100以内的质因数分解并计算完全平方数

代码价值：用时3天

//求100以内的质因数分解，同时计算x!，是否是一个完全平方数 //tips：质因数每项都为偶数个，则x就是一个完全平方数 //运行后观察并结论：任何 x! 都不是完全平方数（除了0,和1以外） #include //ceil #include //printf #include //malloc #include //memset #include //true #include //and const int primes26[] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101 }; //#define MAX_PRIME_DIVISOR_COUNT_UNDER_1024 10 //2^10 = 1024 #define MAX_PRIME_DIVISOR_COUNT_UNDER_128 7 //2^7 = 128 #define PRIME_COUNT_UNDER_101 26 //2^7 = 128 //data structure divisor_array = {int d_count, [d1, d1_count, d2, d2_count, d3, ...]} //data structure divisor_array max len 100 //param n, a nature number //param primes, a int[] prime array //param out, return int[] divisors array as: {d_count, [d1, d1_count, d2, d2_count, d3, ...]} // which d_count is count of divisors at first void PrimeDivisors(int n, const int *const primes, int *const out) { int d_count = 0; switch (n) { case 0: ; case 1: *out = d_count; return; } int factorCount = 0; while (((n & 1) == 0)and(n > 1)) //test factor of 2 { factorCount++; n >>= 1; } int *pout = out + 1; //write power of 2 int denom = 2; //cache =*pprimes=2 int *pprimes = (int *)primes; //pointer to prime array do { if (factorCount > 0) { *pout++ = denom; *pout++ = factorCount; d_count++; } if (n > 1) { pprimes++; denom = *pprimes; int SqrtN; SqrtN = ceil(sqrt(n)); if (denom >= SqrtN) { *pout++ = n; //n is a prime now *pout++ = 1; d_count++; break; } } else //n==1 all end { break; } factorCount = 0; //reset div_t ttt; goto loptest1; do { factorCount++; n = ttt.quot; loptest1: ttt = div(n, denom); } while (0 == ttt.rem); } while (1); *out = d_count; return; } //param in a {array_len, int[]}, //return true if all element are even in array bool IsAbsoluteSquareNumber(int *in) { int d_count = *in; if (d_count == 0) return false; int *p = in + 1; for (int i = 0; i < d_count; i++) { if ((p[i] & 1) == 0) { continue; } else { return false; } } return true; } //out is holds int[] = {count of divisor 2, ... of divisor 3, ... of 5, ...7, ...} //out = in + out void addto(const int *const primes, int *in, int *out) { int d_count_in = in[0]; if (d_count_in == 0) return; int *p_in = in + 1; for (int i = 0; i < d_count_in; i++) { int divisor = *p_in; //search divisor in prime array return its index int iD; for (iD = 0; divisor > primes[iD]; iD++) { } if (divisor < primes[iD]) //bad divisor or bad prime { //exception } p_in++; out[iD] += *p_in; p_in++; } return; } // function search_factorial_is_absolutesquarenumber_under_101 // param range, calc range from 1 to 100 // param primes, a array of prime // param out, a {arraylen, int[]}, element_count, and n1,n2,n3,,,, void search_f_asn101(const int *const primes, int * const out) { int positiveNum_count = 0; int *pout = out + 1; void *const memblock = malloc(sizeof(int)*(1 + PRIME_COUNT_UNDER_101 + 1 + MAX_PRIME_DIVISOR_COUNT_UNDER_128)); int *const pbSum = (int *)memblock; //pointer to a mem block, holds sums of divisors which is divisors of x! int *const pbTempDivisorArray = (int *)(pbSum + 1 + PRIME_COUNT_UNDER_101); //pointer to a block of int //quick init *pbSum = 26; *(pbSum + 1) = 1; memset(pbSum + 2, 0, PRIME_COUNT_UNDER_101 - 1); for (int i = 3; i <= 100; i++) { PrimeDivisors(i, primes, pbTempDivisorArray); addto(primes, pbTempDivisorArray, pbSum+1); //x! = (x-1)! * x if (IsAbsoluteSquareNumber(pbSum)) { positiveNum_count++; *pout++ = i; } printf("%d/n", i); for (int i = 1; i < (1 + PRIME_COUNT_UNDER_101); i++) { printf("%d,", pbSum[i]); } printf("/n"); } free(memblock); *out = positiveNum_count; return; } int main(void) { int *result = (int *)malloc(100 * sizeof(int)); search_f_asn101(primes26, result); int count = *result; if (count > 0) { int *p = result + 1; for (int i = 0; i < count; i++) { printf("%d/t", p[i]); } } free(result); exit(EXIT_SUCCESS); } =============== output =============== 3 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 4 3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 5 3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 6 4,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 7 4,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 8 7,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 9 7,2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 10 8,2,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 11 8,2,2,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 12 10,3,2,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 13 10,3,2,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 14 11,3,2,2,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 15 11,4,3,2,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 16 15,4,3,2,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 17 15,4,3,2,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 18 16,4,3,2,3,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 19 16,4,3,2,3,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 20 18,4,4,2,3,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 21 18,5,4,3,3,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 22 19,5,4,3,4,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 23 19,5,4,3,4,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 24 22,6,4,3,4,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 25 22,6,4,3,4,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 26 23,6,4,3,4,2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 27 23,9,4,3,4,2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 28 25,9,4,4,4,2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 29 25,9,4,4,4,2,1,1,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 30 26,10,5,4,4,2,1,1,1,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 31 26,10,5,4,4,2,1,1,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 32 31,10,5,4,4,2,1,1,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 33 31,11,5,4,5,2,1,1,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 34 32,11,5,4,5,2,2,1,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 35 32,11,6,5,5,2,2,1,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 36 34,11,6,5,6,2,2,1,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 37 34,11,6,5,6,2,2,1,1,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 38 35,11,6,5,6,2,2,2,1,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 39 35,12,6,5,6,3,2,2,1,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 40 38,12,7,5,6,3,2,2,1,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 41 38,12,7,5,6,3,2,2,1,2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 42 39,13,7,6,6,3,2,2,1,2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 43 39,13,7,6,6,3,2,2,1,2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0, 44 41,13,7,6,7,3,2,2,1,2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0, 45 41,15,8,6,7,3,2,2,1,2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0, 46 42,15,8,6,7,3,2,2,2,2,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0, 47 42,15,8,6,7,3,2,2,2,2,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0, 48 46,16,8,6,7,3,2,2,2,2,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0, 49 46,16,8,6,7,3,2,2,2,2,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0, 50 47,16,8,6,7,3,2,2,2,3,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0, 51 47,17,8,6,7,3,3,2,2,3,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0, 52 49,17,8,6,7,4,3,2,2,3,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0, 53 49,17,8,6,7,4,3,2,2,3,1,1,1,1,1,2,0,0,0,0,0,0,0,0,0,0, 54 50,20,8,6,7,4,3,2,2,3,1,1,1,1,1,2,0,0,0,0,0,0,0,0,0,0, 55 50,20,9,6,8,4,3,2,2,3,1,1,1,1,1,2,0,0,0,0,0,0,0,0,0,0, 56 53,20,9,7,8,4,3,2,2,3,1,1,1,1,1,2,0,0,0,0,0,0,0,0,0,0, 57 53,21,9,7,8,4,3,3,2,3,1,1,1,1,1,2,0,0,0,0,0,0,0,0,0,0, 58 54,21,9,7,8,4,3,3,2,4,1,1,1,1,1,2,0,0,0,0,0,0,0,0,0,0, 59 54,21,9,7,8,4,3,3,2,4,1,1,1,1,1,2,1,0,0,0,0,0,0,0,0,0, 60 56,22,10,7,8,4,3,3,2,4,1,1,1,1,1,2,1,0,0,0,0,0,0,0,0,0, 61 56,22,10,7,8,4,3,3,2,4,1,1,1,1,1,2,1,1,0,0,0,0,0,0,0,0, 62 57,22,10,7,8,4,3,3,2,4,2,1,1,1,1,2,1,1,0,0,0,0,0,0,0,0, 63 57,24,10,8,8,4,3,3,2,4,2,1,1,1,1,2,1,1,0,0,0,0,0,0,0,0, 64 63,24,10,8,8,4,3,3,2,4,2,1,1,1,1,2,1,1,0,0,0,0,0,0,0,0, 65 63,24,11,8,8,5,3,3,2,4,2,1,1,1,1,2,1,1,0,0,0,0,0,0,0,0, 66 64,25,11,8,9,5,3,3,2,4,2,1,1,1,1,2,1,1,0,0,0,0,0,0,0,0, 67 64,25,11,8,9,5,3,3,2,4,2,1,1,1,1,2,1,1,1,0,0,0,0,0,0,0, 68 66,25,11,8,9,5,4,3,2,4,2,1,1,1,1,2,1,1,1,0,0,0,0,0,0,0, 69 66,26,11,8,9,5,4,3,3,4,2,1,1,1,1,2,1,1,1,0,0,0,0,0,0,0, 70 67,26,12,9,9,5,4,3,3,4,2,1,1,1,1,2,1,1,1,0,0,0,0,0,0,0, 71 67,26,12,9,9,5,4,3,3,4,2,1,1,1,1,2,1,1,1,1,0,0,0,0,0,0, 72 70,26,12,9,10,5,4,3,3,4,2,1,1,1,1,2,1,1,1,1,0,0,0,0,0,0, 73 70,26,12,9,10,5,4,3,3,4,2,1,1,1,1,2,1,1,1,1,1,0,0,0,0,0, 74 71,26,12,9,10,5,4,3,3,4,2,2,1,1,1,2,1,1,1,1,1,0,0,0,0,0, 75 71,27,12,9,10,5,4,3,3,5,2,2,1,1,1,2,1,1,1,1,1,0,0,0,0,0, 76 73,27,12,9,10,5,4,4,3,5,2,2,1,1,1,2,1,1,1,1,1,0,0,0,0,0, 77 73,27,12,10,11,5,4,4,3,5,2,2,1,1,1,2,1,1,1,1,1,0,0,0,0,0, 78 74,28,12,10,11,6,4,4,3,5,2,2,1,1,1,2,1,1,1,1,1,0,0,0,0,0, 79 74,28,12,10,11,6,4,4,3,5,2,2,1,1,1,2,1,1,1,1,1,1,0,0,0,0, 80 78,28,13,10,11,6,4,4,3,5,2,2,1,1,1,2,1,1,1,1,1,1,0,0,0,0, 81 78,32,13,10,11,6,4,4,3,5,2,2,1,1,1,2,1,1,1,1,1,1,0,0,0,0, 82 79,32,13,10,11,6,4,4,3,5,2,2,2,1,1,2,1,1,1,1,1,1,0,0,0,0, 83 79,32,13,10,11,6,4,4,3,5,2,2,2,1,1,2,1,1,1,1,1,1,1,0,0,0, 84 81,33,13,11,11,6,4,4,3,5,2,2,2,1,1,2,1,1,1,1,1,1,1,0,0,0, 85 81,33,14,11,11,6,5,4,3,5,2,2,2,1,1,2,1,1,1,1,1,1,1,0,0,0, 86 82,33,14,11,11,6,5,4,3,5,2,2,2,2,1,2,1,1,1,1,1,1,1,0,0,0, 87 82,34,14,11,11,6,5,4,3,6,2,2,2,2,1,2,1,1,1,1,1,1,1,0,0,0, 88 85,34,14,11,12,6,5,4,3,6,2,2,2,2,1,2,1,1,1,1,1,1,1,0,0,0, 89 85,34,14,11,12,6,5,4,3,6,2,2,2,2,1,2,1,1,1,1,1,1,1,1,0,0, 90 86,36,15,11,12,6,5,4,3,6,2,2,2,2,1,2,1,1,1,1,1,1,1,1,0,0, 91 86,36,15,12,12,7,5,4,3,6,2,2,2,2,1,2,1,1,1,1,1,1,1,1,0,0, 92 88,36,15,12,12,7,5,4,4,6,2,2,2,2,1,2,1,1,1,1,1,1,1,1,0,0, 93 88,37,15,12,12,7,5,4,4,6,3,2,2,2,1,2,1,1,1,1,1,1,1,1,0,0, 94 89,37,15,12,12,7,5,4,4,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,0,0, 95 89,37,16,12,12,7,5,5,4,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,0,0, 96 94,38,16,12,12,7,5,5,4,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,0,0, 97 94,38,16,12,12,7,5,5,4,6,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,0, 98 95,38,16,12,12,7,5,5,4,6,3,2,2,2,2,3,1,1,1,1,1,1,1,1,1,0, 99 95,40,16,12,13,7,5,5,4,6,3,2,2,2,2,3,1,1,1,1,1,1,1,1,1,0, 100 97,40,16,12,13,7,5,5,4,7,3,2,2,2,2,3,1,1,1,1,1,1,1,1,1,0, Press any key to continue...