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Luogu-P4768 (Kruskal重构树+最短路)
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題目鏈接
思路
- 按照海拔降序建重構樹，這樣每個節點的子樹能表示海拔大于等于它的所有點
- 預處理所有點到1的最短路
- 對于每個詢問找到最低的海拔高度，然后找子樹中所有點到1的最小值
- 找子樹中最小值，可以在建重構樹的時候預處理出來，不用每次都dfsdfsdfs這樣會超時…
#include <bits/stdc++.h>
const int maxn
= 1e6 + 5;
const int inf
= 0x3f3f3f3f;
#define P pair<int,int>
using namespace std
;
struct ac
{int u
, v
, l
, a
;bool operator < (const ac
&t
) {return a
> t
.a
;}
}edge
[maxn
];
int dis
[maxn
], vis
[maxn
];
vector
<ac
> g
[maxn
];
struct reset_kruskal
{struct ac
{int v
, nex
;}edge
[maxn
];struct acc
{int l
, a
;}weight
[maxn
];int head
[maxn
], pre
[maxn
], cnt
, n
, ans
;int dep
[maxn
], vis
[maxn
], fa
[maxn
][31];void init(int t
) {n
= t
;cnt
= 0;for (int i
= 0; i
<= n
; ++i
) {weight
[i
].l
= inf
;pre
[i
] = i
;}fill(head
, head
+n
+1, -1);fill(vis
, vis
+n
+1, 0);}void add(int u
, int v
) {edge
[cnt
] = {v
, head
[u
]};head
[u
] = cnt
++;} void dfs
(int u
) { vis
[u
] = 1;for (int i
= 1; i
<= log2(n
); ++i
) {if (fa
[u
][i
-1] == 0) break;fa
[u
][i
] = fa
[fa
[u
][i
-1]][i
-1];}for (int i
= head
[u
]; ~i
; i
= edge
[i
].nex
) {int v
= edge
[i
].v
;dep
[v
] = dep
[u
] + 1;fa
[v
][0] = u
; dfs(v
);weight
[u
].l
= min(weight
[u
].l
, weight
[v
].l
);}}int lca(int v
, int p
) {for (int i
= log2(dep
[v
]); i
>= 0; --i
) {if (weight
[fa
[v
][i
]].a
> p
) v
= fa
[v
][i
];}return v
;}int find
(int x
) {int t
= x
;while (x
!= pre
[x
]) x
= pre
[x
];while (t
!= pre
[t
]) {int fa
= pre
[t
];pre
[t
] = x
;t
= fa
;}return x
;}
}kru
;
void dijkstra(int s
, int n
) {fill(dis
, dis
+n
+1, inf
);fill(vis
, vis
+n
+1, 0);dis
[s
] = 0;priority_queue
<P
, vector
<P
>, greater
<P
>> que
;que
.push(P(0, s
));while (!que
.empty()) {P top
= que
.top();int u
= top
.second
;que
.pop();if (vis
[u
] || dis
[u
] < top
.first
) continue;vis
[u
] = 1;for (int i
= 0; i
< (int)g
[u
].size(); ++i
) {int v
= g
[u
][i
].v
;int l
= g
[u
][i
].l
;if (vis
[v
] == 0 && dis
[u
] + l
< dis
[v
]) {dis
[v
] = dis
[u
] + l
;que
.push(P(dis
[v
], v
));}}}
}
int main() {ios
::sync_with_stdio(false);cin
.tie(0), cout
.tie(0);int T
;scanf("%d", &T
);while (T
--) {int n
, m
;scanf("%d %d", &n
, &m
);for (int i
= 1; i
<= n
; ++i
) {g
[i
].clear();}for (int i
= 0; i
< m
; ++i
) {int u
, v
, l
, a
;scanf("%d %d %d %d", &u
, &v
, &l
, &a
);edge
[i
] = {u
, v
, l
, a
};g
[u
].push_back({u
, v
, l
, a
});g
[v
].push_back({v
, u
, l
, a
});}dijkstra(1, n
);sort(edge
, edge
+m
);kru
.init(n
*2);int cnt
= n
;for (int i
= 0; i
< m
; ++i
) {int fu
= kru
.find(edge
[i
].u
);int fv
= kru
.find(edge
[i
].v
);if (fu
== fv
) continue;cnt
++;kru
.weight
[cnt
].a
= edge
[i
].a
;kru
.weight
[edge
[i
].u
].l
= dis
[edge
[i
].u
];kru
.weight
[edge
[i
].v
].l
= dis
[edge
[i
].v
];kru
.add(cnt
, fu
);kru
.add(cnt
, fv
);kru
.pre
[fu
] = kru
.pre
[fv
] = cnt
;}for (int i
= cnt
; i
>= 1; --i
) {if (kru
.vis
[i
] == 0) {kru
.dep
[i
] = 1;kru
.fa
[i
][0] = i
;kru
.dfs(i
);}}int ans
= 0;int q
, k
, s
;scanf("%d %d %d", &q
, &k
, &s
);while (q
--) {int v
, p
;scanf("%d %d", &v
, &p
);v
= ((v
+ k
* ans
- 1) % n
) + 1;p
= (p
+ k
* ans
) % (s
+ 1);printf("%d\n", ans
= kru
.weight
[kru
.lca(v
, p
)].l
);}}return 0;
}
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