动态规划

1.求最长公共子串

#pragma once

#pragma once

#include <random>
#include <iostream>
#include <tchar.h>
#include <bitset>
#include <cassert>
#include <crtdbg.h>
using namespace std;

//-----------------------------------------------
//a:97 z:122 A:65 Z:90
//生成随机字符串
//-----------------------------------------------
void CreateStr(string& str,int len)
{
    random_device rv;
    char* buffer = new char(len);
    assert(sizeof(buffer) > 0);
    for (int i = 0; i < len; ++i) {
        int ascii = 0;
        if (rv() % 2) {
            ascii = rv() % 25 + 97;
        } else { //大写
            ascii = rv() % 25 + 65; 
        }
        buffer[i] = ascii;
    }
    buffer[len] = '\0';
    str = buffer;
    cout<<"随机生成字符串："<<endl;
    cout<<str<<endl;
}

void LCS(string stra,string strb,int lena,int lenb)
{
    string str;
    int** array;
    array = new int*[lena];
    for (int i = 0; i < lena; ++i) {
        array[i] = new int[lenb];
    }
    array[0][0] = 0;
    for (int i = 0; i < lena; ++i) {
        array[i][0] = 0;
    }

    for (int j = 0; j < lenb; ++j) {
        array[0][j] = 0;
    }

    for (int i = 1; i < lena; ++i) {
        for (int j = 1; j < lenb; ++j) {
            if (stra[i] == strb[j]) {
                //str += stra[i];
                array[i][j] = array[i-1][j-1] + 1;
                if (str.length() < array[i][j]) {
                    str += stra[i];
                }
            } else {
                array[i][j] = (array[i][j-1] > array[i-1][j]) ? array[i][j-1] : array[i-1][j];
            }
        }
    }
    cout<<str<<endl;
    cout<<array[lena-1][lenb-1]<<endl;
    for (int i = 0; i < lena; ++i) {
        delete [] array[i];
    }
    delete [] array;
}


int _tmain(int argc,TCHAR* argv[])
{
    do {
        int in = 0;
        cin>>in;
        if (!in) {
            break;
        }
        string strA;
        string strB;
        CreateStr(strA,20);
        CreateStr(strB,14);
        LCS(strA,strB,20,14);
    } while (true);
    
    return 0;
}

2.管子切割问题

3.矩阵乘法

4.背包问题