Comet LXIV

Problem

Given an integer between 1 and 20, inclusive, convert the integer to Roman numeral.

30. Comet LXIV, Comet 64

Solution 1

Let n be the input integer, where 1 <= n <= 20. Let q and r be the quotient and remainder, respectively, after dividing n by 10. We have these cases:

1. If q = 2, then n = 20.
2. If q = 1, then 10 <= n < 20.
3. If q = 0, then n < 10.

We isolate the quotient q and remainder r. Convert to Roman numeral on a case-by-case basis.

str = ;                   // S := empty string
reg = input;              // Read the integer n.
int = reg / 10;           // The quotient.
int = int * 10;           // The quotient as tens.
int = reg - int;          // The remainder.
switch int;               // Store the remainder.
int = reg / 10;           // The quotient.
reg = int;                // Quotient q.
switch int;               // Remainder r.
check reg = 2;            // Is q = 2?
jump if true: twenty;     // If so, go to "twenty".
check reg = 1;            // Is q = 1?
jump if true: ten;        // If so, go to "ten".
jump to: units;           // Otherwise, go to "units".
twenty:                   // The "twenty" branch.
    str = XX;             // Append XX to S.
    jump to: units;       // Go to "units".
ten:                      // The "ten" branch.
    str = X;              // Append X to S.
units:                    // The "units" branch.
    check int = 9;        // Is n = 9?
    jump if true: nine;   // If so, go to "nine".
    check int > 4;        // Is n >= 5?
    jump if true: five;   // If so, go to "five".
    check int = 4;        // Is n = 4?
    jump if true: four;   // If so, go to "four".
    check int = 0;        // Is n = 0?
    jump if true: print;  // If so, go to "print".
    str = str + I;        // Append I to S.
    int--;                // n := n - 1
    jump to: units;       // Go to "units".
nine:                     // The "nine" branch.
    str = str + IX;       // Append IX to S.
    jump to: print;       // Go to "print".
five:                     // The "five" branch.
    str = str + V;        // Append V to S.
    int = int - 5;        // n := n - 5
    jump to: units;       // Go to "units".
four:                     // The "four" branch.
    str = str + IV;       // Append IV to S.
print:                    // The "print" branch.
    output = str;         // Print the Roman numeral.

Solution 2

Let n be an integer such that 1 <= n <= 20. Let S be a string representation of the Roman numeral equivalent of n. Initially, S is the empty string. We have these cases to consider, in the order given:

1. If n >= 10, then the Roman numeral has an X. Append X to S and set n := n - 10.
2. If n = 9, then the Roman numeral has IX. Append IX to S and set n := n - 9.
3. If n >= 5, then the Roman numeral has a V. Append V to S and set n := n - 5.
4. If n = 4, then the Roman numeral has IV. Append IV to S and set n := n - 4.
5. If n > 0, then the Roman numeral has an I. Append I to S and set n := n - 1.
6. If n = 0, then we have finished our conversion from decimal to Roman numeral. Print the string S.

int = input;              // Read the decimal number n.
str = ;                   // S := empty string
loop:                     // Start of "loop".
    check int > 9;        // Is n >= 10?
    jump if true: ten;    // If so, go to "ten".
    check int = 9;        // Is n = 9?
    jump if true: nine;   // If so, go to "nine".
    check int > 4;        // Is n >= 5?
    jump if true: five;   // If so, go to "five".
    check int = 4;        // Is n = 4?
    jump if true: four;   // If so, go to "four".
    check int = 0;        // Is n = 0?
    jump if true: print;  // If so, go to "print".
    str = str + I;        // Append I to S.
    int--;                // n := n - 1
    jump to: loop;        // Go to "loop".
ten:                      // The "ten" branch.
    str = str + X;        // Append X to S.
    int = int - 10;       // n := n - 10
    jump to: loop;        // Go to "loop".
nine:                     // The "nine" branch.
    str = str + IX;       // Append IX to S.
    jump to: print;       // Go to "print".
five:                     // The "five" branch.
    str = str + V;        // Append V to S.
    int = int - 5;        // n := n - 5
    jump to: loop;        // Go to "loop".
four:                     // The "four" branch.
    str = str + IV;       // Append IV to S.
print:                    // The "print" branch.
    output = str;         // Print the Roman numeral.

Solution 3

Similar to Solution 2. However, we create a label called units to handle the case where n < 4. As long as 0 < n <= 3, we append I to the string S. If n = 0, then we print the Roman numeral. This solution is optimal, according to the game.

int = input;              // Read the decimal number n.
str = ;                   // S := empty string
loop:                     // Start of "loop".
    check int > 9;        // Is n >= 10?
    jump if true: ten;    // If so, go to "ten".
    check int = 9;        // Is n = 9?
    jump if true: nine;   // If so, go to "nine".
    check int > 4;        // Is n >= 5?
    jump if true: five;   // If so, go to "five".
    check int = 4;        // Is n = 4?
    jump if true: four;   // If so, go to "four".
units:                    // The "units" branch.
    check int = 0;        // Is n = 0?
    jump if true: print;  // If so, go to "print".
    str = str + I;        // Append I to S.
    int--;                // n := n - 1
    jump to: units;       // Go to "units".
ten:                      // The "ten" branch.
    str = str + X;        // Append X to S.
    int = int - 10;       // n := n - 10
    jump to: loop;        // Go to "loop".
nine:                     // The "nine" branch.
    str = str + IX;       // Append IX to S.
    jump to: print;       // Go to "print".
five:                     // The "five" branch.
    str = str + V;        // Append V to S.
    int = int - 5;        // n := n - 5
    jump to: units;       // Go to "units".
four:                     // The "four" branch.
    str = str + IV;       // Append IV to S.
print:                    // The "print" branch.
    output = str;         // Print the Roman numeral.