齐肯多夫定理

tw — Tue, 18 Jan 2011 07:42:00 GMT

/*
齐肯多夫定理表示��M��正整数都可以表示成若�q�个不连�l�的斐�L那契��C��和。这�U�和式称为齐肯多夫表�q�法�?br>对于��M��正整敎ͼ�光��肯多夫表�q�法都可以用贪心��法选出每回最大可能的斐�L那契数�?br>*/
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
#define ull unsigned long long
#define ll long long
#define N 100
ll fab[N], out[N];
int fn;
void init(){
int i;
ull inf = 0x7fffffffffffffff;
ull a;
fab[0] = 1;
fab[1] = 2;
for(i = 2; ; i++){
  a = fab[i-1] + fab[i-2];
  if(a > inf) break;
  fab[i] = a;
}
fn = i;
}
int find(ll* fab, int l, int r, ll k){
int mid;
while(l <= r){
  mid = (l + r) >> 1;
  if(fab[mid] <= k) l = mid + 1;
  else r = mid - 1;
}
return l - 1;
}
void Zeckendorf(ll a){
if(a <= 0){
  printf("%lld=%lld\n", a, a);
  return;
}
ll a0 = a;
int k = 0, i;
while(a0 > 0){
  i = find(fab, 0, fn - 1, a0);
  out[k++] = fab[i];
  a0 -= fab[i];
}
printf("%lld=", a);
for(i = 0; i < k-1; i++) printf("%lld+", out[i]);
printf("%lld\n", out[i]);
}
int main(){
#ifndef ONLINE_JUDGE
//freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif
init();
ll a;
while(~scanf("%lld", &a)){
  Zeckendorf(a);
}
return 0;
}

tw 2011-01-18 15:42 发表评论

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齐肯多夫定理