Eqs
Time Limit: 5000MS | Memory Limit: 65536K | |
Total Submissions: 14093 | Accepted: 6927 |
Description
Consider equations having the following form:
a1x13+ a2x23+ a3x33+ a4x43+ a5x53=0
The coefficients are given integers from the interval [-50,50].
It is consider a solution a system (x1, x2, x3, x4, x5) that verifies the equation, xi∈[-50,50], xi != 0, any i∈{1,2,3,4,5}.
Determine how many solutions satisfy the given equation.
a1x13+ a2x23+ a3x33+ a4x43+ a5x53=0
The coefficients are given integers from the interval [-50,50].
It is consider a solution a system (x1, x2, x3, x4, x5) that verifies the equation, xi∈[-50,50], xi != 0, any i∈{1,2,3,4,5}.
Determine how many solutions satisfy the given equation.
Input
The only line of input contains the 5 coefficients a1, a2, a3, a4, a5, separated by blanks.
Output
The output will contain on the first line the number of the solutions for the given equation.
Sample Input
37 29 41 43 47
Sample Output
654
Source
#include<iostream> 49664K 610MS #include<cstdio> #include<cstring> using namespace std; short hash[25000001]; //hash[sum]表示值等于sum的的解的个数(多对1映射) int main() //用int会MLE<span id="transmark"></span> { int a1,a2,a3,a4,a5; //系数 scanf("%d%d%d%d%d",&a1,&a2,&a3,&a4,&a5); { memset(hash,0,sizeof(hash)); for(int x1=-50; x1<=50; x1++) { if(!x1) continue; for(int x2=-50; x2<=50; x2++) { if(!x2) continue; int sum=(a1*x1*x1*x1+a2*x2*x2*x2); if(sum<0) sum+=25000000; hash[sum]++; } } int num=0; for(int x3=-50; x3<=50; x3++) { if(!x3) continue; for(int x4=-50; x4<=50; x4++) { if(!x4) continue; for(int x5=-50; x5<=50; x5++) { if(!x5) continue; int sum=a3*x3*x3*x3+a4*x4*x4*x4+a5*x5*x5*x5; if(sum>12500000||sum<-12500000) //防止特殊情况发生 continue; if(sum<0) sum+=25000000; if(hash[sum]) num+=hash[sum]; } } } cout<<num<<endl; } return 0; }
#include<iostream> // 1164K 1704MS #include<cstdio> #include<map> using namespace std; int main() { map<int,int>Q; int a,b,c,d,e; scanf("%d%d%d%d%d",&a,&b,&c,&d,&e); Q.clear(); for(int i=-50; i<=50; i++) { if(!i) continue; for(int j=-50; j<=50; j++) { if(!j) continue; int sum=a*i*i*i+b*j*j*j; Q[-sum]++; } } int num=0; for(int i=-50;i<=50;i++) { if(!i) continue; for(int j=-50;j<=50;j++) { if(!j) continue; for(int k=-50;k<=50;k++) { if(!k) continue; int sum=c*i*i*i+d*j*j*j+e*k*k*k; if(Q.count(sum)) num+=Q[sum]; } } } printf("%d ",num); }