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Leetcode skimming -- drip record 016

2022-07-21 05:01:00 【Robust least squares support vector machine】

16. The finger of the sword Offer 10-I. Fibonacci sequence

requirement

Write a function , Input n , Fibonacci, please （Fibonacci） The number of the sequence n term （ namely F(N)）. The Fibonacci series is composed of 0 and 1 Start , The Fibonacci number after that is the sum of the two numbers before . The answer needs to be modelled 1e9+7（1000000007）, If the initial result of calculation is ：1000000008, Please return 1.

Ideas

Dynamic programming method ：

State definition ： set up dp It's a one-dimensional array , among dp[i] The value of represents Fibonacci number one i A digital
Transfer equation ： dp[i] = dp[i - 1] + dp[i - 2], That is, the definition of the corresponding sequence f(n) = f(n - 1) + f(n - 2)
The initial state ： dp[0] = 0, dp[1] = 1, That is, initialize the first two numbers
Return value ： dp[n], That is, the second of the Fibonacci sequence n A digital

Problem solving

#include <iostream>
using namespace std;
#include <vector>

class Solution {
    
public:
    int fib(int n) {
    
        if (n == 0) {
    
            return 0;    //  If you ask  f(0)  Then return directly  0 , initialization  f(0)
        }
        vector<int> dp(n + 1, 0);  //  initialization  dp  list 
        dp[1] = 1;                 //  initialization  f(1)
        for (int i = 2; i <= n; i++) {
    
            dp[i] = (dp[i-1] + dp[i-2]) % 1000000007;  //  State transition calculation  f(2), f(3), ..., f(n) 
        }
        return dp[n];  //  return f[n]
    }
};

void test01()
{
    
    Solution s;
    for (int i = 0; i < 10; i++) {
    
        int f = s.fib(i);
        cout << f << " ";
    }
    cout << endl;

}

int main()
{
    
    test01();

    system("pause");
    return 0;
}