《算法竞赛进阶指南》书上已经给了完整的算法分析，那么我就给出本题标准的C++代码。

#include <bits/stdc++.h>


using namespace std;


int cols[100010], rows[100010];
long long s[100010];


int main(void) {
    int n, m, k;
    scanf("%d%d%d", &n, &m, &k);
    while (k--) {
        int x, y;
        scanf("%d%d", &x, &y);
        ++rows[x];
        ++cols[y];
    }

    long long res_row,
              sum_row = 0;
    for (int i = 1; i <= n; ++i) {
        sum_row += rows[i];
    }
    if (sum_row % n == 0) {
        for (int i = 1; i <= n; ++i) {
            s[i] = s[i - 1] + rows[i] - sum_row / n;
        }
        sort(s + 1, s + n + 1);
        res_row = 0;
        for (int i = 1; i <= n; ++i) {
            res_row += max(s[i] - s[(n + 1) / 2], s[(n + 1) / 2] - s[i]);
        }
    } else {
        res_row = -1;
    }

    long long res_col,
              sum_col = 0;
    for (int i = 1; i <= m; ++i) {
        sum_col += cols[i];
    }
    if (sum_col % m == 0) {
        for (int i = 1; i <= m; ++i) {
            s[i] = s[i - 1] + cols[i] - sum_col / m;
        }
        sort(s + 1, s + m + 1);
        res_col = 0;
        for (int i = 1; i <= m; ++i) {
            res_col += max(s[i] - s[(m + 1) / 2], s[(m + 1) / 2] - s[i]);
        }
    } else {
        res_col = -1;
    }

    if (res_row == -1 && res_col == -1) {
        puts("impossible");
    } else if (res_row == -1) {
        printf("column %lld\n", res_col);
    } else if (res_col == -1) {
        printf("row %lld\n", res_row);
    } else {
        printf("both %lld\n", res_row + res_col);
    }

    return 0;
}