How to use dynamic programming algorithms in C++

How to use the dynamic programming algorithm in C

Dynamic programming is a common algorithm design technique that decomposes the problem into a series of sub-problems and uses the sub-problems to to gradually construct a solution to the problem. In C, we can use dynamic programming algorithms to solve various complex problems. This article describes how to use dynamic programming algorithms in C and provides specific code examples.

1. Basic principles of dynamic programming

The basic principle of dynamic programming algorithm is to use overlapping subproblems and optimal substructures. We first decompose the problem into several sub-problems, solve the sub-problems through recursion, and save the solutions to the sub-problems. When we need to solve a certain sub-problem, we can directly use the saved solution to the sub-problem without recalculation. This avoids repeated calculations and improves the efficiency of the algorithm.

Dynamic programming algorithms generally include the following steps:

1. Define the state of the problem: abstract the problem into a state and determine the representation method of the state.
2. Find the relationship between states: determine the transition equation between states, that is, how to solve the new state from the known state.
3. Define the initial state: Determine the value of the initial state, which is usually the solution in the simplest case.
4. Recursive solution: Use the recursive method of dynamic programming to gradually solve new states based on the known states until the optimal solution to the problem is obtained.

2. Specific code examples

The following takes solving the Fibonacci sequence as an example to demonstrate how to use the dynamic programming algorithm.

Requirement: Given an integer n, find the nth number in the Fibonacci sequence.

1. Define the state of the problem: Abstract the problem into a state F(n), which represents the nth number of the Fibonacci sequence.
2. Find the relationship between states: According to the definition of Fibonacci sequence, the nth number is equal to the sum of the first two numbers, that is, F(n) = F(n-1) F(n- 2).
3. Define the initial state: Determine the value of the initial state. For the Fibonacci sequence, the simplest case is F(0) = 0, F(1) = 1.
4. Recursive solution: Use the recursive method of dynamic programming to gradually solve the new state based on the known state. The code is as follows:

#include <iostream>
using namespace std;

int fibonacci(int n){
    int* fib = new int[n+1];
    fib[0]=0;
    fib[1]=1;
    for(int i=2;i<=n;i++){
        fib[i] = fib[i-1] + fib[i-2];
    }
    return fib[n];
}

int main(){
    int n;
    cout << "请输入整数n：";
    cin >> n;
    cout << "斐波那契数列的第" << n << "个数是：" << fibonacci(n) << endl;
    return 0;
}

The above code defines a fibonacci function, which is used to solve the nth number of the Fibonacci sequence. In the main function, first read in the integer n, then call the fibonacci function to get the result and output it. Run the program, input n=10, and the output is:

请输入整数n：10
斐波那契数列的第10个数是：55

3. Summary

This article introduces how to use the dynamic programming algorithm in C, and provides solutions for solving the Fibonacci sequence specific code examples. Dynamic programming algorithm is a very practical algorithm technology that can solve various complex problems. We hope that through the introduction of this article, readers can have a deeper understanding of dynamic programming algorithms and further improve their programming abilities.

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