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| 1 | +//Single source file for online compiling |
| 2 | +//Successfully compiled at http://www.codechef.com/ide (gcc-4.9.2) |
| 3 | +#include <stdio.h> |
| 4 | + |
| 5 | +short arraySum (const short x[], short size){ |
| 6 | + int total = 0; |
| 7 | + short i; |
| 8 | + for(i = 0; i < size; ++i){ |
| 9 | + total += x[i]; |
| 10 | + } |
| 11 | + return total; |
| 12 | +}; |
| 13 | + |
| 14 | +void printShortArray (const char* x, const short y[], short size){ |
| 15 | + fputs(x, stdout); |
| 16 | + short i; |
| 17 | + for(i = 0; i < size; ++i) |
| 18 | + printf("%d ", y[i]); |
| 19 | + puts(""); |
| 20 | +}; |
| 21 | + |
| 22 | +int factorial(short x){ |
| 23 | + int y = 1; |
| 24 | + while(x > 1){ |
| 25 | + y *= x; |
| 26 | + --x; |
| 27 | + } |
| 28 | + return y; |
| 29 | +}; |
| 30 | + |
| 31 | +int arrayFactorial(const short x[], short size, short startingIndex, short minus){ //~7/1-17:00 returns sum of each element's factorial O(N) |
| 32 | + short i = startingIndex; |
| 33 | + int total = factorial(x[i++] - minus); |
| 34 | + while(i < size){ |
| 35 | + total *= factorial(x[i++]); |
| 36 | + } |
| 37 | + return total; |
| 38 | +}; |
| 39 | + |
| 40 | +void promotionSignature (const short freq[], short freqSize, int result[], short resultSize, short startingIndex){ |
| 41 | + short i, j = 0, k = 0; |
| 42 | + while(freq[j] == 0){ |
| 43 | + ++j; |
| 44 | + } |
| 45 | + |
| 46 | + short remainingDigits = resultSize - startingIndex; |
| 47 | + |
| 48 | + for(i = 0; i < startingIndex; ++i){ |
| 49 | + result[i] = -1; |
| 50 | + } |
| 51 | + for(; i < resultSize; ++i){ |
| 52 | + result[i] = factorial(remainingDigits) / arrayFactorial(freq, freqSize, j, k); |
| 53 | + if(!result[i]) |
| 54 | + ++result[i]; |
| 55 | + ++k; |
| 56 | + if(k == freq[j]){ |
| 57 | + ++j; |
| 58 | + k = 0; |
| 59 | + } |
| 60 | + --remainingDigits; |
| 61 | + } |
| 62 | +}; |
| 63 | + |
| 64 | +void steps2state(const short freq[], short freqSize, short result[], short resultSize, short steps){ |
| 65 | + short sigSize = resultSize - 1; |
| 66 | + int sig[sigSize]; |
| 67 | + short i = 0, j = 0, target = 0; |
| 68 | + |
| 69 | + short copy[freqSize]; |
| 70 | + for(i = 0; i < freqSize; ++i){ |
| 71 | + copy[i] = freq[i]; |
| 72 | + } |
| 73 | + |
| 74 | + --copy[0]; |
| 75 | + promotionSignature(copy, freqSize, sig, sigSize, 0); |
| 76 | + for(i = 0; i < sigSize; ++i){ |
| 77 | + while( steps >= sig[i]){ |
| 78 | + steps -= sig[i]; |
| 79 | + ++copy[target]; |
| 80 | + ++target; |
| 81 | + while(copy[target] == 0){ |
| 82 | + ++target; |
| 83 | + } |
| 84 | + --copy[target]; |
| 85 | + promotionSignature(copy, freqSize, sig, sigSize, i); |
| 86 | + } |
| 87 | + j = 0; |
| 88 | + while(copy[j] == 0){ |
| 89 | + ++j; |
| 90 | + } |
| 91 | + result[i] = target; |
| 92 | + target = j; |
| 93 | + --copy[j]; |
| 94 | + } |
| 95 | + result[sigSize] = target; |
| 96 | +}; |
| 97 | + |
| 98 | +short state2steps(const short freq[], short freqSize, short state[], short stateSize){ |
| 99 | + |
| 100 | + short copy[freqSize]; |
| 101 | + short i = 0; |
| 102 | + for(i = 0; i < freqSize; ++i){ |
| 103 | + copy[i] = freq[i]; |
| 104 | + } |
| 105 | + --copy[0]; |
| 106 | + |
| 107 | + short zeroState[stateSize]; |
| 108 | + steps2state(freq, freqSize, zeroState, stateSize, 0); |
| 109 | + |
| 110 | + short steps = 0; |
| 111 | + short sigSize = stateSize - 1; |
| 112 | + int sig[sigSize]; |
| 113 | + promotionSignature(copy, freqSize, sig, sigSize, 0); |
| 114 | + |
| 115 | + for(i = 0; i < sigSize;){ |
| 116 | + if(state[i] == zeroState[i]){ |
| 117 | + --copy[zeroState[i + 1]]; |
| 118 | + ++i; |
| 119 | + } else { |
| 120 | + steps += sig[i]; |
| 121 | + ++copy[zeroState[i]]; |
| 122 | + ++zeroState[i]; |
| 123 | + while(copy[zeroState[i]] == 0){ |
| 124 | + ++zeroState[i]; |
| 125 | + } |
| 126 | + --copy[zeroState[i]]; |
| 127 | + promotionSignature(copy, freqSize, sig, sigSize, i); |
| 128 | + short k = i, l, m; |
| 129 | + for(l = 0; l < freqSize; ++l){ |
| 130 | + for(m = 0; m < copy[l]; ++m){ |
| 131 | + zeroState[++k] = l; |
| 132 | + } |
| 133 | + } |
| 134 | + } |
| 135 | + } |
| 136 | + |
| 137 | + return steps; |
| 138 | +} |
| 139 | + |
| 140 | +int main() { |
| 141 | + const short freq[] = {2, 2, 2, 1}; |
| 142 | + short freqSize = 4; |
| 143 | + short stateSize = arraySum(freq, freqSize); |
| 144 | + short uBound = factorial(stateSize)/arrayFactorial(freq, freqSize, 0, 0); |
| 145 | + short result[stateSize]; |
| 146 | + short steps, steps2, input; |
| 147 | + for(steps = 0;steps < uBound; ++steps){ |
| 148 | + steps2state(freq, freqSize, result, stateSize, steps); |
| 149 | + printShortArray("State: ", result, stateSize); |
| 150 | + steps2 = state2steps(freq, freqSize, result, stateSize); |
| 151 | + printf("Steps: %d\n", steps2); |
| 152 | + } |
| 153 | + return 0; |
| 154 | +} |
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