BestCoder Round #71 (div.2) (hdu 5620 菲波那切数列变形)
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KK‘s Steel
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 350 Accepted Submission(s): 166
Problem Description
Our lovely KK has a difficult mathematical problem:he has a N(1≤N≤1018) meters steel,he will cut it into steels as many as possible,and he doesn‘t want any two of them be the same length or any three of them can form a triangle.
Input
The first line of the input file contains an integer T(1≤T≤10), which indicates the number of test cases.
Each test case contains one line including a integer N(1≤N≤1018),indicating the length of the steel.
Each test case contains one line including a integer N(1≤N≤1018),indicating the length of the steel.
Output
For each test case, output one line, an integer represent the maxiumum number of steels he can cut it into.
Sample Input
1
6
Sample Output
3
Hint
1+2+3=6 but 1+2=3 They are all different and cannot make a triangle.要求:给一个长整形数n让你把n分成若干份,1、任意两份长度不能相等 2、任意三分不能组成三角形
分析:因为斐波那契数列中的数满足此要求,所以从这个方面入手,只要分成的数满足a+b<=c即可,所以我们在数列1 2 3 5 8 13 21 ......的数中选取,如果前i项的和等于n输出i如果前i项的和大于n输出i-1
#include<stdio.h> #include<string.h> #include<stdlib.h> #include<algorithm> #define MAX 100100 #define INF 0x3f3f3f #define LL long long using namespace std; LL fb[10010]; LL f[1001]; void biao() { LL i,j; fb[1]=1; fb[2]=2; for(i=3;i<120;i++) fb[i]=fb[i-1]+fb[i-2]; f[1]=fb[1]; for(i=2;i<120;i++) f[i]=f[i-1]+fb[i]; } int main() { int t,i,j; LL n; biao(); scanf("%d",&t); while(t--) { scanf("%lld",&n); for(i=1;i<120;i++) { if(n==f[i]) { printf("%d\n",i); break; } if(n<f[i]) { printf("%d\n",i-1); break; } } } return 0; }
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