欧拉公式

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LRJ算法入门经典第二版上面写错了，害得我想了半天。。。

V ：点数， E ：边数 F ：面数

欧拉公式 V - E + F = 2；

V = n + n / 4 sum(i * (n - 2 - i)); [ 0 <= i <= n - 2];

E = n + n / 2 sum((i * (n - 2 - i ) + 1); [ 0 <= i <= n - 2];

代码实现：

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>#include<vector>#include<stack>#include<queue>#include<map>#include<set>#include<list>#include<cmath>#include<string>#include<sstream>#include<ctime>using namespace std;#define _PI acos(-1.0)#define INF (1 << 10)#define esp 1e-9typedef long long LL;typedef unsigned long long ULL;typedef pair<int,int> pill;/*======================================================================================*/LL _V(LL n){  /*求点*/    LL ans = 0;    for(LL i = 0 ; i <= n - 2 ; i++)        ans = ans + i * (n - 2 - i);    LL _ans = n + n * ans / 4;    return _ans;}LL _E(LL n){ /*求面*/    LL ans = 0;    for(LL  i = 0 ; i <= n - 2; i++)        ans = ans + (i * (n - 2 - i) + 1);    LL _ans = n + n * ans / 2;    return _ans;}int main(){    int T;    scanf("%d",&T);    while(T--){        LL N;        scanf("%I64d",&N);        LL V = _V(N);        LL E = _E(N);        printf("%I64d\n",1 + E - V);    }    return 0;}

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