1.链接地址:
http://bailian.openjudge.cn/practice/2810/
http://bailian.openjudge.cn/practice/1543/
http://poj.org/problem?id=1543
2.题目:
Perfect Cubes
Time Limit: 1000MS Memory Limit: 10000K Total Submissions: 13190 Accepted: 6995 Description
For hundreds of years Fermat's Last Theorem, which stated simply that for n > 2 there exist no integers a, b, c > 1 such that a^n = b^n + c^n, has remained elusively unproven. (A recent proof is believed to be correct, though it is still undergoing scrutiny.) It is possible, however, to find integers greater than 1 that satisfy the "perfect cube" equation a^3 = b^3 + c^3 + d^3 (e.g. a quick calculation will show that the equation 12^3 = 6^3 + 8^3 + 10^3 is indeed true). This problem requires that you write a program to find all sets of numbers {a,b,c,d} which satisfy this equation for a <= N.Input
One integer N (N <= 100).Output
The output should be listed as shown below, one perfect cube per line, in non-decreasing order of a (i.e. the lines should be sorted by their a values). The values of b, c, and d should also be listed in non-decreasing order on the line itself. There do exist several values of a which can be produced from multiple distinct sets of b, c, and d triples. In these cases, the triples with the smaller b values should be listed first.Sample Input
24Sample Output
Cube = 6, Triple = (3,4,5) Cube = 12, Triple = (6,8,10) Cube = 18, Triple = (2,12,16) Cube = 18, Triple = (9,12,15) Cube = 19, Triple = (3,10,18) Cube = 20, Triple = (7,14,17) Cube = 24, Triple = (12,16,20)Source
3.思路:
枚举+打表(减少计算次数)
注意a要升序排列,然后b,c,d再升序排列
4.代码:
1 #include <iostream> 2 #include <cstdio> 3 4 #define START_N 2 5 6 using namespace std; 7 8 int main() 9 { 10 int n; 11 cin>>n; 12 13 int *arr_cube = new int[n]; 14 15 int i,j,k,p; 16 for(i = START_N; i <= n; ++i) 17 { 18 arr_cube[i - START_N] = i * i * i; 19 for(j = START_N; j <= i; ++j) 20 { 21 for(k = j; k <= i; ++k) 22 { 23 for(p = k; p <= i; ++p) 24 { 25 if(arr_cube[i - START_N] == arr_cube[j - START_N] 26 + arr_cube[k - START_N] + arr_cube[p - START_N]) 27 { 28 cout<<"Cube = "<<i<<", Triple = ("<<j<<","<<k<<","<<p<<")"<<endl; 29 } 30 } 31 } 32 } 33 34 } 35 36 37 delete [] arr_cube; 38 return 0; 39 }