三角形数
- Description
一定数目的点或圆在等距离的排列下可以形成一个等边三角形，这样的数被称为三角形数。比如10个点可以组成一个等边三角形，因此10是一个三角形数：
ｘ
ｘ ｘ
ｘ ｘ ｘ
ｘ ｘ ｘ ｘ
开始18个三角形数是1、3、6、10、15、21、28、36、45、55、66、78、91、105、120、136、153、171。
请求出第n个三角形数。
- Input
输入数据包含多组测试用例。
每组测试用例为一个整数N，长度不超100。
- Output
对于每组测试用例，输出对应的三角形数。
- Sample Input
1
2
3
4
5
11111111
- Sample Output
1
3
6
10
15
61728399382716
#include<iostream>
#include<cmath>
#include<cstring>
#include<cstdlib>
using namespace std;
const int MAXSIZE = 101;
void Add(char *str1, char *str2, char *str3);
void Minus(char *str1, char *str2, char *str3);
void Mul(char *str1, char *str2, char *str3);
void Div(char *str1, char *str2, char *str3);
int main()
{
// freopen("in.txt","r",stdin);
char str1[MAXSIZE],str2[MAXSIZE],str3[MAXSIZE*MAXSIZE],str11[MAXSIZE],str22[MAXSIZE];
while(scanf("%s",str1)!=EOF)
{
int i=0;
memset(str2,'0',sizeof(str2));
memset(str3,'0',sizeof(str3));
memset(str11,'0',sizeof(str2));
memset(str22,'0',sizeof(str2));
while(str1[i])i++;
if((str1[i-1]-48)%2==0)
{
Div(str1,"2",str11);
Add(str1,"1",str2);
Mul(str11,str2,str3);
puts(str3);
}
else
{
Add(str1,"1",str2);
Div(str2,"2",str22);
Mul(str1,str22,str3);
puts(str3);
}
}
return 0;
}
void Add(char *str1, char *str2, char *str3)
{// str3 = str1 + str2;
int i, j, i1, i2, tmp, carry;
int len1 = strlen(str1), len2 = strlen(str2);
char ch;
i1 = len1-1; i2 = len2-1;
j = carry = 0;
for( ; i1 >= 0 && i2 >= 0; ++j, --i1, --i2 ){
tmp = str1[i1]-'0'+str2[i2]-'0'+carry;
carry = tmp/10;
str3[j] = tmp%10+'0';
}
while( i1 >= 0 ){
tmp = str1[i1--]-'0'+carry;
carry = tmp/10;
carry = tmp/10;
str3[j++] = tmp%10+'0';
}
if( carry ) str3[j++] = carry+'0';
str3[j] = '\0';
for( i=0, --j; i < j; ++i, --j ){
ch = str3[i]; str3[i] = str3[j]; str3[j] = ch;
}
}
void Mul(char *str1, char *str2, char *str3){
int i, j, i1, i2, tmp, carry, jj;
int len1 = strlen(str1), len2 = strlen(str2);
char ch;
jj = carry = 0;
for( i1=len1-1; i1 >= 0; --i1 ){
j = jj;
for( i2=len2-1; i2 >= 0; --i2, ++j ){
tmp =
(str3[j]-'0')+(str1[i1]-'0')*(str2[i2]-'0')+carry;
if( tmp > 9 ){
carry = tmp/10; str3[j] = tmp%10+'0';
}
else {
str3[j] = tmp+'0'; carry = 0;
}
}
if( carry ) {
str3[j] = carry+'0'; carry = 0; ++j;
}
++jj;
}
--j;
while( str3[j] == '0' && j > 0 ) --j;
str3[++j] = '\0';
for( i=0, --j; i < j; ++i, --j ){
ch = str3[i]; str3[i] = str3[j]; str3[j] = ch;
}
}
void Div(char *str1, char *str2, char *str3){
int i1, i2, i, j, jj, tag, carry, cf, c[MAXSIZE];
int len1 = strlen(str1), len2 = strlen(str2), lend;
char d[MAXSIZE];
memset(c, 0, sizeof(c));
memcpy(d, str1, len2);
lend = len2; j = 0;
for( i1=len2-1; i1 < len1; ++i1 ){
if( lend < len2 ){
d[lend] = str1[i1+1]; c[j] = 0;
++j; ++lend;
}
else if( lend == len2 ){
jj = 1;
for( i=0; i < lend; ++i ){
if( d[i] > str2[i] ) break;
else if( d[i] < str2[i] ){
jj = 0; break;
}
}
if( jj == 0 ){
d[lend] = str1[i1+1]; c[j] = 0;
++j; ++lend;
continue;
}
}
if( jj==1 || lend > len2 ){
cf = jj=0;
while( d[jj] <= '0' && jj < lend ) ++jj;
if( lend-jj > len2 ) cf = 1;
else if( lend-jj < len2 ) cf = 0;
else{
i2 = 0; cf = 1;
for( i=jj; i < lend; ++i ){
if( d[i] < str2[i2] ){
cf = 0; break;
}
else if( d[i] > str2[i2] ){
break;
}
++i2;
}
}//else
while( cf ){
i2 = len2-1; cf = 0;
for( i=lend-1; i >= lend-len2; --i ){
d[i] = d[i]-str2[i2]+'0';
if( d[i] < '0' ){
d[i] = d[i]+10; carry = 1;
--d[i-1];
}
else carry = 0;
--i2;
}
++c[j]; jj=0;
while( d[jj] <= '0' && jj < lend ) ++jj;
if( lend-jj > len2 ) cf = 1;
else if( lend-jj < len2 ) cf = 0;
else{
i2 = 0; cf = 1;
for( i=jj; i < lend; ++i ){
if( d[i] < str2[i2] ){
cf = 0; break;
}
else if( d[i] > str2[i2] ){
break;
}
++i2;
}
}//else
}//while
jj = 0;
while( d[jj] <= '0' && jj < lend ) ++jj;
for( i=0;i < lend-jj; ++i ) d[i] = d[i+jj];
d[i] = str1[i1+1]; lend = i+1;
++j;
}//else
}//for
i = tag = 0;
while( c[i] == 0 ) ++i;
for( ; i < j; ++i, ++tag ) str3[tag] = c[i]+'0';
str3[tag] = '\0';
}