Problem F: 等式
Time Limit: 1 Sec Memory Limit: 128 MB
Submit: 104 Solved: 22
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Description
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" 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qt44TpvvNCIEvOYEltYWSv+g2mI5oFCOKlF8O3i+5tOKWbHvHBGZSn5ZwvX0HX4dHhIc2nWneeJ7Kt8qtz7pEL20BtIEvHjvSqM2sp4N9Bk2XC36bT5bLzNaQizWiTEKRkouvF0YEkuFdIShI/iFRo7ZGG68LhMMoOTqwxo9Pp67pG8/D8c7uLfJ7tTGwC9t5r05kdXtCPq8hh4RFt6DNx3y0hgj4piU1HlS5IyqPEb1lCjuOA6yCDKnGQnPtzTyBoGIePiA6XyObGQkPE4kh2pEZC4JrLJkwoaDnHoG23foTs3ddE6/1lWVLLiGhSoXW4MbLO6fnNfd8x6cpFYbzJrzhYEw0/RCbL5Zx1rTsr9hegDro54zjqkrGgF24rVkOVhEQDEcMFP2cthd7uKZS9ELj50mDnHGaXLFLOOgkR4yKFR2eD5cPzpQoyXWUQb9tmrc2OUV04lplpD2SXjZFlyW53wXPPHDAxMkNw0i17pb6lMpDVRrNWYTi1Lf0kAFh+RLa27s+DQY92PJclREgT7Pqu7D6o8/k4rEfvZzkrzgkhjyIX6/UcPsxKCOxytEIqdxf0SUeT9PUYpbq7ovJxYFYXCKN0+x25P8O/8CRkGMClhtIbY8rKba3VdYjSrngQgmbRDpqU29adL9ekPGKja2SXna4zgijZmBsOSxXKz1e+5qLU3MtA1Pa0UELNuZDzPJFiOV+TDesvKVm2FhQkRMQGm+vhAYixiIRN7oLM6CFb2M8uNUf5WQlJh3L0YeSF4BzA1RxAHCwyQLcHBX7MOXj6IDipDYNVzt9hrfeoLc45HSnCerw+RlwpIUBy+3rdgD3c5WTyo3FYQxQcu+0xve0YY/L8M+GXHi3UyxT9oMLecSSx9YI91drIjGpTiEV6NJvkhFahdeefEiK5dPkrXiUgZZb7Sl+AOKS+HvspztdIKwe4yq2Tqt4ueiIJgarpWwqet/TD04lZdTXexqEXs3LMUM7ZpfkfZPawG7hSQvQSTM63Izmcba0glcG/iAnI5EGU9kzyn4g/oAn6jZCIllzNAam5fb065X0JOZWPFYE1exqfwcaSgor8tRJytr69Q74jTHWkpirv1YcEkU5/1A+PJETGZ+VdT8chtmze6l/69HKPRf56tvLa/uJbkHMtcjESV5h02bhi+rLR9FmRNRRFWdcVzXfOebWl/sy5PtEa/FRuBywSDBfGQ9Sf+mx/1gNAAuM4Dvgu2BSKyIS+DBIi7XW5XTC3rbPWIkgV6UGaC5Qmo/64RXaIIAUb5bOlr6IfKqkNZF2FmF0uaCOvYCoIIEwMvgD5EKZfrpdtmtGEyUoI+h2eSmr6sWZPpwS+fmykwVMQT8OoivbF4o2/CC/IfoEoIu8uTqe7ikBWCgb6VecjgHC1rPhdCSkE5c6HL74FSAzIr1j/IlYQ5R6ulu34ruEAZfezFvighGRN/6NxCMNXrk82o5CdAkK0VtMxw7RpEWgpXngjK24El1CO1F9/j/IVZDeS6ENIONEpy3NYmOhFkDUSgstkV7f3vuu6dPs7UlBSeFZCoLgyljAZrXoDrHyJ0Xs30j4st05HX3QeNOsnoXycLoIzp5M90Dn0wI8GslKw9RYLjeyGTh0xEKMZpdOxwtKeOzoRmzqi0YyIlkhr9ET4SYUKw9PU12C4a73BDn3tcsJIyVBGW/DtFk4UZg1H9GHqhaTgKF85P5zdUBs9Quo5jmNzEqKAfhB6FWcvrjykq103Ba5ecYj1u3tlobMR3o9wKyH6NYuyqSmVtzTn3zAOz+RlwBHRaTLs+IDhuPJdZMZhakcXI0dSSMwg6J+6HYglYBP88UJ3GprWvJcpqkPU6hpfLSV9jY1zruHMIHw+OYMilXwUmYS/juw3eglGDBsfmvdZ+Dc2fUW0/5dTMHA1q7lHyz2M4OgWPQ4kXxJx2x0YzcfrNRVR72uvXJNdyOutEWkAKmvvcO4sbRFeK5nWNk3/ZtH/IURE+v9DpDHoj5A+SI7LffZBv0jhPxQQGtrbNg6vjhCdr+mTtZsF1YF9158456KLj9z/mCCUj0CXe2ZZlqdOYZZIQgruewGtHxIFsdcvRrtCd6kEVxCnelqOfWGMwSuRzroNNRE65PN0U3sB/q+FhPxj3Pqm/2vgtBCCZjX7ca9AbGrbNu+93pzWALIj3nt9EvlNbqOXZeCWIaiIzR3vV+mkhBBC/nUkjAma9RURPOGdvXCIT0JIPqIfSC6+k8hEYEOa9qkgASWEEEJII5QQQgghjVBCCCGENEIJIYQQ0gglhBBCSCOUEEIIIY1QQgghhDRCCSGEENIIJYQQQkgjlBBCCCGNUEIIIYQ0QgkhhBDSCCWEEEJII5QQQgghjVBCCCGENEIJIYQQ0gglhBBCSCOUEEIIIY1QQgghhDRCCSGEENIIJYQQQkgjlBBCCCGNUEIIIYQ0Qgn525mmKYTQdq/3fp7n4zg+W6X/ZbZtW9f1t2tByN8CJeRvx1rrvcfP4zgex7Esi3sxz/MwDFci4Zyz1r4pIc4588Ja+05RP4m1VqrtnCtcue/7PM/7vteX7Jw7jsPlSL+REMKyLG81hpC/lWcSMk1T/Uwj77BtG0xS3/fTNPV9P89z3/f7vuNzXDaOY8E8DcOQLpmP43jk1jjnRMP+Rbz3ZQk5z3Pbtq7rbsf2PM8hhG3bxnE8zzN7vfd+GIbow2maCkpPyL/LAwlxztGF/zGO44DFgRdyHEff9zD9IiH4UG4R1RGwAI8YhqHrunoVeSohx3GYP5nnWf4aQhiGAQ5NZR3eLLBGQs7ztNbK8L6y9dbabdvOC/GQx2V9tXVdqSLkv0ethHjvp2n61qqQLJCQaZpENkRC1nXVoi6qA+SW8zxh+Np4KiHe+6ulxnEcXdehVsuydF1XY1LfLDCVkGwMCt0Fuq7LPlEHFQu1vQr3TdPESUT+Y9RKiLWWIawfQ2c7+r4fxxGGchzHYRjmeYZN1IvxiH3f+74Xe2qMaVaRBgm5uh7NkV+HYajxD94sMOuFFAYzgk7Z7tISgoyIzn/I464kBIL3T0cFCYmokpB937OzYlmWvu+NMYi5I0DcwL7v4zgaY7qum+d5mqbmaYZItDGm7/tlWdKodD2fat1xHPM8d11njEHq4tZuagMXQkAKRD4RL6RQjoRcgDHt+yY+KCF93+s6I6r23QVWBrIAxkwhkCU10V2KnW/yc2HTwTzPBeEn5J+jyrKs65pOwnmejTHw99d1Nca0Oen7vnddBy/nOA4IQJvHs20bAuXHcez7DiFpKOf8XOvO8xyGoe97mJ5pmqTYGkIIXddFK2ItIWn0H/uLotpqe/e0bxskZNs2bIiSKJNUQ7cFHfvdBdZLyG26oiAh8oiyhKzr+mO72r6+vn7mQeR/mSoJSRPp3ntjjN4L9Mgyaqy1OuQShSbqQZRA+wrW2ja7/8HWIacthh4lVxpxBOURnEEUC3XQ6fTUHm3bhg7U0TCdV++67lG3pBLi1DZfjeQkJOzpvdcSaIzRRaE3bivwZoGVElKT7o4kJMqjyOMKIlH+62ehhJAfoFFCpmnquk5+xdRtOAEHX0Eba2ttW8gIK1Bdh6jkej7VuvM8kcmQX2HBa25EGE0HPWTLkEjIeZ6SFwGIesFIaaH6yUAWvEn5dZ5nMZptEvJmgTUSsq5rjay+74Usy9IcEa1BywYlhPwAjYGsaL2PzTDRXYgmlUteliWyzl3XRXZ/33fsai0XhZyz/BpCSO1+IaquqWkdHlGuFeqgmzOOoy45hOAV8vm6rtH5j1PZL/25NlghhHmesybsJyUkQtenLZD1ZoG3ErIsS6VbVpAQqVJZQoZh+L5jhl9fX5QQ8sM0ptOjE7+y8hXWdY3C1lkQEtF36XVlCMFaOwwDEiTlPUXWWl0HZB2iByFoFmWnU25bd74WvGXbGl0DlytShWEYUPPUijnn9LYfSahoCUGS4DzP4zjQP78uIdu26W9Kani2ptPfLLAsIdM01dv0QiCrRkLgWVYeDUGUEoO25pavhLo2EfIWjZt6tSnEIj2yjIjIP5IQyaXLX9d1lekdKUS2hno9jhS9/BXL8/N1Tq1sNcqtk6oOw/BIQqBq+pbyOYOyF4KQSFq3X5eQ6Oifzu3rza9n9abeNwu8khAsjB6luPT3FYU6b3dkYVFVHw5dlgWjNDr9U4DKQX6exqOFsjBf1xU7VmFooth9NHXTtxWJ24E1F/ZBHceRvkklylimHgASGHh7BxIqkL0o9AwJkZkcuUGVrcNB6FQPItuh3Q7UH7csywKjABPmvc96RbeBrKxxrJGQR5LwVELQUiyckf2W2wsnAdHP2X5oK1A3Nl0BwG/Ytu3Rayi1hFzdle1/vJzmUTpNlENGSw2UEPLDPHvBicwfvFNIZi9OdUSzsUZCztfr8GCUYSAkYiPgJRZSeFZCcJgOu2/xLkIUK1Zp33cc79BRkayElFsnBztQB7ELWT8J5fd9v20b3keikz3QOfRAWyArBSYsetmJjrpAp+s3ZTXkQpxzOAeDhus/Xb2PBLW6aldDgUIkIfgWpPlYcGBXgv8T9OGyLDLw2k6nhxBEAh/xKJBFyK/wLL7x6Ix6JCGQh4YDH5jkehZVxtAjsCVfzqBIJR8d9cKWJ5gYBMSwgxbL4eYT4NlNX7deyFVR6K5P2R33U2/qjY5Dvl9atNtYSPdBYG2B1JTephylLm4Dj+M4an0i5D/PN77sPZKQq0ViGa0fsPsIYT+1j+u6yi0SMUec6mk59oUxBq8bOc9znuenB0f0G3MRXovM07ZtusdE9pZlKZjaymMQfxvZMy5/G7fvhBf9/rEqEfK7fIuE4IXY2Bpbsx/3CsSmtm1DVOGdDfXIjnjvkdX8yCuHC4GXGuCWIReCl1+9X6V/l3Ecm/9nLULIb/EtEoLDX0KzacCxZOGdlwvhtR8Qko/oB7aWvrNwxvtipWlcuhJC/jn4vxYSQghphBJCCCGkEUoIIYSQRighhBBCGqGEEEIIaYQSQgghpBFKCCGEkEYoIYQQQhr5P0645Ujty4zGAAAAAElFTkSuQmCC" alt="" />
Output
aaarticlea/png;base64,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" alt="" />
Sample Input
Sample Output
题解:
a1*x13+a2*x23+a3*x33+a4*x43+a5*x53 = 0
<==> a1*x13+a2*x23+a3*x33 = -1*(a4*x43+a5*x53)
可以想办法利用三重循环枚举x1,x2,x3,算出a1*x1^3+a2*x2^3+a3*x^3得到的所有的100*100*100个值,先储存起来,假设存在a[ ]数组里。然后利用两重循环枚举x4,x5,逐个算出-1*(a4*x4^3+a5*x5^3)的所有值,如果这个值也存在于a[ ]中,就代表找到一组可行解,答案+1。
现在的问题就变成了如何快速的查找a[ ]中的值,如果从头到尾扫一遍,那时间复杂度和直接五重循环枚举没有什么区别。
这个问题可以用哈希表优化,先不解释哈希表是什么。先考虑如下问题:
如果要存储和查找线性表(1,75,324,43,1353,90,46),有两种基本的思路:一种是定义一个数组A[10],把它们依次存入,但是这会给查找操作带来O(n)的时间复杂度,当数字非常多时,效率也许不可接受;第二种方法是定义数组A[2000],把这几个数字作为下标,即A[1]=1,A[75]=1,A[324]=1,A[43]=1,A[1353]=1,A[90]=1,A[46]=1,这样查找有没有x时只需判断A[x]是否等于1就可以了时间复杂度O(1),但是这种方法的问题也很大,就是空间浪费多,空间复杂度高。
现在考虑优化第二种方法,假设我们设计函数h(x) = x mod 1235789 ,把原来的A[x]=1的操作变成A[ h(x) ] = 1 ,这样一来把数组大小设置为1235789就可以了。这样做也存在一定的问题: a != b 但 h(a) = h(b) = val 的情况是肯定存在的。问题也好解决,假设有m个数的h( )值都等于val,不妨把这m个值都用邻接表存起来(大致相当于A数组变成二维数组,只是第二维长度不定,m个数都存在A[ val ][ ]里 ),当要找q在不在A里时,就在A[ h(q) ][ ]里找,这个查找量比在所有数字中找要小的太多太多了,因为第二维会很短,毕竟h(a)=h(b)的情况并不多。
看懂了上述问题及分析也就知道了这个题怎么做,a1*x1^3+a2*x2^3+a3*x^3得到的所有的100*100*100个值就相当于上面1,75,324那7个值,逐个算出的 -1*(a4*x4^3+a5*x5^3)的所有值就相当于要查找的q,把答案统计出来即可。
注意:负数取模存在问题,而a1*x1^3+a2*x2^3+a3*x^3 与 (a4*x4^3+a5*x5^3)要想成为一组解,肯定互为相反数,不妨用unsigned long long 或 unsigned int类型再取模。
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
typedef unsigned long long ULL;
const int mod = ;
struct A {
ULL val;
int next;
}a[];
int cnt, head[mod];
int a1, a2, a3, a4, a5, a6, ANS;
inline ULL calc(int x,int y) {
return x*y*y*y;
}
inline void insert(int x, int y, int z) {
ULL tmp1 = calc(a1, x) + calc(a2, y) + calc(a3, z);
int tmp2 = int(tmp1 % (ULL)mod);
a[++cnt].val = tmp1;
a[cnt].next = head[tmp2];
head[tmp2] = cnt;
}
inline int ser(int x, int y) {
ULL tmp1 = - * (calc(a4, x) + calc(a5, y));
int tmp2 = int(tmp1 % (ULL)mod);
int ans = ;
for (int i = head[tmp2]; i != -; i = a[i].next) {
if (a[i].val == tmp1) ans++;
}
return ans;
}
int main() {
while (cin >> a1 >> a2 >> a3 >> a4 >> a5) {
cnt = ;
for (int i = ; i < mod; i++) head[i] = -;
for (int i = -; i <= ; i++) {
for (int j = -; j <= ; j++) {
for (int k = -; k <= ; k++) {
if (i != && j != && k != ) {
insert(i, j, k);
}
}
}
}
ANS = ;
for (int i = -; i <= ; i++) {
for (int j = -; j <= ; j++) {
if (i != && j != ) {
ANS += ser(i, j);
}
}
}
cout << ANS << endl;
}
return ;
}
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