The 29th day of force deduction (DP topic)

problem Ⅰ

509. Fibonacci Number
The Fibonacci numbers, commonly denoted F(n) form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,

F(0) = 0, F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n > 1.
Given n, calculate F(n).

Example 1:

Input: n = 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.

Example 2:

Input: n = 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.

Example 3:

Input: n = 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.

solution DP

class Solution {
    
public:
    int fib(int n) {
    
        if(!n)return 0;
        if(n==1)return 1;
        int st = 0, nd = 1;
        n--;
        while(n--){
    
            int tmp = nd;
            nd = st + nd;
            st = tmp;
        }
        return nd;
    }
};

NOTE:
this probem’s difficulty is easy, my solution use two temporary variables to store the status of DP

problem Ⅱ

1137. N-th Tribonacci Number
The Tribonacci sequence Tn is defined as follows:

T0 = 0, T1 = 1, T2 = 1, and Tn+3 = Tn + Tn+1 + Tn+2 for n >= 0.

Given n, return the value of Tn.

Example 1:

Input: n = 4
Output: 4
Explanation:
T_3 = 0 + 1 + 1 = 2
T_4 = 1 + 1 + 2 = 4

Example 2:

Input: n = 25
Output: 1389537

solution 1 DP

class Solution {
    
public:
    int tribonacci(int n) {
    
        if(!n)return 0;
        if(n==1 || n==2)return 1;
        int st=0, nd=1, rd=1;
        n -= 2;
        while(n--){
    
            int sum = st+nd+rd;
            st = nd;
            nd = rd;
            rd = sum;
        }
        return rd;
    }
};

solution 2 short code

class Solution {
    
public:
    int tribonacci(int n) {
    
        int dp[3] = {
    0, 1, 1};
        for(int i=3; i<=n; ++i)
            dp[i%3] += dp[(i+1)%3] + dp[(i+2)%3];
        return dp[n%3];
    }
};

problem Ⅲ

746. Min Cost Climbing Stairs
You are given an integer array cost where cost[i] is the cost of ith step on a staircase. Once you pay the cost, you can either climb one or two steps.

You can either start from the step with index 0, or the step with index 1.

Return the minimum cost to reach the top of the floor.

Example 1:

Input: cost = [10,15,20]
Output: 15
Explanation: You will start at index 1.
- Pay 15 and climb two steps to reach the top.
The total cost is 15.

Example 2:

Input: cost = [1,100,1,1,1,100,1,1,100,1]
Output: 6
Explanation: You will start at index 0.
- Pay 1 and climb two steps to reach index 2.
- Pay 1 and climb two steps to reach index 4.
- Pay 1 and climb two steps to reach index 6.
- Pay 1 and climb one step to reach index 7.
- Pay 1 and climb two steps to reach index 9.
- Pay 1 and climb one step to reach the top.
The total cost is 6.

solution

class Solution {
    
public:
    int minCostClimbingStairs(vector<int>& cost) {
    
        int n = cost.size();
        for(int i=2; i<n; i++)
            cost[i] += min(cost[i-1], cost[i-2]);
        return min(cost[n-1], cost[n-2]);
    }
};