思维/构造 HDOJ 5353 Average

题目传送门

 /*
     思维/构造：赛后补的，当时觉得3题可以交差了，没想到这题也是可以做的。一看到这题就想到了UVA_11300(求最小交换数)
             这题是简化版，只要判断行不行和行的方案就可以了，做法是枚举x[1],x[n]的所有可能，x[2~n-1]能递推出来
             x[i]表示i给i+1的值(0/-1/1) 那么 a[i] - x[i] + x[i-1] == ave，详细看代码
 */
 /************************************************
 * Author        :Running_Time
 * Created Time  :2015-8-7 8:51:48
 * File Name     :A.cpp
  ************************************************/

 #include <cstdio>
 #include <algorithm>
 #include <iostream>
 #include <sstream>
 #include <cstring>
 #include <cmath>
 #include <string>
 #include <vector>
 #include <queue>
 #include <deque>
 #include <stack>
 #include <list>
 #include <map>
 #include <set>
 #include <bitset>
 #include <cstdlib>
 #include <ctime>
 using namespace std;

 #define lson l, mid, rt << 1
 #define rson mid + 1, r, rt << 1 | 1
 typedef long long ll;
 const int MAXN = 1e5 + ;
 const int INF = 0x3f3f3f3f;
 const int MOD = 1e9 + ;
 int a[MAXN];
 int x[MAXN];
 int n, tot;
 ll ave;

 bool work(void) {
     tot = ;
     if (x[] != )  tot++;
     if (x[n] != )  tot++;
     if (x[n-] != )    tot++;
     for (int i=; i<=n-; ++i)  {
         if (abs (a[i] - ave + x[i-]) > )  return false;
         x[i] = a[i] - ave + x[i-];
         if (x[i] != )  tot++;
     }
     if (a[n-] - x[n-] + x[n-] != ave)    return false;
     return true;
 }

 bool judge(void)    {
     for (int i=-; i<=; ++i)   {
         for (int j=-; j<=; ++j)   {
             x[] = i, x[n] = j;
             if (abs (ave - a[n] + x[n]) <= )   {
                 x[n-] = ave - a[n] + x[n];
                 if (work ())    return true;
             }
         }
     }
     return false;
 }

 int main(void)    {     //HDOJ 5353 Average
     int T;  scanf ("%d", &T);
     while (T--) {
         scanf ("%d", &n);   ll sum = ;
         for (int i=; i<=n; ++i)    {
             scanf ("%d", &a[i]);    sum += a[i];
         }
         if (sum % n != )   {
             puts ("NO");    continue;
         }
         ave = sum / n;   bool flag = true, same = true;
         for (int i=; i<=n; ++i)    {
             if (a[i] < ave -  || a[i] > ave + )   {
                 flag = false;  break;
             }
             if (a[i] != ave)   same = false;
         }
         if (!flag)   {
             puts ("NO");    continue;
         }
         if (same)   {
             printf ("YES\n0\n");    continue;
         }

         memset (x, , sizeof (x));
         if (!judge ())  {
             puts ("NO");    continue;
         }
         puts ("YES");   printf ("%d\n", tot);
         for (int i=; i<=n; ++i)    {
             if (x[i] == )  continue;
             else if (x[i] == ) printf ("%d %d\n", i, (i == n) ?  : i + );
             else    printf ("%d %d\n", (i == n) ?  : i + , i);
         }
     }

     return ;
 }