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UVALive 2889(回文数字)

题意:给定i,输出第i个回文数字。

分析:1,2,3,4,……,9------------------------------------------------------------------------------------------9个

   11,12,13,14,……,19-------------------------------------------------------------------------------------9个

   101,111,121,131,141,151,161,171,181,191,202,212,222,232,……,979,989,999-------------------------------90个

   1001,1111,1221,1331,1441,……,9889,9999----------------------------------------------------------------90个

   10001,10101,10201,10301,……,99899,99999--------------------------------------------------------------900个

   规律是把回文串一分为二看,例如第四行,前两个数字是从10到99,共90个数字。而第三行也是从10到99,区别在于,需要去掉最后一位再反转,才是另一半(后两个数字)。

思路:先确定i所对应的回文数字的位数,再确定具体值。

 

 1 #include<cstdio> 2 #include<cstring> 3 #include<cctype> 4 #include<cstdlib> 5 #include<cmath> 6 #include<iostream> 7 #include<sstream> 8 #include<iterator> 9 #include<algorithm>10 #include<string>11 #include<vector>12 #include<set>13 #include<map>14 #include<deque>15 #include<queue>16 #include<stack>17 #include<list>18 #define fin freopen("in.txt", "r", stdin)19 #define fout freopen("out.txt", "w", stdout)20 #define pr(x) cout << #x << " : " << x << "   "21 #define prln(x) cout << #x << " : " << x << endl22 typedef long long ll;23 typedef unsigned long long llu;24 const int INT_INF = 0x3f3f3f3f;25 const int INT_M_INF = 0x7f7f7f7f;26 const ll LL_INF = 0x3f3f3f3f3f3f3f3f;27 const ll LL_M_INF = 0x7f7f7f7f7f7f7f7f;28 const double pi = acos(-1.0);29 const double EPS = 1e-6;30 const int dx[] = {0, 0, -1, 1};31 const int dy[] = {-1, 1, 0, 0};32 const ll MOD = 1e9 + 7;33 const int MAXN = 1000000 + 10;34 const int MAXT = 10000 + 10;35 using namespace std;36 ll a[25];37 void init()38 {39     ll tmp = ll(9);40     for(int i = 1; i < 20; i += 2)41     {42         a[i] = a[i - 1] = tmp;43         tmp *= ll(10);44     }45 }46 ll POW(ll x)47 {48     ll w = 1;49     for(ll i = 1; i <= x; ++i)50         w *= ll(10);51     return w;52 }53 int main()54 {55     init();56     int n;57     while(scanf("%d", &n) == 1 && n)58     {59         int cnt = 0;60         while(n > a[cnt])61         {62             n -= a[cnt];63             ++cnt;64         }65         if(cnt == 0)66         {67             printf("%d\n", n);68             continue;69         }70         else if(cnt == 1)71         {72             printf("%d%d\n", n, n);73             continue;74         }75         else76         {77             int tmp = cnt / 2;78             char str[50];79             memset(str, 0, sizeof str);80             ll ans = POW(ll(cnt / 2)) + ll(n - 1);81             sprintf(str, "%lld", ans);//把数字变为指定格式的字符串82             printf("%s", str);83             string s = string(str);84             int len = s.size();85             if(cnt % 2 == 0) s.resize(len - 1);86             reverse(s.begin(), s.end());87             printf("%s\n", s.c_str());88         }89     }90     return 0;91 }

 

 

   

UVALive 2889(回文数字)