你见过或做过哪些令人拍案叫绝的数字论证?

TEAM青茅西木野的更低赞，给个流程：

你见过或做过什么样更让人叹为不雅行的位数深切研究?3045 赞成 · 174 文章发问 #include <iostream>#include <string>#include <cmath>#include <cstdlib> using namespace std; const double PRECISION = 1E-6; int COUNT_OF_NUMBER = 4; int NUMBER_TO_BE_CAL = 24; double srcdata[][7] = { {1, 114514, }, {2, 1, 14514, }, {2, 11, 4514, }, {2, 114, 514, }, {2, 1145, 14, }, {2, 11451, 4, }, {3, 1, 1, 4514, }, {3, 1, 14, 514, }, {3, 1, 145, 14, }, {3, 1, 1451, 4, }, {3, 11, 4, 514, }, {3, 11, 45, 14, }, {3, 11, 451, 4, }, {3, 114, 5, 14, }, {3, 114, 51, 4, }, {3, 1145, 1, 4, }, {4, 1, 1, 4, 514, }, {4, 1, 1, 45, 14, }, {4, 1, 1, 451, 4, }, {4, 1, 14, 5, 14, }, {4, 1, 14, 51, 4, }, {4, 1, 145, 1, 4, }, {4, 11, 4, 5, 14, }, {4, 11, 4, 51, 4, }, {4, 11, 45, 1, 4, }, {4, 114, 5, 1, 4, }, {5, 11, 4, 5, 1, 4, }, {5, 1, 14, 5, 1, 4, }, {5, 1, 1, 45, 1, 4, }, {5, 1, 1, 4, 51, 4, }, {5, 1, 1, 4, 5, 14, }, {6, 1, 1, 4, 5, 1, 4}, }; string srcstr[][6] = { {"114514", }, {"1", "14514", }, {"11", "4514", }, {"114", "514", }, {"1145", "14", }, {"11451", "4", }, {"1", "1", "4514", }, {"1", "14", "514", }, {"1", "145", "14", }, {"1", "1451", "4", }, {"11", "4", "514", }, {"11", "45", "14", }, {"11", "451", "4", }, {"114", "5", "14", }, {"114", "51", "4", }, {"1145", "1", "4", }, {"1", "1", "4", "514", }, {"1", "1", "45", "14", }, {"1", "1", "451", "4", }, {"1", "14", "5", "14", }, {"1", "14", "51", "4", }, {"1", "145", "1", "4", }, {"11", "4", "5", "14", }, {"11", "4", "51", "4", }, {"11", "45", "1", "4", }, {"114", "5", "1", "4", }, {"11", "4", "5", "1", "4", }, {"1", "14", "5", "1", "4", }, {"1", "1", "45", "1", "4", }, {"1", "1", "4", "51", "4", }, {"1", "1", "4", "5", "14", }, {"1", "1", "4", "5", "1", "4"}, }; bool Search(int n, int limit, double number[], string expression[]) { if (n == 1) { if (fabs(number[0] - limit) < PRECISION) { cout << limit << " = " << expression[0] << endl; return true; } else { return false; } } for (int i = 0; i < n - 1; i++) { int j = i + 1; double a, b; int k; string expa, expb; a = number[i]; b = number[j]; expa = expression[i]; expb = expression[j]; for (k = j; k < n - 1; k++) { number[k] = number[k + 1]; expression[k] = expression[k + 1]; } expression[i] = ( + expa + + + expb + ); number[i] = a + b; if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = ( + expa + - + expb + ); number[i] = a - b; if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = "(-" + expa + + + expb + ); number[i] = b - a; if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = ( + expa + * + expb + ); number[i] = a * b; if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = ( + expa + "*(-" + expb + "))"; number[i] = a * -b; if (Search(n - 1, limit, number, expression)) { return true; } if (b != 0) { expression[i] = ( + expa + / + expb + ); number[i] = a / b; if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = ( + expa + "/(-" + expb + "))"; number[i] = a / -b; if (Search(n - 1, limit, number, expression)) { return true; } } expression[i] = ( + expa + ^ + expb + ); number[i] = powf(a, b); if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = ( + expa + "^-(" + expb + "))"; number[i] = powf(a, -b); if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = "((" + expa + ")^-" + expb + ); number[i] = powf(-a, b); if (Search(n - 1, limit, number, expression)) { return true; } expression[i] = "((" + expa + ")^-(" + expb + "))"; number[i] = powf(-a, -b); if (Search(n - 1, limit, number, expression)) { return true; } for (k = n - 1; k >= j; k--) { number[k] = number[k - 1]; expression[k] = expression[k - 1]; } number[i] = a; number[j] = b; expression[i] = expa; expression[j] = expb; } return false; } void resetdata(double *number, double *tmp, string *expression, string *tmps, int n) { for (int i = 0; i < n; i++) { number[i] = tmp[i]; expression[i] = tmps[i]; } } int main() { COUNT_OF_NUMBER = 6; int i; double *number = new double[COUNT_OF_NUMBER]; double *tmp = new double[COUNT_OF_NUMBER]; string *expression = new string[COUNT_OF_NUMBER]; string *tmps = new string[COUNT_OF_NUMBER]; bool flag = true; for (NUMBER_TO_BE_CAL = 0; NUMBER_TO_BE_CAL <= 161; NUMBER_TO_BE_CAL++) { for (i = 0; i < 32; i++) { resetdata(number, &srcdata[i][1], expression, srcstr[i], srcdata[i][0]); if (Search(srcdata[i][0], NUMBER_TO_BE_CAL, number, expression)) { flag = false; break; } } if (flag) { cout << NUMBER_TO_BE_CAL << "无解" << endl; } flag = true; } delete[]tmp; delete[]number; delete[]tmps; delete[]expression; return 0; }

没好的算法，间接递归爆搜，那题没加剪枝（次要是我懒，究竟结果那不是刷OJ），后来补加了次方。只要四则运算的情况下第一个无解的是109，加了次方后第一个无解的是162。不加次方还能跑一炮，加了次方无解情况会搜太久。因为能够负数的情况下，a^b，a^-b，(-a)^b，(-a)^-b是四种情况，那种爆搜每加一个城市极大的增大施行时间。乘法是a*b和a*-b（因为-a*b成果和a*-b一样，-a*-b的成果和a*b一样）除法也同理，而加减同理，a+-b相当于a-b，-a+b相当于b-a，a--b相当于a+b，-a-b相当于-(a+b)，而-(a+b)参与的情况跟a+b没啥区别，不会增加新的成果，所以也就省略了。加减乘除一共才7种，相当于搜完全7叉树，加了次方就成了搜完全11叉树了，层数一高复杂度一下就飞了（更低有6层），找不到会跑很久很久。

别的，懒得再写一个递归切分了，间接手动分了一下，构造了两个数组，理论上两个数组应该是输入后递归构造，我间接写死了，有需要其他位数的能够考虑写一下那个算法。仓皇写的，代码比力乱，此中递归部门参考了网上的24点代码（我认可是因为我太懒了）。因为此次位数位置是固定的，所以做了很多改动。如今还算不变。今天挂了一晚上，早上起来发现才跑了两千多……后面有大量的无解情况，能够考虑加上阶乘等运算看看能不克不及胜利率高一些，不外我不筹算改了，谁有兴趣就当个功课练练吧。

以下是前161行的运行成果。从162起头呈现无解。超越163的能够本身修改并施行我的流程。

0 = (11^-(4514)) 1 = (1^14514) 2 = (1+(1^4514)) 3 = (-(1^1451)+4) 4 = ((1^1451)*4) 5 = ((1^1451)+4) 6 = (114/(5+14)) 7 = ((11-4)+(5^-(14))) 8 = ((1+(1^451))*4) 9 = (-((1^14)*5)+14) 10 = (((1^14)-5)+14) 11 = (11+(4^-(514))) 12 = (-(1+(1^45))+14) 13 = (-(1^145)+14) 14 = ((1^145)*14) 15 = ((1^145)+14) 16 = ((1+(1^45))+14) 17 = (((1+14)/5)+14) 18 = (-((1^14)-5)+14) 19 = (((1^14)*5)+14) 20 = ((-11+45)-14) 21 = (((11-4)*5)-14) 22 = (-((1-14)+5)+14) 23 = (((1*14)-5)+14) 24 = (((1+14)-5)+14) 25 = (((11*4)-5)-14) 26 = (((11-4)+5)+14) 27 = (((114-5)-1)/4) 28 = ((1+(1^45))*14) 29 = ((-(1+1)+45)-14) 30 = ((-(1*1)+45)-14) 31 = (((1-1)+45)-14) 32 = (((1*1)+45)-14) 33 = (((1+1)+45)-14) 34 = (((1+14)+5)+14) 35 = (-1+((145-1)/4)) 36 = (((1-145)*1)/(-4)) 37 = (1+((145-1)/4)) 38 = (-((11-45)*1)+4) 39 = (-((11-45)-1)+4) 40 = (-((1+14)-51)+4) 41 = (-((1*14)-51)+4) 42 = ((11+45)-14) 43 = ((((11*4)-5)*1)+4) 44 = (114-(5*14)) 45 = ((11+(4*5))+14) 46 = ((-(1^14)+51)-4) 47 = (((1^14)*51)-4) 48 = (-(11-45)+14) 49 = (((11-4)*5)+14) 50 = (((11+4)-5)*(1+4)) 51 = (((1-14)*(-5))-14) 52 = (((11+45)*1)-4) 53 = (((11*4)-5)+14) 54 = (-((1^14)-51)+4) 55 = (-(1+14)+(5*14)) 56 = (((1*14)*5)-14) 57 = (-((1+1)-45)+14) 58 = (-((1*1)-45)+14) 59 = ((114-51)-4) 60 = (((1*1)+45)+14) 61 = (((1+1)+45)+14) 62 = ((1+1)*(45-14)) 63 = ((11-4)*(-(5-14))) 64 = (((11+4)*(5-1))+4) 65 = (-11+(4*(5+14))) 66 = (11*((4*5)-14)) 67 = ((114-51)+4) 68 = (-((1-14)-51)+4) 69 = (((1/14)-5)*(-14)) 70 = ((11+45)+14) 71 = (((1/14)+5)*14) 72 = ((((11+4)*5)+1)-4) 73 = (-11+(((4*5)+1)*4)) 74 = (((11+4)*5)-(1^4)) 75 = (((11+4)*5)*(1^4)) 76 = (((1+1)*45)-14) 77 = ((11-4)+(5*14)) 78 = ((((11+4)*5)-1)+4) 79 = (-((1-14)*5)+14) 80 = ((((11+4)+5)*1)*4) 81 = ((((11+4)/5)*1)^4) 82 = (-((1-14)*(5+1))+4) 83 = (-(1-14)+(5*14)) 84 = (((1*14)*5)+14) 85 = ((1+14)+(5*14)) 86 = (((11+4)*(5+1))-4) 87 = (11+(4*(5+14))) 88 = ((11*4)*((5+1)-4)) 89 = (((1+14)*5)+14) 90 = (-114+(51*4)) 91 = (((11*4)+51)-4) 92 = ((11*((4+5)-1))+4) 93 = ((11+(4*5))*(-(1-4))) 94 = (114-((5*1)*4)) 95 = ((114-5)-14) 96 = (((11*(4+5))+1)-4) 97 = ((1*1)+((4*(5+1))*4)) 98 = (114-((5-1)*4)) 99 = (((11*4)+51)+4) 100 = (((11+4)+5)*(1+4)) 101 = ((1*1)+((4*5)*(1+4))) 102 = ((11-45)*(1-4)) 103 = (((11*(4+5))*1)+4) 104 = (((1+1)*45)+14) 105 = ((114+5)-14) 106 = (((114-5)+1)-4) 107 = (11+((4*(5+1))*4)) 108 = ((114-5)-(1^4)) 109 = ((114-5)*(1^4)) 110 = ((11-451)/(-4)) 111 = (11+((4*5)*(1+4))) 112 = (-1+((1+451)/4)) 113 = (((1*1)+451)/4) 114 = (114+(5^-(14))) 115 = (-11+((4+5)*14)) 116 = (((114+5)+1)-4) 117 = ((1-14)*(5-14)) 118 = ((1+1)*(45+14)) 119 = ((114+5)*(1^4)) 120 = ((114+5)+(1^4)) 121 = ((11*(45-1))/4) 122 = (((114+5)-1)+4) 123 = ((114-5)+14) 124 = (((11*45)+1)/4) 125 = (-1+((14-5)*14)) 126 = (((1*14)-5)*14) 127 = (1+((14-5)*14)) 128 = (((11+(4*5))+1)*4) 129 = (114-(5*(1-4))) 130 = ((-1+145)-14) 131 = ((1*145)-14) 132 = ((1+145)-14) 133 = ((114+5)+14) 134 = (114+((5*1)*4)) 135 = ((1+14)*(-(5-14))) 136 = (((11-45)*1)*(-4)) 137 = (11+((4+5)*14)) 138 = (114+((5+1)*4)) 139 = (((-1+145)-1)-4) 140 = (((1+14)-5)*14) 141 = (((1+145)-1)-4) 142 = (((1+145)*1)-4) 143 = (((1+145)+1)-4) 144 = (((1+14)-51)*(-4)) 145 = ((1+145)-(1^4)) 146 = ((1+145)*(1^4)) 147 = (-1+((14-51)*(-4))) 148 = (((1*14)-51)*(-4)) 149 = (1-((14-51)*4)) 150 = (((1+145)*1)+4) 151 = (((1+145)+1)+4) 152 = (((1-14)+51)*4) 153 = (((1-(1/4))*51)*4) 154 = ((11*(4-5))*(-14)) 155 = ((11+(4*5))*(1+4)) 156 = ((((11*4)-5)*1)*4) 157 = (-(((1*1)-4)*51)+4) 158 = (-(1-145)+14) 159 = ((1*145)+14) 160 = ((1+145)+14) 161 = ((114+51)-4)

0的成果算是个小彩蛋，仅四则运算的情况下搜到的是((1-1)*4514)，如今的那个牛逼了~~那个位数差不多是1.4237E-4701，而double的极限低值为4.94E-324。也就是说在double的精度下，那个位数就是0。更何况浮点数判0的前提一般只切确到1E-6。

留言看到了，7确实也是一样的，5^-14是1.6384E-10，也当成0了。我把校验阈值改成了1E-12后搜到的是((11+(4^-(51)))-4)……有点玄幻，我要不要考虑去掉负指数……

更新一波去掉负指数后的前161：

0 = ((1-1)*4514) 1 = (1^14514) 2 = (1+(1^4514)) 3 = (-(1^1451)+4) 4 = ((1^1451)*4) 5 = ((1^1451)+4) 6 = (114/(5+14)) 7 = ((((11+4)-5)+1)-4) 8 = ((1+(1^451))*4) 9 = (-((1^14)*5)+14) 10 = (((1^14)-5)+14) 11 = (-((1+14)/5)+14) 12 = (-(1+(1^45))+14) 13 = (-(1^145)+14) 14 = ((1^145)*14) 15 = ((1^145)+14) 16 = ((1+(1^45))+14) 17 = (((1+14)/5)+14) 18 = (-((1^14)-5)+14) 19 = (((1^14)*5)+14) 20 = ((-11+45)-14) 21 = (((11-4)*5)-14) 22 = (-((1-14)+5)+14) 23 = (((1*14)-5)+14) 24 = (((1+14)-5)+14) 25 = (((11*4)-5)-14) 26 = (((11-4)+5)+14) 27 = (((114-5)-1)/4) 28 = ((1+(1^45))*14) 29 = ((-(1+1)+45)-14) 30 = ((-(1*1)+45)-14) 31 = (((1-1)+45)-14) 32 = (((1*1)+45)-14) 33 = (((1+1)+45)-14) 34 = (((1+14)+5)+14) 35 = (-1+((145-1)/4)) 36 = (((1-145)*1)/(-4)) 37 = (1+((145-1)/4)) 38 = (-((11-45)*1)+4) 39 = (-((11-45)-1)+4) 40 = (-((1+14)-51)+4) 41 = (-((1*14)-51)+4) 42 = ((11+45)-14) 43 = ((((11*4)-5)*1)+4) 44 = (114-(5*14)) 45 = ((11+(4*5))+14) 46 = ((-(1^14)+51)-4) 47 = (((1^14)*51)-4) 48 = (-(11-45)+14) 49 = (((11-4)*5)+14) 50 = (((11+4)-5)*(1+4)) 51 = (((1-14)*(-5))-14) 52 = (((11+45)*1)-4) 53 = (((11*4)-5)+14) 54 = (-((1^14)-51)+4) 55 = (-(1+14)+(5*14)) 56 = (((1*14)*5)-14) 57 = (-((1+1)-45)+14) 58 = (-((1*1)-45)+14) 59 = ((114-51)-4) 60 = (((1*1)+45)+14) 61 = (((1+1)+45)+14) 62 = ((1+1)*(45-14)) 63 = ((11-4)*(-(5-14))) 64 = (((11+4)*(5-1))+4) 65 = (-11+(4*(5+14))) 66 = (11*((4*5)-14)) 67 = ((114-51)+4) 68 = (-((1-14)-51)+4) 69 = (((1/14)-5)*(-14)) 70 = ((11+45)+14) 71 = (((1/14)+5)*14) 72 = ((((11+4)*5)+1)-4) 73 = (-11+(((4*5)+1)*4)) 74 = (((11+4)*5)-(1^4)) 75 = (((11+4)*5)*(1^4)) 76 = (((1+1)*45)-14) 77 = ((11-4)+(5*14)) 78 = ((((11+4)*5)-1)+4) 79 = (-((1-14)*5)+14) 80 = ((((11+4)+5)*1)*4) 81 = ((((11+4)/5)*1)^4) 82 = (-((1-14)*(5+1))+4) 83 = (-(1-14)+(5*14)) 84 = (((1*14)*5)+14) 85 = ((1+14)+(5*14)) 86 = (((11+4)*(5+1))-4) 87 = (11+(4*(5+14))) 88 = ((11*4)*((5+1)-4)) 89 = (((1+14)*5)+14) 90 = (-114+(51*4)) 91 = (((11*4)+51)-4) 92 = ((11*((4+5)-1))+4) 93 = ((11+(4*5))*(-(1-4))) 94 = (114-((5*1)*4)) 95 = ((114-5)-14) 96 = (((11*(4+5))+1)-4) 97 = ((1*1)+((4*(5+1))*4)) 98 = (114-((5-1)*4)) 99 = (((11*4)+51)+4) 100 = (((11+4)+5)*(1+4)) 101 = ((1*1)+((4*5)*(1+4))) 102 = ((11-45)*(1-4)) 103 = (((11*(4+5))*1)+4) 104 = (((1+1)*45)+14) 105 = ((114+5)-14) 106 = (((114-5)+1)-4) 107 = (11+((4*(5+1))*4)) 108 = ((114-5)-(1^4)) 109 = ((114-5)*(1^4)) 110 = ((11-451)/(-4)) 111 = (11+((4*5)*(1+4))) 112 = (-1+((1+451)/4)) 113 = (((1*1)+451)/4) 114 = (1+((1+451)/4)) 115 = (-11+((4+5)*14)) 116 = (((114+5)+1)-4) 117 = ((1-14)*(5-14)) 118 = ((1+1)*(45+14)) 119 = ((114+5)*(1^4)) 120 = ((114+5)+(1^4)) 121 = ((11*(45-1))/4) 122 = (((114+5)-1)+4) 123 = ((114-5)+14) 124 = (((11*45)+1)/4) 125 = (-1+((14-5)*14)) 126 = (((1*14)-5)*14) 127 = (1+((14-5)*14)) 128 = (((11+(4*5))+1)*4) 129 = (114-(5*(1-4))) 130 = ((-1+145)-14) 131 = ((1*145)-14) 132 = ((1+145)-14) 133 = ((114+5)+14) 134 = (114+((5*1)*4)) 135 = ((1+14)*(-(5-14))) 136 = (((11-45)*1)*(-4)) 137 = (11+((4+5)*14)) 138 = (114+((5+1)*4)) 139 = (((-1+145)-1)-4) 140 = (((1+14)-5)*14) 141 = (((1+145)-1)-4) 142 = (((1+145)*1)-4) 143 = (((1+145)+1)-4) 144 = (((1+14)-51)*(-4)) 145 = ((1+145)-(1^4)) 146 = ((1+145)*(1^4)) 147 = (-1+((14-51)*(-4))) 148 = (((1*14)-51)*(-4)) 149 = (1-((14-51)*4)) 150 = (((1+145)*1)+4) 151 = (((1+145)+1)+4) 152 = (((1-14)+51)*4) 153 = (((1-(1/4))*51)*4) 154 = ((11*(4-5))*(-14)) 155 = ((11+(4*5))*(1+4)) 156 = ((((11*4)-5)*1)*4) 157 = (-(((1*1)-4)*51)+4) 158 = (-(1-145)+14) 159 = ((1*145)+14) 160 = ((1+145)+14) 161 = ((114+51)-4)

再更一个只要四则运算的：

0 = ((1-1)*4514) 1 = ((11/(45-1))*4) 2 = (-((11-4)+5)+14) 3 = ((11*(4-5))+14) 4 = ((11+45)/14) 5 = (((1*14)+5)-14) 6 = (114/(5+14)) 7 = ((((11+4)-5)+1)-4) 8 = ((((11+4)/5)+1)+4) 9 = (((1+14)-51)/(-4)) 10 = (-(11/4)+(51/4)) 11 = (-((1+14)/5)+14) 12 = (-((11-4)-5)+14) 13 = ((((11+4)-5)-1)+4) 14 = (((1-1)*45)+14) 15 = ((114/(5+1))-4) 16 = (((1-14)-51)/(-4)) 17 = (((1+14)/5)+14) 18 = (-(11-4)+(5*(1+4))) 19 = ((((11+4)*5)+1)/4) 20 = ((-11+45)-14) 21 = (((11-4)*5)-14) 22 = (-((1-14)+5)+14) 23 = (((1*14)-5)+14) 24 = (((1+14)-5)+14) 25 = (((11*4)-5)-14) 26 = (((11-4)+5)+14) 27 = (((114-5)-1)/4) 28 = (-1+(145/(1+4))) 29 = ((-(1+1)+45)-14) 30 = ((-(1*1)+45)-14) 31 = (((1-1)+45)-14) 32 = (((1*1)+45)-14) 33 = (((1+1)+45)-14) 34 = (((1+14)+5)+14) 35 = (-1+((145-1)/4)) 36 = (((1-145)*1)/(-4)) 37 = (1+((145-1)/4)) 38 = (-((11-45)*1)+4) 39 = (-((11-45)-1)+4) 40 = (-((1+14)-51)+4) 41 = (-((1*14)-51)+4) 42 = ((11+45)-14) 43 = ((((11*4)-5)*1)+4) 44 = (114-(5*14)) 45 = ((11+(4*5))+14) 46 = (((11-4)*(5+1))+4) 47 = (11-(4*(5-14))) 48 = (-(11-45)+14) 49 = (((11-4)*5)+14) 50 = (((11+4)-5)*(1+4)) 51 = (((1-14)*(-5))-14) 52 = (((11+45)*1)-4) 53 = (((11*4)-5)+14) 54 = (((11-4)+51)-4) 55 = (-(1+14)+(5*14)) 56 = (((1*14)*5)-14) 57 = (-((1+1)-45)+14) 58 = (-((1*1)-45)+14) 59 = ((114-51)-4) 60 = (((1*1)+45)+14) 61 = (((1+1)+45)+14) 62 = ((1+1)*(45-14)) 63 = ((11-4)*(-(5-14))) 64 = (((11+4)*(5-1))+4) 65 = (-11+(4*(5+14))) 66 = (11*((4*5)-14)) 67 = ((114-51)+4) 68 = (-((1-14)-51)+4) 69 = (((1/14)-5)*(-14)) 70 = ((11+45)+14) 71 = (((1/14)+5)*14) 72 = ((((11+4)*5)+1)-4) 73 = (-11+(((4*5)+1)*4)) 74 = (((1-14)*(-(5+1)))-4) 75 = (11+((4*(5-1))*4)) 76 = (((1+1)*45)-14) 77 = ((11-4)+(5*14)) 78 = ((((11+4)*5)-1)+4) 79 = (-((1-14)*5)+14) 80 = ((((11+4)+5)*1)*4) 81 = (1+(((14+5)+1)*4)) 82 = (-((1-14)*(5+1))+4) 83 = (-(1-14)+(5*14)) 84 = (((1*14)*5)+14) 85 = ((1+14)+(5*14)) 86 = (((11+4)*(5+1))-4) 87 = (11+(4*(5+14))) 88 = ((11*4)*((5+1)-4)) 89 = (((1+14)*5)+14) 90 = (-114+(51*4)) 91 = (((11*4)+51)-4) 92 = ((11*((4+5)-1))+4) 93 = ((11+(4*5))*(-(1-4))) 94 = (114-((5*1)*4)) 95 = ((114-5)-14) 96 = (((11*(4+5))+1)-4) 97 = ((1*1)+((4*(5+1))*4)) 98 = (114-((5-1)*4)) 99 = (((11*4)+51)+4) 100 = (((11+4)+5)*(1+4)) 101 = ((1*1)+((4*5)*(1+4))) 102 = ((11-45)*(1-4)) 103 = (((11*(4+5))*1)+4) 104 = (((1+1)*45)+14) 105 = ((114+5)-14) 106 = (((114-5)+1)-4) 107 = (11+((4*(5+1))*4)) 108 = ((11+(4*(5-1)))*4) 109无解 110 = ((11-451)/(-4)) 111 = (11+((4*5)*(1+4))) 112 = (-1+((1+451)/4)) 113 = (((1*1)+451)/4) 114 = (1+((1+451)/4)) 115 = (-11+((4+5)*14)) 116 = (((114+5)+1)-4) 117 = ((1-14)*(5-14)) 118 = ((1+1)*(45+14)) 119 = (-1+(((1+4)*(5+1))*4)) 120 = ((11+4)*((5-1)+4)) 121 = ((11*(45-1))/4) 122 = (((114+5)-1)+4) 123 = ((114-5)+14) 124 = (((11*45)+1)/4) 125 = (-1+((14-5)*14)) 126 = (((1*14)-5)*14) 127 = (1+((14-5)*14)) 128 = (((11+(4*5))+1)*4) 129 = (114-(5*(1-4))) 130 = ((-1+145)-14) 131 = ((1*145)-14) 132 = ((1+145)-14) 133 = ((114+5)+14) 134 = (114+((5*1)*4)) 135 = ((1+14)*(-(5-14))) 136 = (((11-45)*1)*(-4)) 137 = (11+((4+5)*14)) 138 = (114+((5+1)*4)) 139 = (((-1+145)-1)-4) 140 = (((1+14)-5)*14) 141 = (((1+145)-1)-4) 142 = (((1+145)*1)-4) 143 = (((1+145)+1)-4) 144 = (((1+14)-51)*(-4)) 145无解 146 = (11-(45*(1-4))) 147 = (-1+((14-51)*(-4))) 148 = (((1*14)-51)*(-4)) 149 = (1-((14-51)*4)) 150 = (((1+145)*1)+4) 151 = (((1+145)+1)+4) 152 = (((1-14)+51)*4) 153 = (((1-(1/4))*51)*4) 154 = ((11*(4-5))*(-14)) 155 = ((11+(4*5))*(1+4)) 156 = ((((11*4)-5)*1)*4) 157 = (-(((1*1)-4)*51)+4) 158 = (-(1-145)+14) 159 = ((1*145)+14) 160 = ((1+145)+14) 161 = ((114+51)-4)

不带负数玩的：

0 = ((1-1)*4514) 1 = ((11/(45-1))*4) 2 = (11-(45/(1+4))) 3 = ((11*(4-5))+14) 4 = ((11+45)/14) 5 = (((1*14)+5)-14) 6 = (114/(5+14)) 7 = ((((11+4)-5)+1)-4) 8 = ((((11+4)/5)+1)+4) 9 = ((((11-4)+5)+1)-4) 10 = (((11+4)/(5+1))*4) 11 = (11+(((4-5)+1)*4)) 12 = ((((11+4)/5)*1)*4) 13 = ((((11+4)-5)-1)+4) 14 = (((1-1)*45)+14) 15 = ((114/(5+1))-4) 16 = (((11-4)-5)+14) 17 = (((1+14)/5)+14) 18 = (((1+(14*5))+1)/4) 19 = ((((11+4)*5)+1)/4) 20 = (11+(45/(1+4))) 21 = (((11-4)*5)-14) 22 = (11+((45-1)/4)) 23 = (((1*14)-5)+14) 24 = (((1+14)-5)+14) 25 = (((11*4)-5)-14) 26 = (((11-4)+5)+14) 27 = (((114-5)-1)/4) 28 = (((11-4)-5)*14) 29 = ((1*145)/(1+4)) 30 = (1+(145/(1+4))) 31 = (((1-1)+45)-14) 32 = (((1*1)+45)-14) 33 = (((1+1)+45)-14) 34 = (((1+14)+5)+14) 35 = (((11*4)+5)-14) 36 = (((1*145)-1)/4) 37 = (1+((145-1)/4)) 38 = ((((11-4)*5)-1)+4) 39 = ((11+4)+((5+1)*4)) 40 = ((((11+4)-5)*1)*4) 41 = (1+(((14-5)+1)*4)) 42 = ((11+45)-14) 43 = ((((11*4)-5)*1)+4) 44 = (114-(5*14)) 45 = ((11+(4*5))+14) 46 = (((11-4)*(5+1))+4) 47 = (11-(4*(5-14))) 48 = ((1-145)/(1-4)) 49 = (((11-4)*5)+14) 50 = (((11+4)-5)*(1+4)) 51 = (((11+45)-1)-4) 52 = (((11+45)*1)-4) 53 = (((11*4)-5)+14) 54 = (((11-4)+51)-4) 55 = ((((11*4)*5)*1)/4) 56 = (((1*14)*5)-14) 57 = ((1-14)+(5*14)) 58 = (1-((14+5)*(1-4))) 59 = ((114-51)-4) 60 = (((1*1)+45)+14) 61 = (((1+1)+45)+14) 62 = ((1+1)*(45-14)) 63 = (((11*4)+5)+14) 64 = (((11+4)*(5-1))+4) 65 = ((((1*14)*5)-1)-4) 66 = (11*((4*5)-14)) 67 = ((114-51)+4) 68 = ((11*4)+((5+1)*4)) 69 = (((1*14)+51)+4) 70 = ((11+45)+14) 71 = (((1/14)+5)*14) 72 = ((((11+4)*5)+1)-4) 73 = ((((1*14)*5)-1)+4) 74 = ((((1*14)*5)*1)+4) 75 = (11+((4*(5-1))*4)) 76 = (((1+1)*45)-14) 77 = ((11-4)+(5*14)) 78 = ((((11+4)*5)-1)+4) 79 = ((((11+4)*5)*1)+4) 80 = ((((11+4)+5)*1)*4) 81 = (1+(((14+5)+1)*4)) 82 = ((1+1)*((45*1)-4)) 83无解 84 = (((1*14)*5)+14) 85 = ((1+14)+(5*14)) 86 = (((11+4)*(5+1))-4) 87 = (11+(4*(5+14))) 88 = ((11*4)*((5+1)-4)) 89 = (((1+14)*5)+14) 90 = (114-((5+1)*4)) 91 = (((11*4)+51)-4) 92 = ((11*((4+5)-1))+4) 93 = ((((1+1)*45)-1)+4) 94 = (114-((5*1)*4)) 95 = ((114-5)-14) 96 = (((11*(4+5))+1)-4) 97 = ((1*1)+((4*(5+1))*4)) 98 = (114-((5-1)*4)) 99 = (((11*4)+51)+4) 100 = (((11+4)+5)*(1+4)) 101 = ((1*1)+((4*5)*(1+4))) 102 = ((11-45)*(1-4)) 103 = (((11*(4+5))*1)+4) 104 = (((1+1)*45)+14) 105 = ((114+5)-14) 106 = (((114-5)+1)-4) 107 = (11+((4*(5+1))*4)) 108 = ((11+(4*(5-1)))*4) 109无解 110 = (((1+1)+(4*5))*(1+4)) 111 = (11+((4*5)*(1+4))) 112 = (((114-5)-1)+4) 113 = (((1*1)+451)/4) 114 = (1+((1+451)/4)) 115 = (((114+5)*1)-4) 116 = (((114+5)+1)-4) 117 = ((1-14)*(5-14)) 118 = ((1+1)*(45+14)) 119无解 120 = ((11+4)*((5-1)+4)) 121 = ((11*(45-1))/4) 122 = (((114+5)-1)+4) 123 = ((114-5)+14) 124 = (((11*45)+1)/4) 125 = ((((1*1)+4)*5)*(1+4)) 126 = (((1*14)-5)*14) 127 = (1+((14-5)*14)) 128 = (((11+(4*5))+1)*4) 129 = (114-(5*(1-4))) 130 = (114+((5-1)*4)) 131 = ((1*145)-14) 132 = ((1+145)-14) 133 = ((114+5)+14) 134 = (114+((5*1)*4)) 135 = ((11+4)*((5*1)+4)) 136 = ((((11-4)*5)-1)*4) 137 = (11+((4+5)*14)) 138 = (114+((5+1)*4)) 139 = (114+(5*(1+4))) 140 = (((1+14)-5)*14) 141 = (((1+145)-1)-4) 142 = (((1+145)*1)-4) 143 = (((1+145)+1)-4) 144 = ((((11-4)*5)+1)*4) 145无解 146 = (11-(45*(1-4))) 147无解 148 = (((1*145)-1)+4) 149 = (1-((14-51)*4)) 150 = (((1+145)*1)+4) 151 = (((1+145)+1)+4) 152 = (((1-14)+51)*4) 153 = (((1-(1/4))*51)*4) 154 = (11*(((4+5)+1)+4)) 155 = ((11+(4*5))*(1+4)) 156 = ((((11*4)-5)*1)*4) 157无解 158 = ((1-((1-4)*51))+4) 159 = ((1*145)+14) 160 = ((1+145)+14) 161 = ((114+51)-4)

择优取用~~固然很臭

祝好。