[编程题]最大和子矩阵

采用动态规划策略，python实现与C++实现等价。

Python  代码：

# -*- coding:utf-8 -*-
class SubMatrix:
    def fun(self, tempList):
       maxVal=tempList[0]
       temp=tempList[0]
       
       i=1 
       while(i<len(tempList)):
           if temp<0:
               temp=tempList[i]
           else:
               temp+=tempList[i]
           
           maxVal=max(temp, maxVal)

           i+=1 
       return maxVal        

    def sumOfSubMatrix(self, mat, n):
        # write code here
        maxAllVal=-1000000
        for i in xrange(n):
            maxAllVal=max(maxAllVal, self.fun(mat[i]))
            for j in xrange(i+1, n):
                for k in xrange(n):
                    mat[i][k]+=mat[j][k]
                maxAllVal=max(maxAllVal, self.fun(mat[i]))
        return maxAllVal

a=[[-16,-23,-13,-24],[14,-22,28,16],[25,-2,19,-10],[6,9,-17,20]]
b=4
#a=[[-6,13,-21,-19],[21,19,5,-22],[-16,10,0,-11],[-15,-4,-8,-15]]
print SubMatrix().sumOfSubMatrix(a, b)

C++  代码：

#include <vector>
#include <iostream>
using namespace std;

class SubMatrix 
{
public:
    int sumOfSubMatrix(vector<vector<int> > mat, int n) {
        int maxVal = -(1<<31);
        for(int i = 0; i < n; i++){
            vector<int> temp = mat[i];
            maxVal = max(maxVal,helper(temp));
            for(int j = i + 1; j < n; j++){
                for(int k = 0; k < n; k++){
                    temp[k] += mat[j][k];
                }
                 maxVal = max(maxVal,helper(temp));
            }
        }
        return maxVal;
    }

    //找出该数组的最大子数组和
    int helper(vector<int> &a){
        int temp = a[0];
        int maxVal = temp;
        for(int i = 1; i < a.size(); i++){
            if(temp < 0){
                temp = a[i];
            }else{
                temp +=a[i];
            }
            if(temp > maxVal){
                maxVal = temp;
            }
        }
        return maxVal;
    }
};

int main()
{
SubMatrix X;
vector< vector<int> > mat;
vector<int> temp;
temp.push_back(-16);
temp.push_back(-23);
temp.push_back(-13);
temp.push_back(-24);
mat.push_back(temp);

vector<int> temp1;
temp1.push_back(14);
temp1.push_back(-22);
temp1.push_back(28);
temp1.push_back(16);
mat.push_back(temp1);


vector<int> temp2;
temp2.push_back(25);
temp2.push_back(-2);
temp2.push_back(19);
temp2.push_back(-10);
mat.push_back(temp2);


vector<int> temp3;
temp3.push_back(6);
temp3.push_back(9);
temp3.push_back(-17);
temp3.push_back(20);
mat.push_back(temp3);

int n=4;

cout<<X.sumOfSubMatrix(mat, n)<<endl;
return 0;
}