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动态规划 (Dynamic Programming)

动态规划 (Dynamic Programming). 1. 什么是动态规划？. Fibonacci 序列. Fibonacci 序列被定义如下： F(n) = F(n - 1) + F(n - 2), n ≥ 3 F(2) = 1 F(1) = 1 问题：如何计算第 n 个 Fibonacci 数 F(n)?. F(1) = 1 F(2) = 1 F(n) = F(n - 1) + F(n - 2), n ≥ 3. F (n) if (n == 1) return 1; if (n == 2) return 1;

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动态规划 (Dynamic Programming)

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  1. 动态规划(Dynamic Programming)

  2. 1. 什么是动态规划？

  3. Fibonacci序列 Fibonacci序列被定义如下： • F(n) = F(n - 1) + F(n - 2), n≥ 3 • F(2) = 1 • F(1) = 1 问题：如何计算第n个Fibonacci数F(n)?

  4. F(1) = 1 F(2) = 1 F(n) = F(n - 1) + F(n - 2), n≥ 3 F(n) if (n == 1) return 1; if (n == 2) return 1; return F(n - 1) + F(n - 2); 算法1

  5. F(n) if (n == 1) return 1; if (n == 2) return 1; return F(n - 1) + F(n - 2); 算法1的效率

  6. F(n) if (n == 1) return 1; if (n == 2) return 1; return F(n - 1) + F(n - 2); 目标：计算F(100)。 问题：在计算F(100)的过程中， F(99)被调用(计算)多少次？ F(98)被计算多少次? … … F(3)被计算多少次? 算法1的效率

  7. F(100)的执行过程 … …

  8. 算法2 F(n) Fib[1] = 1; Fib[2] = 1; for i = 3 to n Fib[i] = Fib[i – 1] + Fib[i – 2]; return Fib[n]; Fib[1..n]是一维数组, 用Fib[i]来存储F(i)的值。

  9. 算法1 vs 算法2

  10. 什么是动态规划？ • 对于有些问题，解决该问题的过程中需要重复解决该问题的子问题。 • 动态规划是一种解决此类问题的方法。其核心思想是：“重用子问题的计算结果，避免重复计算”。

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