将多个1作为起点，BFS扩展这些起点，每个点第一次访问时必定为最小距离。

#include<cstdio>
#include<queue>
using namespace std;
 
const int N = 1010;
char maps[N][N];
int dis[N][N];
bool vis[N][N];
 
int x_turn[4]={1, -1, 0, 0};
int y_turn[4]={0, 0, 1, -1};
 
int main() {
	int n, m;
	scanf("%d %d", &n, &m);
	for (int i = 1; i <= n; ++i) {
		scanf("\n%s", maps[i]+1);
	}
	queue<pair<int, int> >qu;
	for (int i = 1; i <= n; ++i)
		for (int j = 1; j <= m; ++j)
			if(maps[i][j] == '1') {
				qu.push(make_pair(i, j));
				vis[i][j] = true;
			}
	while(!qu.empty()) {
		pair<int, int>now = qu.front();
		qu.pop();
		for (int i = 0; i < 4; ++i) {
			int xx = now.first + x_turn[i], yy = now.second + y_turn[i];
			if(vis[xx][yy] || xx < 1 || xx > n || yy < 1 || yy > m)continue;
			vis[xx][yy] = true;
			dis[xx][yy] = dis[now.first][now.second] + 1;
			qu.push(make_pair(xx, yy));
		}
	}
 
	for (int i = 1; i <= n; ++i) {
		for (int j = 1; j <= m; ++j) {
			printf("%d ", dis[i][j]);
		}
		printf("\n");
	}
	return 0;
}