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  • [CF949C]Data Center Maintenance

    题目大意:$n$个点,每个点有一个值$w_i$。$m$个条件,每个条件给出$x,y$,要求$w_x ot =w_y$。选择最少的点,使其值加$1$后,所有条件成立(数据保证有解)。

    题解:对于每个条件,若$(w_x+1)mod h=w_y$,连上$x->y$;若$(w_y+1)mod h=w_x$,连上$y->x$。一条边的含义是,若起点加一,终点也要加一。缩点,强连通分量内的点要一起加。发现答案就是找最小的没有出边的点

    卡点:

    C++ Code:

    #include <cstdio>
    #define maxn 100010
    #define maxm maxn
    #define gethour(x) ((x + 1) % h)
    int n, m, h;
    int w[maxn];
    
    int head[maxn << 1], cnt;
    struct Edge {
    	int from, to, nxt;
    } e[maxm << 2];
    inline void addE(int a, int b) {
    	e[++cnt] = (Edge) {a, b, head[a]}; head[a] = cnt;
    }
    
    int DFN[maxn], low[maxn], idx, sz[maxn];
    int S[maxn], top, res[maxn], CNT;
    bool ins[maxn];
    inline int min(int a, int b) {return a < b ? a : b;}
    void tarjan(int u) {
    	DFN[u] = low[u] = ++idx;
    	ins[S[++top] = u] = true;
    	int v;
    	for (int i = head[u]; i; i = e[i].nxt) {
    		v = e[i].to;
    		if (!DFN[v]) {
    			tarjan(v);
    			low[u] = min(low[u], low[v]);
    		} else if (ins[v]) low[u] = min(low[u], DFN[v]);
    	}
    	if (DFN[u] == low[u]) {
    		CNT++;
    		do {
    			ins[v = S[top--]] = false;
    			sz[res[v] = CNT]++;
    			addE(CNT + n, v);
    		} while (u != v);
    	}
    }
    
    int oud[maxn];
    int main() {
    	scanf("%d%d%d", &n, &m, &h);
    	for (int i = 1; i <= n; i++) scanf("%d", w + i);
    	for (int i = 0, a, b; i < m; i++) {
    		scanf("%d%d", &a, &b);
    		if (w[a] == gethour(w[b])) addE(b, a);
    		if (w[b] == gethour(w[a])) addE(a, b);
    	}
    	int cnt_now = cnt;
    	for (int i = 1; i <= n; i++) if (!DFN[i]) tarjan(i);
    	for (int i = 1; i <= cnt_now; i++) {
    		int u = e[i].from, v = e[i].to;
    		if (res[u] != res[v]) oud[res[u]]++;
    	}
    	int ans = 0x3f3f3f3f, mini = n + 1;
    	for (int i = 1; i <= CNT; i++) if (!oud[i] && ans > sz[i]) {
    		ans = sz[i];
    		mini = i + n;
    	}
    	printf("%d
    ", ans);
    	for (int i = head[mini]; i; i = e[i].nxt) printf("%d ", e[i].to);
    	puts("");
    	return 0;
    }
    

      

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  • 原文地址:https://www.cnblogs.com/Memory-of-winter/p/9745756.html
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