题意：给定fibonacci数列，输入前缀，求出下标。题目中fibonacci数量达到100000，而题目输入的前缀顶多为40位数字，这说明我们只需要精确计算fibinacci数前40位即可。查询时使用字典树。在计算时，为了保证前40位精确无误。在此我计算了前60位。以保证前面不在进位。
注意点：
1）关于表示进位问题，需要控制计算的数位数在60以内，切记计算时不要错位（相同位要对齐）。
2）坑点：题目给出的数插入字典树最好插入前40位即可，否则MLE.
3）坑点：题目只要求计算下标不超过100000，计算到100000或者以上均会WA，因为输出值不是-1
下面是数组的AC代码：824ms
#define _CRT_SECURE_NO_DEPRECATE
#include<iostream>
#include<string>
#include<map>
#include<fstream>
#include<ctime>
#include<queue>
#include<vector>
#include<numeric>
#include<string.h>
#include<iomanip>
#include<sstream>
#include<algorithm>
using namespace std;
typedef pair<int,int> PII;
typedef vector<int> BigInterger;
const int maxn = 100000;
const int maxsize = 10;
const int maxnum =65;
struct TrieNode{
TrieNode(int d = -1) :id(d){ memset(next, NULL, sizeof(next)); }
int id;
TrieNode*next[maxsize];
};
TrieNode*T = new TrieNode;
void insert(char*str,const int&index){
int len = strlen(str);
TrieNode*p = T;
int t = 0;
for (int i = len-1; i>=0&&t<40;i--,t++){
int id =str[i]-'0';
if (!p->next[id])p->next[id] = new TrieNode(index);
p = p->next[id];
}
}
int search(char*str){
TrieNode*p = T;
while (*str != ' '){
int id = *str++ - '0';
if (!p->next[id])return -1;
p = p->next[id];
}
return p->id;
}
void init(){
char f[3][maxnum];
f[1][0] ='1'; f[1][1] = ' ';
f[0][0] ='1'; f[0][1] = ' ';
insert("1", 0);
for (int i = 2; i<maxn; i++){
int g = 0,j=0,cnt = 0, x;
int r1 = (i - 1) % 3, r2 = (i - 2) % 3, r = i % 3;
int lena = strlen(f[r1]);
int lenb = strlen(f[r2]);
if (lena >= maxnum - 5){
memcpy(f[r1], f[r1]+1, lena - 1); f[r1][lena - 1] = ' ';
memcpy(f[r2], f[r2]+1, lenb - 1); f[r2][lenb - 1] = ' ';
lena--, lenb--;
}
while (g || j < lena||j<lenb){
x = g;
if (j < lena)x += f[r1][j]-'0';
if (j < lenb)x += f[r2][j]-'0';
f[r][cnt++] = x % 10+'0';
g = x / 10;
j++;
}
f[r][cnt] = ' ';
insert(f[r], i);
}
}
int main(){
init();
int T,kase=1;
char str[50];
scanf("%d", &T);
while(T--){
scanf("%s", str);
printf("Case #%d: %d
",kase++,search(str));
}
return 0;
}
采用向量AC的代码624ms(传值要用引用，否则多了不必要的复制)：
#define _CRT_SECURE_NO_DEPRECATE
#include<iostream>
#include<string>
#include<map>
#include<fstream>
#include<ctime>
#include<queue>
#include<vector>
#include<numeric>
#include<string.h>
#include<iomanip>
#include<sstream>
#include<algorithm>
using namespace std;
typedef pair<int,int> PII;
typedef vector<int> BigInterger;
const int maxn = 100000;
const int maxsize = 10;
const int maxnum =65;
struct TrieNode{
TrieNode(int d = -1) :id(d){ memset(next, NULL, sizeof(next)); }
int id;
TrieNode*next[maxsize];
};
TrieNode*T = new TrieNode;
void insert(const BigInterger&v,const int&index){
int len=v.size();
TrieNode*p = T;
int t = 0;
for (int i = len-1; i>=0&&t<40;i--,t++){
int id =v[i];
if (!p->next[id])p->next[id] = new TrieNode(index);
p = p->next[id];
}
}
int search(char*str){
TrieNode*p = T;
while (*str != ' '){
int id = *str++ - '0';
if (!p->next[id])return -1;
p = p->next[id];
}
return p->id;
}
//引用传值，避免赋值，效率更高
void add(BigInterger &a, BigInterger &b, BigInterger&c){
int lena = a.size(), lenb = b.size();
int g=0, x,i=0;
c.clear();
if (lena > maxnum - 5 || lenb > maxnum - 5){
a.erase(a.begin()), b.erase(b.begin());
lena--, lenb--;
}
while (g || i < lena || i < lenb){
x = g;
if (i < lena)x += a[i];
if (i < lenb)x += b[i];
c.push_back(x % 10);
g = x / 10;
i++;
}
}
void init(){
BigInterger a[3];
a[0].push_back(1);
a[1].push_back(1);
insert(a[1], 0);
for (int i = 2; i<maxn; i++){
add(a[(i - 1) % 3], a[(i - 2) % 3], a[i % 3]);
insert(a[i % 3], i);
}
}
int main(){
init();
int T,kase=1;
char str[50];
scanf("%d", &T);
while(T--){
scanf("%s", str);
printf("Case #%d: %d
",kase++,search(str));
}
return 0;
}