* * * x * * ------- * * * <-- partial product 1 * * * <-- partial product 2 ------- * * * *Digits can appear only in places marked by `*'. Of course, leading zeroes are not allowed. Note that the 'partial products' are as taught in USA schools. The first partial product is the product of the final digit of the second number and the top number. The second partial product is the product of the first digit of the second number and the top number.
Write a program that will find all solutions to the cryptarithm above for any subset of digits from the set {1,2,3,4,5,6,7,8,9}.
PROGRAM NAME: crypt1
INPUT FORMAT
Line 1: | N, the number of digits that will be used |
Line 2: | N space separated digits with which to solve the cryptarithm |
SAMPLE INPUT (file crypt1.in)
5 2 3 4 6 8
OUTPUT FORMAT
A single line with the total number of unique solutions. Here is the single solution for the sample input:2 2 2 x 2 2 ------ 4 4 4 4 4 4 --------- 4 8 8 4
SAMPLE OUTPUT (file crypt1.out)
1
Ad hoc - iteration - simulation
There are two ways to solve this problem.
First you can easily iterate from a=100 to a=999 and from b=10 to b=99 in nested for loops, then you can produce the product of a and b and check whether the digits of a, b and a*b are valid or not, if yes increment your output. This approach runs in O(1000 * 100).
Second you can set the digits of a and b, a[0], a[1], a[2] and b[0], b[1] from your input, in this way you don't have to check the validity of a[i] and b[i] and then produce the product of a and b, and now check whether the digits of a*b are valid or not. This approach runs in O(9^5) that is a little better but harder to implement.
I just wanna know what this problem is trying to ask. I am unable to understand the question please help!!
ReplyDeleteI can't understand the question, please help!!
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ReplyDeleteThe hard task for me in this problem is to understand the statement. :(
ReplyDeleteThanks a lot,i solved it through second approach.Can you give me the solution solved by first approach?.i can't keep digits in a[0],b[0],c[0,d[0],e[0] in npr(i think there is npr possible permutation) way.Help me.
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