【Codeforces650C】Table Compression【并查集】【拓扑排序】

先排序，把大小相同的元素合并成一个集合。注意这些元素不一定在位置上相邻。

然后再排序，从小到大建边。

最后做个bfs，每个点的答案为并查集中的最大值。

/* Footprints In The Blood Soaked Snow */
#include <cstdio>
#include <algorithm>

using namespace std;

const int maxn = 1000005, maxq = maxn;

int n, m, head[maxn], cnt, mat[maxn], dp[maxn], du[maxn], q[maxq], fa[maxn];

struct _edge {
	int v, next;
} g[maxn << 1];

struct _point {
	int x, y;
} num[maxn];

inline int iread() {
	int f = 1, x = 0; char ch = getchar();
	for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;
	for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
	return f * x;
}

inline void add(int u, int v) {
	g[cnt] = (_edge){v, head[u]};
	head[u] = cnt++;
	du[v]++;
}

inline int getid(int x, int y) {
	return (x - 1) * m + y;
}

inline int find(int x) {
	return x == fa[x] ? x : fa[x] = find(fa[x]);
}

inline void bfs() {
	int h = 0, t = 0;
	for(int i = n * m; i >= 1; i--) if(!du[i]) dp[q[t++] = i] = 1;
	while(h != t) {
		int u = q[h++];
		for(int i = head[u]; ~i; i = g[i].next) {
			dp[g[i].v] = max(dp[g[i].v], dp[u] + 1);
			du[g[i].v]--;
			if(!du[g[i].v]) q[t++] = g[i].v;
		}
	}
}

inline bool cmp(_point a, _point b) {
	return mat[getid(a.x, a.y)] < mat[getid(b.x, b.y)];
}

int main() {
	n = iread(); m = iread();
	for(int i = 0; i < maxn; i++) fa[i] = i, head[i] = -1; cnt = 0;

	for(int i = 1; i <= n; i++) for(int j = 1; j <= m; j++) mat[getid(i, j)] = iread();

	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= m; j++) num[j] = (_point){i, j};
		sort(num + 1, num + 1 + m, cmp);
		for(int j = 2; j <= m; j++) if(mat[getid(num[j - 1].x, num[j - 1].y)] == mat[getid(num[j].x, num[j].y)])
			fa[find(getid(num[j - 1].x, num[j - 1].y))] = find(getid(num[j].x, num[j].y));
	}
	for(int i = 1; i <= m; i++) {
		for(int j = 1; j <= n; j++) num[j] = (_point){j, i};
		sort(num + 1, num + 1 + n, cmp);
		for(int j = 2; j <= n; j++) if(mat[getid(num[j - 1].x, num[j - 1].y)] == mat[getid(num[j].x, num[j].y)])
			fa[find(getid(num[j - 1].x, num[j - 1].y))] = find(getid(num[j].x, num[j].y));
	}
	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= m; j++) num[j] = (_point){i, j};
		sort(num + 1, num + 1 + m, cmp);
		for(int j = 2; j <= m; j++) if(mat[getid(num[j - 1].x, num[j - 1].y)] != mat[getid(num[j].x, num[j].y)])
			add(find(getid(num[j - 1].x, num[j - 1].y)), find(getid(num[j].x, num[j].y)));
	}
	for(int i = 1; i <= m; i++) {
		for(int j = 1; j <= n; j++) num[j] = (_point){j, i};
		sort(num + 1, num + 1 + n, cmp);
		for(int j = 2; j <= n; j++) if(mat[getid(num[j - 1].x, num[j - 1].y)] != mat[getid(num[j].x, num[j].y)])
			add(find(getid(num[j - 1].x, num[j - 1].y)), find(getid(num[j].x, num[j].y)));
	}

	bfs();

	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= m; j++) printf("%d ", dp[find(getid(i, j))]);
		printf("\n");
	}
	return 0;
}