POJ1060 Modular multiplication of polynomials
题目来源：http://poj.org/problem?id=1060
题目大意：
考虑系数为0和1的多项式。两个多项式的加法可以通过把相应次数项的系数相加而实现。但此处我们用模2加法来计算系数之和。一个实例：
(x^6 + x^4 + x^2 + x + 1) + (x^7 + x + 1) = x^7 + x^6 + x^4 + x^2
同样，多项式的减法我们在求系数之差时也用模2减法，例如：
(x^6 + x^4 + x^2 + x + 1) - (x^7 + x + 1) = x^7 + x^6 + x^4 + x^2
多项式的乘法与平常的做法一致，但同次项系数相加时使用模二加法，例如：
(x^6 + x^4 + x^2 + x + 1) (x^7 + x + 1) = x^13 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^3 + 1
两个多项式f(x)和g(x)模多项式h(x)是求f(x)*g(x)除以h(x)的余数。例如：
(x^6 + x^4 + x^2 + x + 1) (x^7 + x + 1) modulo (x^8 + x^4 + x^3 + x + 1) = x^7 + x^6 + 1
多项式中最高次数称为degree。给出f(x) g(x)和h(x)，写一个程序求出 f(x)*g(x) mod h(x) 的结果。假定f(x)和g(x)的degree都小于h(x)，多项式的degree都小于1000。
由于系数都是0或1，假设多项式的degree为d，那么该多项式可以由一个次数指示整数(d + 1)和d+1个二进制位来表示。比如x^7 + x^6 + 1 可表示为： 8 1 1 0 0 0 0 0 1.
输入：由T个测试用例组成，并在输入的第一行给出T的值。每个用例由三行组成，分别为f(x)，g(x)，h(x)。多项式的表示方法如前所述。
输出：用如前所述的表示方式表达f(x)*g(x)%h(x)的值。每行对应一个输出的多项式。
Sample Input
2 7 1 0 1 0 1 1 1 8 1 0 0 0 0 0 1 1 9 1 0 0 0 1 1 0 1 1 10 1 1 0 1 0 0 1 0 0 1 12 1 1 0 1 0 0 1 1 0 0 1 0 15 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1
Sample Output
8 1 1 0 0 0 0 0 1 14 1 1 0 1 1 0 0 1 1 1 0 1 0 0
模拟题， 需要注意的两个地方：
1. 虽然题目中涉及的f(x) g(x) h(x)和输出的结果r(x)最高次都不会超过1000, 但中间结果f(x) * g(x)的最高次可能会超过1000，最大到2000.
2. 余数为0情况应输出0 0.
第一次用bitset.
1 //////////////////////////////////////////////////////////////// 2 // POJ1060 Modular multiplication of polynomials 3 // Memory: 224K Time: 63MS 4 // Language: C++ Result : Accepted 5 /////////////////////////////////////////////////////////////// 6 7 #include <iostream> 8 #include <bitset> 9 10 using namespace std; 11 12 bitset<1001> fx; 13 bitset<1001> gx; 14 bitset<1001> hx; 15 bitset<2002> rx; 16 int dfx, dgx, dhx, drx; 17 18 int main(void) { 19 int T; 20 cin >> T; 21 for (int case_id = 0; case_id < T; ++case_id) { 22 23 fx.reset(); 24 gx.reset(); 25 hx.reset(); 26 rx.reset(); 27 28 //读取输入 29 cin >> dfx; 30 int buf; 31 for (int d = dfx - 1; d >= 0; --d) { 32 cin >> buf; 33 fx[d] = buf; 34 } 35 cin >> dgx; 36 for (int d = dgx - 1; d >= 0; --d) { 37 cin >> buf; 38 gx[d] = buf; 39 } 40 cin >> dhx; 41 for (int d = dhx - 1; d >= 0; --d) { 42 cin >> buf; 43 hx[d] = buf; 44 } 45 46 //乘法计算 47 for (int d1 = dfx - 1; d1 >= 0; --d1) { 48 for (int d2 = dgx - 1; d2 >= 0; --d2) { 49 rx[d1 + d2] = fx[d1] & gx[d2] ^ rx[d1 + d2]; 50 } 51 } 52 for (drx = 2001; drx >= 0; --drx) { 53 if (rx[drx] == 1) { 54 ++drx; 55 break; 56 } 57 } 58 59 //除法计算 60 while (drx >= dhx && drx > 0) { 61 int t = drx - dhx; 62 for (int d = dhx - 1; d >= 0; --d) { 63 rx[d + t] = hx[d] ^ rx[d + t]; 64 } 65 while (drx >= 0 && rx[drx] == 0) { 66 --drx; 67 } 68 ++drx; 69 } 70 71 //输出 72 cout << drx; 73 for (int d = drx - 1; d > 0; --d) { 74 cout << " " << rx[d]; 75 } 76 cout << " " << rx[0] << endl; 77 } 78 return 0; 79 }
附测试数据：
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