洛谷P2294 [HNOI2005]狡猾的商人

\(\large{题目链接}\)
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\(\Large\textbf{Solution: } \large{因为每次提供的是一段时间的利润，具体的每个月并不清楚，所以考虑直接判断前缀和是否合法即可。}\)
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\(\Large\textbf{Summary: } \large{像这种判断是否合法或者两者之间关系的题目，可以往图上想一想。}\)
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\(\Large\textbf{Code: }\)

#include <bits/stdc++.h>
#define gc() getchar() 
#define LL long long
#define rep(i, a, b) for (int i = (a); i <= (b); ++i)
#define _rep(i, a, b) for (int i = (a); i >= (b); --i)
using namespace std;
const int N = 105;
const int M = 1005;
const int inf = 0x7fffffff;
int w, n, m, cnt, head[N], vis[N], r[N], dis[N];

struct Edge {
	int to, next, val;
}e[M << 1];

inline int read() {
	int x = 0, flg = 1;
	char ch = gc();
	while (!isdigit(ch)) {
		if (ch == '-') flg = -1;
		ch = gc();
	}
	while (isdigit(ch)) x = x * 10 + ch - '0', ch = gc();
	return x * flg; 
}

inline void add(int x, int y, int w) {
	e[++cnt].to = y;
	e[cnt].val = w;
	e[cnt].next = head[x];
	head[x] = cnt;
}

inline bool Spfa() {
	queue <int> q;
	memset(vis, 0, sizeof (vis));
	rep(i, 0, n) dis[i] = inf;
	dis[0] = 0; vis[0] = 1; q.push(0);
	while (!q.empty()) {
		int x = q.front(); q.pop();
		vis[x] = 0;
		for (int i = head[x]; i ; i = e[i].next) {
			int u = e[i].to;
			if (dis[u] == inf) {
				dis[u] = dis[x] + e[i].val;
				if (!vis[u]) vis[u] = 1, q.push(u);
			}
			else if (dis[u] != dis[x] + e[i].val) return false;
		}
	}
	return true;
}

int main() {
	w = read();
	while (w--) {
		cnt = 0;
		memset(head, 0, sizeof (head));
		n = read(), m = read();
		int x, y, w;
		while (m--) x = read(), y = read(), w = read(), add(x - 1, y, w), add(y, x - 1, -w);
		int flg = Spfa();
		flg ? puts("true") : puts("false");
	}
	return 0;
} 

来源：https://www.cnblogs.com/Miraclys/p/12584914.html