分治法

一.快排

二.归并

三.钢条切割

#include<iostream>
using namespace std;

#define max(a,b) (((a) > (b)) ? (a) : (b))

int Cut_Rod(int A[], int length)
{
    if (A == NULL || length <= 0)
    {
        return 0;
    }
    if (length == 1)
    {
        return A[1];
    }
    int q = -1;
    for (int i = 2; i <= length; i++)
    {
        q = max(q, A[i - 1] + Cut_Rod(A, length - i));
    }
    return q;
}

int main()
{
    int A[] = { 1, 5, 8, 9, 10, 17, 17, 20, 24, 30};

    cout << Cut_Rod(A, 10) << endl; // 30
    return 0;
}

四.矩阵链乘法

#include<iostream>
using namespace std;

inline int  min(int a, int b)
{
    if (a > b)
    {
        return b;
    }
    else
    {
        return a;
    }
}

int Matrix_Chain_Order(int matrix[], int low, int high)
{
    int q;
    if (low == high)
    {
        return 0;
    }

    else if (low < high)
    {
        for (int i = low; i <= high - 1; i++)
        {
            if (i == low)
            {
                q = Matrix_Chain_Order(matrix, low, i) + Matrix_Chain_Order(matrix, i + 1, high) + matrix[low * 2 - 2] * matrix[i * 2 - 1] * matrix[high * 2 - 1];
            }
            else
            {
                q = min(q, Matrix_Chain_Order(matrix, low, i) + Matrix_Chain_Order(matrix, i + 1, high) + matrix[low * 2 - 2] * matrix[i * 2 - 1] * matrix[high * 2 - 1]);
            }
        }
    }
    return q;
}

int main()
{
    int A[] = { 30, 35, 35, 15, 15, 5, 5, 10, 10, 20, 20, 25};
    cout << Matrix_Chain_Order(A, 1, 6); //15125
    cout << endl;
    return 0;
}

五.LCS

#include<iostream>
using namespace std;

int max(int a, int b)
{
    if (a > b)
    {
        return a;
    }
    else
    {
        return b;
    }
}

int LCS(char x[], char y[], int i, int j)
{
    if (x == NULL || y == NULL || i <= 0 || j <= 0)
    {
        return 0;
    }
    if (x[i - 1] == y[j - 1])
    {
        return LCS(x, y, i - 1, j - 1) + 1;
    }
    else
    {
        return max(LCS(x, y, i - 1, j), LCS(x, y, i, j - 1));
    }
}

int main()
{
    char x[] = "BDCABA";
    char y[] = "ABCBDAB";
    cout << LCS(x, y, 6, 7) << endl; //4
    return 0;
}