leetcode(c++)(坐标DP)

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#include <iostream>
#include <vector>
#include <stack>

using namespace std;

int uniquePaths(int m, int n)
{
    vector<vector<int>>dp(m,vector<int>(n));
    for(int i = 0;i < m; ++i)
    {
        dp[i][0] = 1;
    }
    for(int i = 0; i < n; ++i)
    {
        dp[0][i] = 1;
    }
    for(int i = 1; i < m; ++i)
    {
        for(int j = 1; j < n ; ++j)
        {
            dp[i][j] = dp[i-1][j] + dp[i][j-1];
        }
    }
    return dp[m-1][n-1];
}

int uniquePathsI(int m, int n)
{
    vector<int>dp(n,1);
    for(int i = 1; i < m; ++i)
    {
        for(int j = 1; j < n; ++j)
        {
            dp[j] = dp[j] + dp[j-1];
        }
    }
    return dp[n-1];
}

int uniquePaths(const vector<vector<int>>paths)
{
    int m = paths.size(), n = paths[0].size();
    vector<vector<int>>dp(m,vector<int>(n));
    for(int i = 0; i < m; ++i)
    {
        if(paths[i][0] == 1)
        break;
        dp[i][0] = 1;
    }
    for(int i = 0;i < n; ++i)
    {
        if(paths[0][i] == 1)
        break;
        dp[0][i] = 1;
    }
    for(int i = 1;i < m; ++i)
    {
        for(int j = 1; j < n; ++j)
        {
            dp[i][j] = paths[i][j]== 1 ? 0 : dp[i-1][j] + dp[i][j-1];
        }
    }
    return dp[m-1][n-1];    
}

int minimmTotal(const vector<vector<int>>& triangle)
{
    int n = triangle.size();
    vector<vector<int>>dp(n+1,vector<int>(n+1,0));
    for(int i = n-1; i >= 0 ;--i)
    {
        for(int j = i; j >= 0; --j)
        {
            dp[i][j] = min(dp[i+1][j],dp[i+1][j+1])+triangle[i][j];
        }
    }
    return dp[0][0];
}

int minPathSum(vector<vector<int>>& grid)
{
    int m = grid.size(), n = grid[0].size();  
    for(int i = 0; i < m; ++i)
    {
        for(int j = 0; j < n; ++j)
        {
            if(i == 0)grid[i][j] += grid[i][j-1];
            else if(j == 0)grid[i][j] += grid[i-1][j];
            else
            grid[i][j]+=min(grid[i-1][j],grid[i][j-1]);
        }
    }
    return grid[m-1][n-1];
}

int minFallingPathSum(vector<vector<int>>& A)
{
    int m = A.size(), n = A[0].size();
    for(int i = m - 2; i >= 0; --i)
    {
        for(int j = 0;j < n; ++j)
        {
            int minVal = A[i+1][j];
            if(j > 0)minVal = min(minVal,A[i+1][j-1]);
            if(j+1 < n)minVal = min(minVal,A[i+1][j+1]);
            A[i][j]+=minVal;
        }
    }
    sort(A[0].begin(),A[0].end());
    return A[0][0];
}

int minFallingPathSumI(vector<vector<int>>& grid)
{
    int m = grid.size(), n = grid[0].size();
    vector<vector<int>>dp(m,vector<int>(n));
    for(int i = 0;i < n ; ++i)dp[0][i] = grid[0][i];
    for(int i = 1; i < m; ++i)
    {
       
        for(int j = 0; j < n; ++j)
        {
             int preRowMin = INT_MAX;
             for(int k = 0; k < n; ++k)
             {
                 if(j != k) preRowMin = min(preRowMin,dp[i-1][k]);
                 dp[i][j] = grid[i][j] + preRowMin;
             }
        }        
    }
    int res = INT_MAX;
    for(int i = 0;i < n ; ++i)
    {
        res = min(res,dp[m-1][i]);
    }
    return res;
}

int maxSuqare(const vector<vector<string>>& matrix)
{
    int m = matrix.size(), n = matrix[0].size();
    int maxVal = INT_MIN;
    vector<vector<int>>dp(m,vector<int>(n));
    for(int i = 0; i < m; ++i)
    {
        for(int j = 0; j < n; ++j)
        {
            if(i == 0 || j == 0)
            {
                if(matrix[i][j] == "1")dp[i][j] = 1;                
            }
            else
            {
                if(matrix[i][j] == "1")
                dp[i][j] = min(dp[i-1][j],min(dp[i][j-1],dp[i-1][j-1])) + 1;
            }
            maxVal = max(maxVal,dp[i][j]); 
        } 
          
    }
    return maxVal*maxVal;
}

int largestRectangle(vector<int>& height)
{
    stack<int>st;
    int res = 0;
    for(int i = 0; i < height.size(); ++i)
    {
        while(!st.empty() && height[i] <= height[st.top()])
        {
            int preHeight = height[st.top()];
            st.pop();
            int width = i - (st.empty() ? 0:st.top() + 1);
            res = max(res,preHeight * width);
        }
        st.push(i);
    }
    while(!st.empty())
    {
        int preHeight = height[st.top()];
        st.pop();
        int width = height.size() - (st.empty() ? 0 :st.top() + 1);
        res = max(res,preHeight * width);
    }
    return res;
}

int maxRectangle(const vector<vector<string>>& matrix)
{
    int m = matrix.size();
    if(m == 0)return 0;
    int n = matrix[0].size();
    vector<int>height(n);
    int res = 0;
    for(int i = 0; i < m; ++i)
    {
        for(int j = 0;j < n; ++j)
        {
            if(matrix[i][j] == "0")height[j]=0;
            else ++height[j];        
        }
        res = max(res,largestRectangle(height));
    }
    return res;
}

int main()
{
    //LeetCode62
    cout << uniquePaths(3,2) << endl;
    cout << uniquePathsI(3,2) << endl;

    //LeetCode63
    // vector<vector<int>>paths{{0,0,0},{0,1,0},{0,0,0}};
    vector<vector<int>>paths{{0,1},{0,0}};
    cout << uniquePaths(paths) << endl;

    //LeetCode120
    vector<vector<int>>triangle={{2},{3,4},{6,5,7},{4,1,8,3}};
    cout << minimmTotal(triangle) << endl;

    //LeetCode64
    vector<vector<int>>grid{{1,3,1},{1,5,1},{4,2,1}};
    cout << minPathSum(grid) << endl;

    //LeetCode931
    vector<vector<int>>grids{{1,2,3},{4,5,6},{7,8,9}};
    // cout << minFallingPathSum(grids) << endl;

    //LeetCode1289
    cout << minFallingPathSumI(grids) << endl;

    //LeetCode221
    vector<vector<string>>matrix{{"1","0","1","0","0"},{"1","0","1","1","1"},{"1","1","1","1","1"},{"1","0","0","1","0"}};
    cout << maxSuqare(matrix) << endl;

    //LeetCode85    
    cout << maxRectangle(matrix) << endl;
    return 0;
}

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