POJ 1543 Perfect Cubes(我的水题之路——四重暴力水)
2012-01-30 18:31
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Perfect Cubes
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
Sample Output
Source
Mid-Central USA 1995
要求寻找N(N<=100)以下的,a^3=b^3+c^3+d^3的所有组合。要求按照以a为升序输出,同时,(b,c,d)中必须有b<=c<=d
四重暴力,不解释。
注意点:
1)如果四重暴力时候,上限均取为100,那么在查找数组的时候,循环条件如果是A<=N,必须考虑到N=100的情况
代码(1AC):
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 10707 | Accepted: 5739 |
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
24
Sample 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
Mid-Central USA 1995
要求寻找N(N<=100)以下的,a^3=b^3+c^3+d^3的所有组合。要求按照以a为升序输出,同时,(b,c,d)中必须有b<=c<=d
四重暴力,不解释。
注意点:
1)如果四重暴力时候,上限均取为100,那么在查找数组的时候,循环条件如果是A<=N,必须考虑到N=100的情况
代码(1AC):
#include <cstdio> #include <cstdlib> int answer[100][4]; int top = 0; void initsolve(){ int i, j; int a, b, c, d; for (a = 2; a <= 100; a++){ for (b = 2; b <= 100; b++){ for (c = b; c <= 100; c++){ for (d = c; d <= 100; d++){ if (a * a * a == b * b * b + c * c * c + d * d * d){ answer[top][0] = a; answer[top][1] = b; answer[top][2] = c; answer[top][3] = d; top++; //printf("a=%d, b=%d, c=%d, d=%d\n", a, b, c, d); } } } } } } int main(void){ int N; int i; initsolve(); while (scanf("%d", &N) != EOF){ for (i = 0; i < top && answer[i][0] <= N; i++){ printf("Cube = %d, Triple = (%d,%d,%d)\n", answer[i][0], answer[i][1], answer[i][2], answer[i][3]); } } return 0; }
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