PAT程序设计练习——甲级1002（两个多项式的解析与合并）

题目原文链接：点击打开链接

翻译题目要求：

程序输入为两行：均为一个多项式，按 K
N1 An1 N2 An2......Nk Ank，K代表的是多项式的非零项数，范围闭区间是[1,10]，N1到Nk的范围区间是 1<= Nk <= ......<= N1 <= 1000;

Nk是指数，Ank是系数，遇到相同的指数，系数进行累加，从而合并成一个多项式。

例子输入：

2 1 2.4 0 3.2
2 2 1.5
1 0.5

可以解析成：

第一行： 2个子项---1*2.4 + 0*3.2

第二行： 2个子项---2*1.5 + 1*0.5

其中指数部分，二者有重合，可以累加，结果有 1*（2.4 + 0.5）

输出：

3 2 1.5
1 2.9 0 3.2

可以理解成： 3个子项---2*1.5 + 1*2.9 + 0*3.2

设计思路如下：

在控制台情况下输入两行，按照格式解析出多项式后，用结构体保存每一项系数和指数：

typedef struct
{
int exponents;                                          //系数
float coeffients;                                       //指数
}Polynomials;

再使用归并排序的类似实现把两个多项式合并在一起,完整代码如下：

#include <stdio.h>
#include <string.h>

typedef struct
{
int exponents;
float coeffients;
}Polynomials;

int size1 = 0;
int size2 = 0;
int size3 = 0;
Polynomials poly1[10] = {0};
Polynomials poly2[10] = {0};
Polynomials poly3[20] = {0};
// 把scanf输入保存到多项式结构体中
int save( char* input, Polynomials* poly, int& size )
{
int expo = 0;
float coeff = 0;
char* p = NULL;
char* q = NULL;
char szbuffer[100] = {0};

sscanf(input, "%d %s", &size, szbuffer );
p = input;

for ( int i = 0; i < size; i++ )
{
memset(szbuffer, 0, sizeof(szbuffer) );
while( *p != ' ') p++;
q = p + 1 ;
while( *q != ' ') q++;
q++;
while( *q != ' ')
{
q++;
if ( (q - input) == strlen(input) )//the end case
break;
}
q--;

strncpy( szbuffer, p, q-p+1 );
sscanf( szbuffer, "%d %f",&expo, &coeff );
poly[i].coeffients = coeff;
poly[i].exponents = expo;
p = q+1;
}
return 0;
}
// 仿照归并排序的思路合并多项式
int sort()
{
int poly_index1 = 0, poly_index2 = 0;
int result_size = size1 + size2;

for ( int i = 0; i < result_size; i++ )
{
int expo1 = -1;
int expo2 = -1;
if ( poly_index1 != size1 )
{
expo1 = poly1[poly_index1].exponents;
}
if ( poly_index2 != size2 )
{
expo2 = poly2[poly_index2].exponents;
}
if ( expo1 > expo2 )
{
poly3[i].exponents = expo1;
poly3[i].coeffients = poly1[poly_index1].coeffients;
poly_index1++;
}
else if ( expo1 < expo2 )
{
poly3[i].exponents = expo2;
poly3[i].coeffients = poly2[poly_index2].coeffients;
poly_index2++;
}
else
{
poly3[i].exponents = expo1;
poly3[i].coeffients = poly1[poly_index1].coeffients + poly2[poly_index2].coeffients;
poly_index1++;
poly_index2++;

result_size--;                                     //出现重复可以累加的合并项，总长度减一
}
}
size3 = result_size;
return 0;
}

// 打印多项式结果
int print()
{
char szResult[200] = {0};
sprintf_s(szResult,"%d",size3);

for ( int i = 0; i < size3; i++ )
{
char buffer[20] = {0};
sprintf_s(buffer, " %d %.1f", poly3[i].exponents, poly3[i].coeffients );
strcat(szResult, buffer);
}
printf( "%s\n", szResult );
return 0;
}
/************************************************************************/
//Input
//2 1 2.4 0 3.2
//2 2 1.5 1 0.5

//Output
//3 2 1.5 1 2.9 0 3.2
/************************************************************************/
int main()
{
char szInput[100] = {0};
printf("Please input first Polynomials:\n");
scanf("%[^\n]",szInput);
save(szInput,poly1,size1);

memset(szInput, 0, sizeof(szInput));
printf("Please input second Polynomials:\n");
getchar();
scanf("%[^\n]",szInput);
save(szInput,poly2,size2);

sort();

print();
return 0;
}

Python代码如下：

#the struct definition
class Polynomials:
def __init__(self,exponents,coeffients):
self.exponents = int(exponents)
self.coeffients = float(coeffients)

#the list array
poly1=[]
poly2=[]
poly_result=[]
poly_size1 = []
poly_size2 = []
poly_size3 = []

#main function
def __main():
str_input = raw_input("Please input the first polynomials:\n")
print("the input is:",str_input)
parse( str_input, poly1, poly_size1 )
str_input = raw_input("Please input the second polynomials:\n")
print("the input is:",str_input)
parse( str_input, poly2, poly_size2 )
calc()
output()

#parse the polynomials from the parameters
def parse( str_input, poly_list, poly_size ):
poly_size.append(str_input.split(' ',1)[0])
str_input = str_input.split(' ',1)[1]
str_input = str_input.split(' ')
#print( str_input[0], len(str_input), str_input[1] )
for i in range(0,len(str_input),2):
tmp = Polynomials( str_input[i],str_input[i+1] )
poly_list.append(tmp)

#calculate the combination of 2 polynomials
def calc():
poly_index1 = 0
poly_index2 = 0
result_size = int(poly_size1[0]) + int(poly_size2[0])
print( "calc, result_size:", poly_size1[0], poly_size2[0], result_size )
print( "poly1,poly2", poly1[0].exponents,poly2[0].exponents )
print( "poly1, poly2", poly1[1].exponents, poly2[1].exponents )
for i in range(0,result_size):
expo1 = -1; expo2 = -1
if( poly_index1 != int(poly_size1[0]) ):
expo1 = poly1[poly_index1].exponents
if( poly_index2 != int(poly_size2[0]) ):
expo2 = poly2[poly_index2].exponents
if( expo1 is -1 and expo2 is -1 ):
break;
if( expo1 > expo2 ):
tmp = Polynomials( expo1, poly1[poly_index1].coeffients )
poly_result.append(tmp)
poly_index1 += 1
print( ">>1<<")
elif( expo1 < expo2 ):
tmp = Polynomials( expo2, poly2[poly_index2].coeffients )
poly_result.append(tmp)
poly_index2 += 1
print( ">> 2<<")
else:
tmp = Polynomials( expo1, poly1[poly_index1].coeffients + poly2[poly_index2].coeffients )
poly_result.append(tmp)
poly_index1 += 1
poly_index2 += 1
result_size -= 1
print(">> 3 <<")
poly_size3.append(result_size)
print("poly_size3:",poly_size3[0])
print("result_size:",result_size )

def output():
print( "result:", poly_size3[0] )
print( "content:", poly_result[0].exponents, poly_result[0].coeffients,  poly_result[1].exponents, poly_result[1].coeffients, poly_result[2].exponents, poly_result[2].coeffients )
for i in range(0,poly_size3[0] ):
print("exponents:coeffients",poly_result[i].exponents,poly_result[i].coeffients )
#run the main function
__main()

可能还有其他更优化的办法，正在考虑当中。。。