高精度计算练习2
高精度运算_乘法
AYYZOJ p1445
1 program p1445; 2 const 3 max=5000; 4 var 5 a,b,c:array[1..max] of word; 6 n1,n2:string; 7 lena,lenb,lenc,i,j,x:integer; 8 begin 9 readln(n1); 10 readln(n2); 11 lena:=length(n1); lenb:=length(n2); 12 for i:=1 to lena do a[lena-i+1]:=ord(n1[i])-ord('0'); 13 for i:=1 to lenb do b[lenb-i+1]:=ord(n2[i])-ord('0'); 14 for i:=1 to lena do 15 begin 16 x:=0; 17 for j:=1 to lenb do 18 begin 19 C[i+j-1]:= A[i]*B[j]+ x + C[i+j-1]; 20 x:= C[i+j-1] div 10; 21 C[i+j-1]:= C[i+j-1] mod 10 22 end; 23 c[i+j]:= x; 24 end; 25 lenc:=i+j; 26 while (c[lenc]=0) and (lenc>1) do dec(lenc); 27 for i:=lenc downto 1 do write(c[i]); 28 end.
高精度运算_A/B问题1
AYYZOJ p1446
1 program p1446; 2 const e=20; 3 var 4 a,d,x:array[0..e] of integer; 5 n,m,t:integer; 6 begin 7 read(n,m); 8 write(n,'/',m,'='); 9 a[0]:=n; d[0]:=n div m; 10 x[0]:=n mod m; 11 write(d[0],'.'); 12 for t:=1 to e do 13 begin 14 //if x[t-1]=0 then exit; {去掉也能A} 15 a[t]:=x[t-1]*10; 16 d[t]:=a[t] div m; 17 write(d[t]); 18 x[t]:=a[t] mod m; 19 end; 20 end.
高精度运算_A/B问题2
AYYZOJ p1447
1 const max=200;dot=100; 2 var a,c:array[0..max] of byte; 3 x,n2:longint; n1:string; 4 lena:integer; code,i,j:integer; 5 begin 6 readln(n1); 7 readln(n2); 8 lena:=length(n1); 9 for i:=1 to lena do a[i] := ord(n1[i]) - ord('0'); 10 x:=0; 11 for i:=1 to lena do begin 12 c[i]:=(x*10+a[i]) div n2; 13 x:=(x*10+a[i]) mod n2; 14 end; 15 j:=1; 16 while (c[j]=0) and (j<lena) do inc(j); 17 if j<>1 then 18 for i:=j to lena do begin c[i-j+1]:=c[i];c[i]:=0;end; 19 c[0]:=lena-j+1; 20 if x=0 then begin 21 for i:=1 to c[0] do write(c[i]); 22 writeln;halt; 23 end; 24 j:=c[0]+dot; 25 for i:=1 to dot do begin 26 c[c[0]+i]:=x*10 div n2; 27 x:=x*10 mod n2; 28 if x=0 then begin j:=c[0]+i;break;end; 29 end; 30 for i:=1 to j do 31 if i=c[0] then write(c[i],'.') 32 else write(c[i]); 33 writeln 34 end.
高精度运算_3的n次幂
AYYZOJ p1450
思路：高精度数乘单精度数
1 program p1450; 2 var 3 a:array[1..500] of byte; 4 i,j,c,n,l:integer; 5 begin 6 readln(n); 7 a[1]:=1;l:=1; 8 for i:=1 to n do 9 begin 10 c:=0; 11 for j:=1 to l do 12 begin 13 a[j]:=a[j]*3+c; 14 c:=a[j] div 10; 15 a[j]:=a[j] mod 10; 16 end; 17 if c>0 then begin inc(l);a[l]:=c;end; 18 end; 19 for i:=l downto 1 do write(a[i]); 20 writeln; 21 end.
高精度运算_求s=1+2+...+n
AYYZOJ p1451
1 var 2 n:longint; 3 a,b,c:array[1..100] of integer; 4 la,lb,lc,k,i,j:integer; 5 procedure mul(x,y:longint); 6 begin 7 la:=0; 8 while x>0 do 9 begin 10 inc(la); 11 a[la]:=x mod 10; 12 x:=x div 10; 13 end; 14 lb:=0; 15 while y>0 do 16 begin 17 inc(lb); 18 b[lb]:=y mod 10; 19 y:=y div 10; 20 end; 21 for i:=1 to la do 22 begin 23 k:=0; 24 for j:=1 to lb do 25 begin 26 c[i+j-1]:=a[i]*b[j]+k+c[i+j-1]; 27 k:=c[i+j-1] div 10; 28 c[i+j-1]:=c[i+j-1] mod 10; 29 end; 30 c[i+j]:=k; 31 end; 32 lc:=i+j; 33 while(c[lc]=0) and (lc>1) do dec(lc); 34 for i:=lc downto 1 do write(c[i]);writeln; 35 end; 36 begin 37 readln(n); 38 if n mod 2=0 then mul(n div 2,n+1) {等差数列求和公式} 39 else mul(n,(n+1) div 2); 40 end.
高精度运算_求n的阶乘
【优化方法】
AYYZOJ p1452
1 const maxn=3001;maxm=10000; 2 type arr=array[1..maxm] of integer; 3 var 4 ans:arr; 5 p,num:array[1..maxn] of integer; 6 n,i,j,k:longint; 7 flag:boolean;la:integer; 8 procedure add(x:longint); 9 var i:longint; 10 begin 11 i:=1; 12 while p[i]<=x do begin 13 while (x mod p[i]=0) do 14 begin 15 inc(num[i],1); 16 x:=x div p[i]; 17 end; 18 inc(i); 19 end; 20 end; 21 procedure mul(var a:arr;c:longint;var la:integer); 22 var i:longint; 23 begin 24 a[1]:=a[1]*c; 25 for i:=2 to la do 26 begin 27 a[i]:=a[i]*c; 28 a[i]:=a[i]+a[i-1] div 10; 29 a[i-1]:=a[i-1] mod 10; 30 end; 31 while a[la]>=10 do 32 begin 33 inc(la); 34 a[la]:=a[la-1] div 10; 35 a[la-1]:=a[la-1] mod 10; 36 end; 37 end; 38 begin 39 p[1]:=2;k:=1; 40 for i:=3 to maxn do begin 41 flag:=false; 42 for j:=2 to trunc(sqrt(i)) do 43 if i mod j=0 then begin flag:=true;break;end; 44 if not flag then begin inc(k);p[k]:=i;end; 45 end; 46 fillchar(ans,sizeof(ans),0); 47 fillchar(num,sizeof(num),0); 48 readln(n); 49 for i:=2 to n do add(i); 50 ans[1]:=1; la:=1; 51 for i:=1 to maxn do 52 if p[i]>n then break else for j:=1 to num[i] do mul(ans,p[i],la); 53 for i:=la downto 1 do write(ans[i]);writeln; 54 end.
1 可以初始化定义常量数组P为10000以内整数的质因子表 2 const p:array[1..1229] of integer=(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973);
N!
1 const m=10000000; 2 var a:array[1..m] of integer; 3 f:real; 4 y,c,i,j,n,k,l,t:longint; 5 st1,st2:string; 6 begin 7 write('input a number n:'); 8 read(n); 9 // for i:=1 to n do 10 // f:=f+ln(i)/ln(10); 11 // t:=trunc(f)+1; {计算可能需要的位数} 12 a[1]:=1;l:=1;k:=1; 13 for i:=1 to n do 14 begin 15 c:=0; 16 while a[k]=0 do k:=k+1; 17 for j:=k to l do 18 begin 19 y:=a[j]*i+c; {该位上的数乘以I加上低位的进位} 20 c:=y div 10000; {每四位数占用1个数组单元,c是进位} 21 a[j]:=y mod 10000 22 end; 23 if c>0 then begin 24 l:=l+1; 25 a[l]:=c; {若有进位则数组的下标指针加1,增加一} 26 end; {个存储单元} 27 end; 28 write(n,'!='); 29 for i:=l downto 1 do {输出处理} 30 begin 31 if i=l then write(a[i]) 32 else begin 33 str(a[i],st1); 34 while length(st1)<4 do 35 st1:='0'+st1; 36 write(st1); 37 end; 38 end; 39 writeln; 40 end.
