找鞍点

鞍点：

矩阵A_m×n中的元素A[i][j]是第i行中的最小值，同时是第j列中的最大值，则此元素为该矩阵的一个鞍点。

试编写程序，确定鞍点在矩阵中的位置。

思路：

1、分别将行最小、列最大存在两个三元表里

2、暴力查找

#include <iostream>
using namespace std;

const int MAX_COL = 10, MAX_ROW = 10;
struct elemt
{
    int row, col;
    int val;
};
//Init
void Init(int &nr, int &nc, int a[][MAX_COL]);
//solve
void solveIt(int a[][MAX_COL], int nr, int nc);
//AppendElemt(n_rowMin, n_row, min, i, j);
void AppendElemt(elemt tgt[], int &n, int val, int i, int j);

int main()
{
    int a[MAX_ROW][MAX_COL], nr, nc;
    Init(nr, nc, a);
    solveIt(a, nr, nc);
    system("pause");
    return 0;
}
void solveIt(int a[][MAX_COL], int nr, int nc)
{
    elemt n_rowMin[MAX_COL*MAX_ROW], n_colMax[MAX_COL*MAX_ROW];
    int n_row, n_col = n_row = 0;
    
    //行最小
    for (int i = 0; i < nr; i++)
    {
        //判断行最小是否唯一
        int min = a[i][0], counter = 1;
        for (int j = 0; j < nc; j++)
        {
            if (a[i][j] < min)
            {
                min = a[i][j];
                counter = 1;
            }
            else if (a[i][j] == min)
            {
                counter++;
            }
            else
                continue;
        }
        //如果只有一个最小值，找到存完就break
        for (int j = 0; j < nc; j++)
            if (a[i][j] == min && !(counter - 1))
            {
                AppendElemt(n_rowMin, n_row, min, i, j);
                break;
            }
            else if (a[i][j] == min && (counter-1))
            {
                AppendElemt(n_rowMin, n_row, min, i, j);
            }
            else
                continue;
    }

    //列最大
    for (int i = 0; i < nc; i++)
    {
        //判断列最大是否唯一
        int max = a[0][i], counter = 1;
        for (int j = 0; j < nr; j++)
        {
            if (a[j][i] > max)
            {
                max = a[j][i];
                counter = 1;
            }
            else if (a[j][i] == max)
            {
                counter++;
            }
            else
                continue;
        }
        for (int j = 0; j < nr; j++)
            if (a[j][i] == max && !(counter - 1))
            {
                AppendElemt(n_colMax, n_col, max, j, i);
                break;
            }
            else if (a[j][i] == max && (counter - 1))
            {
                AppendElemt(n_colMax, n_col, max, j, i);
            }
            else
                continue;
    }
    int nSP = 0;
    for (int i = 0; i < n_row; i++)
    {
        for (int j = 0; j < n_col; j++)
        {
            if (n_rowMin[i].row == n_colMax[j].row&&n_rowMin[i].col == n_colMax[j].col&&n_rowMin[i].val == n_colMax[j].val)
            {
                nSP++;
                cout << "(" << n_rowMin[i].row+1 << "," << n_rowMin[i].col+1 << ")=" << n_rowMin[i].val << endl;
            }
        }
    }
    cout << "共有" << nSP << "个鞍点" << endl;
}
void Init(int &nr, int &nc, int a[][MAX_COL])
{
    cout << "请输入矩阵的行、列：" << endl;
    cin >> nr >> nc;
    cout << "请输入此矩阵：" << endl;
    for (int i = 0; i < nr; i++)
        for (int j = 0; j < nc; j++)
            cin >> a[i][j];
}
void AppendElemt(elemt tgt[], int &n, int val, int i, int j)
{
    tgt[n].row = i;
    tgt[n].col = j;
    tgt[n++].val = val;
}

使用循环的方法

思路：

1、遍历每一行的每一个元素（因为最值可能不唯一），假设该元素为鞍点，即行最小、列最大

2、验证，顺序输出

//循环实现找鞍点
#include <iostream>
using namespace std;
const int MAX = 10;//存储矩阵的阶数

int arr[MAX][MAX];
int nr,nc;//阶数
void Init();
void Find();

int main()
{
    Init();
    Find();
        return 0;
}
void Find()
{
    //鞍点：行最小值&&列最大值

    bool br, bc;//判断列最大和行最小
    int min_e, max_e;
    int flag = 0;//记录鞍点的个数
    for (int i = 0; i < nr; i++) {

        for (int j = 0; j < nc; j++)
        {
            //判断arr[i][j]是否为为行最小
            min_e = arr[i][j];
            br = true;//假设为行最小
            int t = nc;
            while (t--) {
                if (arr[i][t] < min_e) {
                    br = false;
                    break;
                }
            }
            //判断arr[i][j]是否为列最大
            bc = true;
            t = nr;
            max_e = arr[i][j];
            while (t--) {
                if (arr[t][j] > max_e) {
                    bc = false;
                    break;
                }
            }
            //结合
            if (br&&bc) {
                cout << "(" << i + 1 << "," << j + i << ")" << endl;
                flag++;
            }
        }
    }
    if (!flag) {
        cout << "无鞍点" << endl;
    }
    else
        cout << "共" << flag << "个" << endl;
}
void Init() {
    cout << "请输入矩阵的行数和列数：";
    cin >> nr >> nc;
    cout << "请输入该矩阵：";
    for (int i = 0; i < nr; i++)
        for (int j = 0; j < nc; j++)
            cin >> arr[i][j];
}