鄰國不同色問題

#include <iostream>
#include <ctime>
#include <vector>
#include <algorithm>
#include <set>
using namespace std;
// some constants
const int MAXC = 105;
const int N = 30;
const int MAXN = 32;
const int dx[] = {0, 0, 1, -1}, dy[] = {1, -1, 0, 0}; // used to check the block around it
vector<int> countries;// used to discrete the countrie numbers
set<int> graph[MAXC]; // use set to get rid of the same number
int color[MAXC]; // save each country's color
int mat[MAXN][MAXN]; // save the map
int c = -1; // current number of colors
bool ans; // check if find the answer yet
int firstseen[MAXC];
bool comp(int x, int y) {
	return firstseen[x] < firstseen[y];
}
void build() {
    // input with 1-based
    for(int i = 1; i <= N; ++i) {
        for(int j = 1; j <= N; ++j) {
            scanf("%2d", &mat[i][j]);
            // save the countries
            if(mat[i][j]) {
				int u = mat[i][j];
				countries.push_back(u); 
       			if(!firstseen[u]) firstseen[u] = j + i * N; // used for coloring order	
			}
		}
    }
    // discrete
    sort(countries.begin(), countries.end(), comp);
    countries.erase(unique(countries.begin(), countries.end()), countries.end());
	for(auto u : countries) {
		cerr << u << ' ';
	}
	cerr << '\n';
    for(int i = 1; i <= N; ++i) {
        for(int j = 1; j <= N; ++j) {
            if(mat[i][j]) mat[i][j] = lower_bound(countries.begin(), countries.end(), mat[i][j], comp) - countries.begin() + 1;
        }
    }
	// build an adjacentlist
    for(int i = 1; i <= N; ++i) { 
        for(int j = 1; j <= N; ++j) {
            int u = mat[i][j];
			if(u) {
            	for(int k = 0; k < 4; ++k) { // different directions
                	int v = mat[i + dx[k]][j + dy[k]];
                	if(v && v < u) { // save edges to node with its number less
                    	graph[u].insert(v);
               		}
            	}
        	}
		}
    }
	// for test only
    for(int i = 1; i <= countries.size(); ++i) {
        cerr << i << ':';
        for(auto p : graph[i]) {
            cerr << p << ' ';
        }
        cerr << '\n';
    }
}
// u : current country, cmx : the greatest number of color now
void dfs(int u = 1, int cmx = 0) { 
	// check if it ends
    if(u > countries.size()) {
        ans = 1;
        return;
    }
	// enumerate the possibilities
    for(int i = 1; i <= min(c, cmx + 1); ++i) { 
		// check if there is any color the same
        bool flag = 1;
        for(auto it = graph[u].begin(); it != graph[u].end(); ++it) {
            if(color[*it] == i) {
                flag = 0;
                break;
            }
        }
		// continue the recursion
        if(flag) {
            color[u] = i;
            dfs(u + 1, max(i, cmx));
            if(ans) return;
        }
    }
}
void solve() {
    int sttime, edtime;
	// record the start time period
    sttime = time(NULL);
	// redirect the in/out stream
    freopen("./input.txt", "r", stdin);
    freopen("./output.txt", "w", stdout);
	// input and build the graph
    build();
	// searching for answer
    while(!ans) {
		// check if c colors can satisfy the condition
        cerr << "Checking number of color: "<< (++c) << '\n';
        dfs();
    }
	// output
    cout << "My name is lemonilemon.\n\n";
    cout << "Colored with " << c << " colors.\n\n";
    for(int i = 1; i <= N; ++i) {
        for(int j = 1; j <= N; ++j) {
            int u = mat[i][j];
            cout << (char)(color[u] + 'a' - 1) << " \n"[j == 30];
        }
    }
	// record the end time period
    edtime = time(NULL);
	// compute time
    cout << "Finish in " << edtime - sttime << " second(s).\n";
}

int main() {
    solve();
    return 0;
}