[leetcode] Minimum Path Sum

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Minimum Path Sum

dp入门题，状态fun[i][j]=min(fun[i-1][j],fun[i][j-1])+grid[i][j];

class Solution {public:    int minPathSum(vector<vector<int> > &grid) {//        int row=grid.size();//行数        if (row==0) {            return 0;        }        int column=grid[0].size();//列数                vector<vector<int>> fun(row,vector<int>(column));//开辟相同大小的矩阵        //处理边界        fun[0][0]=grid[0][0];        int i,j;        for (i=1; i<row; ++i) {//第一列            fun[i][0]=fun[i-1][0]+grid[i][0];        }        for (j=1; j<column; ++j) {//第一行            fun[0][j]=fun[0][j-1]+grid[0][j];        }                for (i=1; i<row; ++i) {            for (j=1; j<column; ++j) {                fun[i][j]=min(fun[i-1][j],fun[i][j-1])+grid[i][j];//min()为库函数            }        }        return fun[row-1][column-1];    }};

class Solution {public:    //状态定义为从起点--当前节点的最小路径和    int minPathSum(vector<vector<int> > &grid) {        if(grid.size()==0){            return 0;        }        int sum[grid.size()][grid[0].size()];        //状态初始化        sum[0][0]=grid[0][0];        for(int i=1;i<grid.size();++i){            sum[i][0]=grid[i][0]+sum[i-1][0];        }        for(int j=1;j<grid[0].size();++j){            sum[0][j]=grid[0][j]+sum[0][j-1];        }        //状态转移        for(int i=1;i<grid.size();++i){//行            for(int j=1;j<grid[0].size();++j){//列                sum[i][j]=grid[i][j]+min(sum[i][j-1],sum[i-1][j]);            }        }        return sum[grid.size()-1][grid[0].size()-1];    }};

class Solution {public:    int minPathSum(vector<vector<int>>& grid) {        int m=grid.size();//row        int n=grid[0].size();//column        vector<vector<int> > dp(m,vector<int>(n));//二维        for(int i=0;i<m;++i){            for(int j=0;j<n;++j){                if(i==0){                    if(j==0){                        dp[i][j]=grid[i][j];                    }else{                        dp[i][j]=grid[i][j]+dp[i][j-1];                    }                }else if(j==0){                    dp[i][j]=grid[i][j]+dp[i-1][j];                }else{                    dp[i][j]=min(dp[i-1][j],dp[i][j-1])+grid[i][j];                }            }        }        return dp[m-1][n-1];    }};

优化空间

class Solution {public:    int minPathSum(vector<vector<int>>& grid) {        int m=grid.size();//row        int n=grid[0].size();//column        vector<int> dp(n);//一维        for(int i=0;i<m;++i){            for(int j=0;j<n;++j){                if(i==0){                    if(j==0){                        dp[j]=grid[i][j];                    }else{                        dp[j]=grid[i][j]+dp[j-1];                    }                }else if(j==0){                    dp[j]=grid[i][j]+dp[j];                }else{                    dp[j]=min(dp[j],dp[j-1])+grid[i][j];                }            }        }        return dp[n-1];    }};

参考：Minimum path sum

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