Project Euler Problem 67 (C++和Python)

Problem 67 : Maximum path sum II

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.
3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom in triangle.txt (right click and ‘Save Link/Target As…’), a 15K text file containing a triangle with one-hundred rows.

NOTE: This is a much more difficult version of Problem 18. It is not possible to try every route to solve this problem, as there are 299 altogether! If you could check one trillion (1012) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)

C++ 代码

#include <iostream>
#include <fstream>
#include <sstream>
#include <cassert>
    
using namespace std;

class PE0067
{
private:
    static const int max_rows = 100;
    int triangleMatrix[max_rows+1][max_rows+1];

    void readDataFromFile(char filename[]);
    int  getMaximumTotalFromTopToBottom(int numOfRows);

public:
    void run_unit_test();
    int  findMaximumTotalInFile();
};

void PE0067::run_unit_test()
{
    // 3
    // 7 4
    // 2 4 6
    // 8 5 9 3
    memset(triangleMatrix, 0, sizeof(triangleMatrix));

    int data[10] = {3, 7, 4, 2, 4, 6, 8, 5, 9, 3};
    int i = 0;
    for (int row=1; row<=4; row++)
    {
        for (int col=1; col<=row; col++)
        {
            triangleMatrix[row][col] = data[i++];
        }
    }

    assert(23 == getMaximumTotalFromTopToBottom(4));
}

int PE0067::findMaximumTotalInFile()
{
    readDataFromFile("p067_triangle.txt");

    return getMaximumTotalFromTopToBottom(max_rows);
}

void PE0067::readDataFromFile(char filename[])
{
    ifstream in(filename);

    if (!in) return;

    int row = 1, col, number;
    char szBuf[512];

    memset(triangleMatrix, 0, sizeof(triangleMatrix));

    while(in.getline(szBuf, 512))
    {
        col = 1;
        string strText = szBuf;
        istringstream s(strText);
        while (row>=col)
        {
            s >> number;
            triangleMatrix[row][col++] = number;
        }
        row++;
    }
    in.close();
}

int PE0067::getMaximumTotalFromTopToBottom(int numOfRows)
{
    int maxTotal = 0;
    for(int row=1; row<=numOfRows; row++)
    {
        for(int col=1; col<=row; col++)
        {
            triangleMatrix[row][col] += \
                    max(triangleMatrix[row-1][col-1], triangleMatrix[row-1][col]);
            maxTotal = max(maxTotal, triangleMatrix[row][col]);
        }
    }

    return maxTotal;
}     

int main()
{
    PE0067 pe0067;

    pe0067.run_unit_test();

    cout << "The maximum total from top to bottom is ";
    cout << pe0067.findMaximumTotalInFile() << "." << endl;

    return 0;
}

Python代码

import numpy as np

def run_unit_test():
    """
        3
       7 4
      2 4 6
     8 5 9 3
    """
    triangleMatrix = np.zeros((4+1, 4+1))
    i, data = 0, [3, 7, 4, 2, 4, 6, 8, 5, 9, 3]

    for row in range(1, 5):
        for col in range(1, row+1):
            triangleMatrix[row][col] = data[i]
            i += 1
    assert 23 == getMaximumTotalFromTopToBottom(4, triangleMatrix)

def readDataFromFile(filename):
    triangleMatrix = np.zeros((100+1, 100+1))
    i, data = 0, []
    for line in open(filename).readlines():
        data += map(int, line.split()) 
    
    for row in range(1, 101):
        for col in range(1, row+1):
            triangleMatrix[row][col] = data[i]
            i += 1
    return  triangleMatrix

def findMaximumTotalInFile():
    triangleMatrix = readDataFromFile("p067_triangle.txt")
    return getMaximumTotalFromTopToBottom(100, triangleMatrix)

def getMaximumTotalFromTopToBottom(numOfRows, triangleMatrix):
    maxTotal = 0
    for row in range(1, numOfRows+1):
        for col in range(1, row+1):
            triangleMatrix[row][col] += \
                    max(triangleMatrix[row-1][col-1], triangleMatrix[row-1][col])
            maxTotal = max(maxTotal, triangleMatrix[row][col])

    return int(maxTotal)

def main():
    run_unit_test()

    print("The maximum total from top to bottom is %d." % findMaximumTotalInFile())

if  __name__ == '__main__':
    main()