c - Count permutations - store counter in array -

input: have arrays, like:

1, 2, 3, 4, 5 2, 1, 3, 4, 5 3, 2, 5, 4, 1 5, 4, 3, 1, 2 ..... 

all of them non repeating permutations of 5 digits - 5c5. rows can repeat, digit in row unique.

aim: count how many arrays of each type (permutation) in input data.

my thoughts: 5c5 says there's 120 unique rows can be. can store counters in int[120] array. , increment them while reading input.

my question: there efficient algorithm convert (hash) array array index?

preferable language c, it's pointers , manual memory management. in perfect, i'm trying like:

file *f; int counters[120] = {0}; char seq[20]; parse_line(f, seq); #scans , parses string array counters[hash(seq)]++; 

ps: inspired question solving "uva 157 - recycling". later saw solutions , understood misunderstood task, question left unanswered.

do base conversion. first digit in base 5, second in base 4, base 3, , base 2. so, example:

1, 2, 3, 4, 5 -> 0 * 4*3*2*1 + 0 * 3*2*1 + 0 * 2*1 + 0 * 1 ->   0 2, 1, 3, 4, 5 -> 1 * 4*3*2*1 + 0 * 3*2*1 + 0 * 2*1 + 0 * 1 ->  24 3, 2, 5, 4, 1 -> 2 * 4*3*2*1 + 1 * 3*2*1 + 2 * 2*1 + 1 * 1 ->  59 5, 4, 3, 1, 2 -> 4 * 4*3*2*1 + 3 * 3*2*1 + 2 * 2*1 + 0 * 1 -> 118 5, 4, 3, 2, 1 -> 4 * 4*3*2*1 + 3 * 3*2*1 + 2 * 2*1 + 1 * 1 -> 119 

remember count numbers haven't seen when choosing digit! walking through third row of above:

3, 2, 5, 4, 1 

at first, have following mapping of numbers digits:

1 2 3 4 5 0 1 2 3 4 

since first number 3, first digit 2. delete 3 numbers, giving

1 2 4 5 0 1 2 3 

the next number 2, next digit 1. mapping now

1 4 5 0 1 2 

the next number 5, next digit 2. mapping now

1 4 0 1 

the next number 4, next digit 1. last digit 0 though won't contribute sum -- last digit in unary, 0. numbers 32541 correspond digits 21210.

to calculate value of number in base 10, use usual base conversion routine: multiply "column value" current column's base, add in value of current digit times column value. so:

  0 * 1 + 1 * (1*1) + 2 * (2*1*1) + 1 * (3*2*1*1) + 2 * (4*3*2*1*1) -----------------  59 

see wikipedia page on factorial number systems.