uva 10519 - !! Really Strange !!（规律）
题目链接：uva 10519 - !! Really Strange !!
题目大意：给出n，问用n个圆最多能将平面分割成几份。
解题思路：公式c[i] = i * i - i + 2，首先可以分析出c[i] = c[i - 1] + 2 * i - 2, 然后带入c[i - 1] = c[i - 2] + 2 * (i - 1) - 2,重复带入可得c[i] = c[1] + 2 * ∑(1≤j≤i) j - 2 * i, 化简的到上面的公式。（大数处理）
#include <stdio.h>#include <string.h>#include <iostream>using namespace std;const int N = 305;char n[N];struct bign {int len, sex;int s[N];bign() {this -> len = 1;this -> sex = 0;memset(s, 0, sizeof(s));}bign operator = (const char *number) {int begin = 0;len = 0;sex = 1;if (number[begin] == '-') {sex = -1;begin++;}else if (number[begin] == '+')begin++;for (int j = begin; number[j]; j++)s[len++] = number[j] - '0';}bign operator = (int number) {char string[N];sprintf(string, "%d", number);*this = string;return *this;}bign (int number) {*this = number;}bign (const char* number) {*this = number;}bign change(bign cur) {bign now;now = cur;for (int i = 0; i < cur.len; i++)now.s[i] = cur.s[cur.len - i - 1];return now;}void delZore() {// 删除前导0.bign now = change(*this);while (now.s[now.len - 1] == 0 && now.len > 1) {now.len--;}*this = change(now);}void put() { // 输出数值。delZore();if (sex < 0 && (len != 1 || s[0] != 0))cout << "-";for (int i = 0; i < len; i++)cout << s[i];}bign operator + (const bign &cur){ bign sum, a, b; sum.len = 0;a = a.change(*this);b = b.change(cur);for (int i = 0, g = 0; g || i < a.len || i < b.len; i++){ int x = g; if (i < a.len) x += a.s[i]; if (i < b.len) x += b.s[i]; sum.s[sum.len++] = x % 10; g = x / 10; } return sum.change(sum); } bign operator * (const bign &cur){ bign sum, a, b;sum.len = 0; a = a.change(*this);b = b.change(cur);for (int i = 0; i < a.len; i++){ int g = 0; for (int j = 0; j < b.len; j++){ int x = a.s[i] * b.s[j] + g + sum.s[i + j]; sum.s[i + j] = x % 10; g = x / 10; } sum.len = i + b.len; while (g){ sum.s[sum.len++] = g % 10; g = g / 10; } } return sum.change(sum); } bign operator - (const bign &cur) {bign sum, a, b;sum.len = len;a = a.change(*this);b = b.change(cur);for (int i = 0; i < b.len; i++) {sum.s[i] = a.s[i] - b.s[i] + sum.s[i];if (sum.s[i] < 0) {sum.s[i] += 10;sum.s[i + 1]--;}}for (int i = b.len; i < a.len; i++) {sum.s[i] += a.s[i];if (sum.s[i] < 0) {sum.s[i] += 10;sum.s[i + 1]--;}}return sum.change(sum);}};int main () {bign tmp = 2;while (scanf("%s", n) == 1) {if (strlen(n) == 1 && n[0] == '0')printf("1\n");else {bign num = n;bign sum = num * num - num + tmp;sum.put();printf("\n");}}return 0;}