LC 1414. Find the Minimum Number of Fibonacci Numbers Whose Sum Is K

link

class Solution {
public:
    int findMinFibonacciNumbers(int k) {
        vector<int> fibo;
        fibo.push_back(1);
        fibo.push_back(1);
        while(true){
            int i=fibo[fibo.size()-1]+fibo[fibo.size()-2];
            if(i>k) break;
            fibo.push_back(i);
        }
        int res=0;
        while(k>0){
            res++;
            int cur=search(k,fibo);
            k-=fibo[cur];
        }
        return res;
    }
    
    int search(int sum, vector<int>& fibo){
        int left=0;
        int right=fibo.size()-1;
        while(left<=right){
            int mid=(left+right)/2;
            if(fibo[mid]<=sum) left=mid+1;
            else right=mid-1;
        }
        return right;
    }
};

证明：

https://proofwiki.org/wiki/Zeckendorf%27s_Theorem

https://proofwiki.org/wiki/Sum_of_Non-Consecutive_Fibonacci_Numbers