, if d == 0, the second range is empty.
// An empty range cannot overlap another range.
//
// Write two conditions:
//
//     1. The first should determine whether the ranges
//        overlap.
//
//     2. The second should determine whether the ranges
//        do not overlap.
//
// Do not use the logical NOT operator (!) in either
// condition.

// Function declarations
int main();

// Function definitions
int main() {
    int a{};

    std::cout << "Enter a first integer 'a': ";
    std::cin >> a;

    int b{};

    std::cout << "Enter a non-negative range 'b': ";
    std::cin >> b;

    if ( b < 0 ) {
        std::cout << "The range must be non-negative."
                  << std::endl;

        return 0;
    }

    int c{};

    std::cout << "Enter a second integer 'c': ";
    std::cin >> c;

    int d{};

    std::cout << "Enter a non-negative range 'd': ";
    std::cin >> d;

    if ( d < 0 ) {
        std::cout << "The range must be non-negative."
                  << std::endl;

        return 0;
    }

    // Enter a condition that is true precisely when
    //
    //     [a, a + b)
    //
    // and
    //
    //     [c, c + d)
    //
    // overlap.
    //
    // Do not use the logical NOT operator (!).

    if ( true ) {
        std::cout << "The ranges overlap."
                  << std::endl;
    } else {
        std::cout << "The ranges do not overlap."
                  << std::endl;
    }

    // Now enter a condition that is true precisely when
    // the two ranges do NOT overlap.
    //
    // Again, do not use the logical NOT operator (!).

    if ( false ) {
        std::cout << "The ranges do not overlap."
                  << std::endl;
    } else {
        std::cout << "The ranges overlap."
                  << std::endl;
    }

    return 0;
}









































// Hint:
//
// First consider the case where both ranges are nonempty.
//
// The ranges
//
//     [a, a + b)
//
// and
//
//     [c, c + d)
//
// overlap precisely when
//
//     a < c + d
//
// AND
//
//     c < a + b.
//
// Why?
//
// The first condition says that the first range begins
// before the second range ends:
//
//     a < c + d.
//
// The second says that the second range begins before the
// first range ends:
//
//     c < a + b.
//
// Both conditions must be true for the ranges to overlap.
//
// However, remember that if
//
//     b == 0
//
// or
//
//     d == 0,
//
// one of the ranges is empty and therefore the ranges
// cannot overlap.









































// There is another useful way to think about the problem.
//
// Two nonempty ranges do NOT overlap if one lies entirely
// before the other.
//
// The first range lies before the second if
//
//     a + b <= c.
//
// The second range lies before the first if
//
//     c + d <= a.
//
// Thus, the ranges do not overlap if either of these
// conditions is true.
//
// Also remember that the ranges do not overlap if either
// range is empty.









































// Here is one solution:

/*
    // The ranges overlap only if both are nonempty and
    // each range begins before the other range ends.

    if ( (b > 0) && (d > 0)
         && (a < c + d) && (c < a + b) ) {
        std::cout << "The ranges overlap."
                  << std::endl;
    } else {
        std::cout << "The ranges do not overlap."
                  << std::endl;
    }

    // The ranges do not overlap if either range is empty
    // or if one range lies entirely before the other.

    if ( (b == 0) || (d == 0)
         || (a + b <= c) || (c + d <= a) ) {
        std::cout << "The ranges do not overlap."
                  << std::endl;
    } else {
        std::cout << "The ranges overlap."
                  << std::endl;
    }
*/