CCC '12 S2 - Aromatic Numbers - DMOJ: Modern Online Judge

CCC '12 S2 - Aromatic Numbers

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Points: 5

Time limit: 2.0s

Memory limit: 256M

Problem type

Canadian Computing Competition: 2012 Stage 1, Senior #2

This question involves calculating the value of aromatic numbers which are a combination of Arabic digits and Roman numerals.

An aromatic number is of the form $ARARAR \dots AR$ ~ARARAR \dots AR~, where each $A$ ~A~ is an Arabic digit, and each $R$ ~R~ is a Roman numeral. Each pair $AR$ ~AR~ contributes a value described below, and by adding or subtracting these values together we get the value of the entire aromatic number.

An Arabic digit $A$ ~A~ can be 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9. A Roman numeral $R$ ~R~ is one of the seven letters I, V, X, L, C, D, or M. Each Roman numeral has a base value:

Symbol	I	V	X	L	C	D	M
Base value	1	5	10	50	100	500	1000

The value of a pair $AR$ ~AR~ is $A$ ~A~ times the base value of $R$ ~R~. Normally, you add up the values of the pairs to get the overall value. However, wherever there are consecutive symbols $ARA^{\prime}R^{\prime}$ ~ARA^{\prime}R^{\prime}~ with $R^{\prime}$ ~R^{\prime}~ having a strictly bigger base value than $R$ ~R~, the value of pair $AR$ ~AR~ must be subtracted from the total, instead of being added.

For example, the number $3M1D2C$ ~3M1D2C~ has the value $3 \times 1000 + 1 \times 500 + 2 \times 100 = 3700$ and $3X2I4X$ ~3X2I4X~ has the value $3 \times 10 - 2 \times 1 + 4 \times 10 = 68$ .

Write a program that computes the values of aromatic numbers.

Input Specification

The input is a valid aromatic number consisting of between $2$ ~2~ and $20$ ~20~ symbols.

Output Specification

The output is the decimal value of the given aromatic number.

Sample Input 1

3M1D2C

Output for Sample Input 1

Sample Input 2

2I3I2X9V1X

Output for Sample Input 2

-16

Comments

1

jrkws commented on April 20, 2024, 8:36 p.m.

For sample input 2:

2I3I2X9V1X = 2×1 + 3×1 + 2×10 + 9×5 + 1×10

However, wherever there are consecutive symbols ARA'R' with R' having a strictly bigger base value than R, the value of pair AR must be subtracted from the total, instead of being added.

This means that 3×1 + 2×10 becomes -3×1 + 2×10 and 9×5 + 1×10 becomes -9×5 + 1×10. So the equation is rewritten as:

2I3I2X9V1X = 2×1 - 3×1 + 2×10 - 9×5 + 1×10 = -16

Hope this helps :)

1

XianBinChen0712 commented on Jan. 13, 2024, 3:16 a.m.

Confusing cuz' no explanation

14

Tommy_Shan commented on Sept. 1, 2021, 6:37 p.m.

Just a note, subtract AR NOT A'R'

However, wherever there are consecutive symbols ARA′R′ with R′ having a strictly bigger base value than R, the value of pair AR must be subtracted from the total, instead of being added.

11

Badmode commented on Jan. 22, 2021, 5:18 a.m.

I am confusion

16

John commented on Sept. 14, 2020, 3:33 p.m.

This problem is extremely unclear and needs revised instructions, as well as an explanation for at least one sample. It should be harder to complete the coding challenge than to actually read the instructions for it.

10

c commented on Sept. 14, 2020, 8:54 p.m.

DMOJ does not generally modify problem statements that we get from other sources (this is a CCC problem).

If you have any feedback about CCC feel free to get in touch with the CEMC.

21

kylezheng7 commented on May 16, 2020, 9:01 p.m.

Can dmoj not speak english?

35

GD_FrostByte commented on Nov. 17, 2019, 2:37 p.m. ← edited →

confusion noises

5

Evanhyd commented on Oct. 29, 2019, 11:03 p.m.

Note: From the example 3X2I4X, because 2I(AR)'s base is smaller than 4X(A′R′), so 2I(AR) should be subtracted from the total(-2 * I = -2 * 1)

-47

bobhob314 commented on Jan. 6, 2015, 12:24 a.m.

For sample input 2 "2I3I2X9V1X", the sum should be 2+3-20+45-10. This amounts to 20, not -16.

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