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Shiroha白羽的博客

Golang 踩坑 —— interface 为参数的时候传 nil 指针 Codeforces Round 925 (Div. 3) Codeforces Round 924 (Div. 2) Codeforces Round 923 (Div. 3) Codeforces Round 922 (Div. 2) Codeforces Round 921 (Div. 2) Educational Codeforces Round 161 (Rated for Div. 2) Codeforces Round 920 (Div. 3) Codeforces Round 919 (Div. 2) Hello 2024 Good Bye 2023 Codeforces Round 918 (Div. 4) 个人备份的常用 macOS 清理命令 Codeforces Round 917 (Div. 2) Pinely Round 3 (Div. 1 + Div. 2) Educational Codeforces Round 160 (Rated for Div. 2) Codeforces Round 915 (Div. 2) Codeforces Round 914 (Div. 2) Codeforces Round 913 (Div. 3) Educational Codeforces Round 159 (Rated for Div. 2) Codeforces Round 912 (Div. 2) Codeforces Round 911 (Div. 2) CodeTON Round 7 (Div. 1 + Div. 2, Rated, Prizes!) Educational Codeforces Round 158 (Rated for Div. 2) Codeforces Round 910 (Div. 2) Codeforces Round 909 (Div. 3) Codeforces Round 908 (Div. 2) Educational Codeforces Round 157 (Rated for Div. 2) C++自定义的字面量 Codeforces Round 907 (Div. 2)
【2019多校第一场补题 / HDU6582】2019多校第一场E题1005Path...
Shiroha · 2019-07-23 · via Shiroha白羽的博客

在一张有向图中,有一个起点和一个终点,你需要删去部分路径,使得起点到终点的最短距离增加(并不要求需要使得距离变成最大值),且删除的路径长度最短。求删去的路径总长为多少

一开始理解错题意了,以为是在保证路径变成最长的路径之后,求删去的路径和最小是多少。然后就自闭了很久,还WA了好几发。后来看到题目中是 longer 而不是 longest 。突然醒悟。直接最短路径 +网络流就行,中间重新建图。
大致的过程是先跑最短路径(我用了SPFA算法,因为当数据量较大时,图为稀疏图,所以用邻接表形式),然后求出起点到每一个点的距离(保存在数组 dist 中)。然后删掉所有的边,对满足下面等式的边进行重建(网络流的边,即同时需要搭建反向的边,只不过流量为0),然后跑网络流(我用了ISAP算法,仍然是邻接表)

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#include <bits/stdc++.h>

using namespace std;

#define MAXN 20100
#define MAXM 20100

bool visited[MAXN]; //标记数组
long long dist[MAXN]; //源点到顶点i的最短距离
long long path[MAXN]; //记录最短路的路径
long long enqueue_num[MAXN]; //记录入队次数
long long vertex_num; //顶点数
long long edge_num; //边数
long long source; //源点

struct Edge {
long long to, next, cap, flow;
} edge[MAXM];
long long head[MAXN];
long long tot;
long long gap[MAXN], dep[MAXN], cur[MAXN];

void init() {
tot = 0;
memset(head, -1, sizeof(head));
}

void addedge(long long u, long long v, long long w) {
edge[tot].to = v;
edge[tot].cap = w;
edge[tot].next = head[u];
edge[tot].flow = 0;
head[u] = tot++;
}

bool SPFA() {
memset(visited, 0, sizeof(visited));
memset(enqueue_num, 0, sizeof(enqueue_num));
for (long long i = 0; i < vertex_num; i++) {
dist[i] = __LONG_LONG_MAX__;
path[i] = source;
}

queue<long long> Q;
Q.push(source);
dist[source] = 0;
visited[source] = true;
enqueue_num[source]++;
while (!Q.empty()) {
long long u = Q.front();
Q.pop();
visited[u] = 0;
for (long long curnode = head[u]; curnode != -1; curnode = edge[curnode].next) {
if (dist[u] + edge[curnode].cap < dist[edge[curnode].to]) {
dist[edge[curnode].to] = dist[u] + edge[curnode].cap;
path[edge[curnode].to] = u;
if (!visited[edge[curnode].to]) {
Q.push(edge[curnode].to);
enqueue_num[edge[curnode].to]++;
if (enqueue_num[edge[curnode].to] >= vertex_num)
return false;
visited[edge[curnode].to] = 1;
}
}
}
}
return true;
}

long long Q[MAXN];

void BFS(long long start, long long end) {
memset(dep, -1, sizeof(dep));
memset(gap, 0, sizeof(gap));
gap[0] = 1;
long long front = 0, rear = 0;
dep[end] = 0;
Q[rear++] = end;
while (front != rear) {
long long u = Q[front++];
for (long long i = head[u]; i != -1; i = edge[i].next) {
long long v = edge[i].to;
if (dep[v] != -1)
continue;
Q[rear++] = v;
dep[v] = dep[u] + 1;
gap[dep[v]]++;
}
}
}

long long S[MAXN];

long long sap(long long start, long long end, long long N) {
BFS(start, end);
memcpy(cur, head, sizeof(head));
long long top = 0;
long long u = start;
long long ans = 0;
while (dep[start] < N) {
if (u == end) {
long long Min = __LONG_LONG_MAX__;
long long inser;
for (long long i = 0; i < top; i++) {
if (Min > edge[S[i]].cap - edge[S[i]].flow) {
Min = edge[S[i]].cap - edge[S[i]].flow;
inser = i;
}
}
for (long long i = 0; i < top; i++) {
edge[S[i]].flow += Min;
edge[S[i] ^ 1].flow -= Min;
}
ans += Min;
top = inser;
u = edge[S[top] ^ 1].to;
continue;
}
bool flag = false;
long long v;
for (long long i = cur[u]; i != -1; i = edge[i].next) {
v = edge[i].to;
if (edge[i].cap - edge[i].flow && dep[v] + 1 == dep[u]) {
flag = true;
cur[u] = i;
break;
}
}
if (flag) {
S[top++] = cur[u];
u = v;
continue;
}
long long Min = N;
for (long long i = head[u]; i != -1; i = edge[i].next)
if (edge[i].cap - edge[i].flow && dep[edge[i].to] < Min) {
Min = dep[edge[i].to];
cur[u] = i;
}
gap[dep[u]]--;
if (!gap[dep[u]])
return ans;
dep[u] = Min + 1;
gap[dep[u]]++;
if (u != start)
u = edge[S[--top] ^ 1].to;
}
return ans;
}

long long n, m;
int a[MAXN], b[MAXN], c[MAXN];

void reISAP() {
init();
for (int i = 0; i < m; i++) {
if (c[i] == dist[b[i]] - dist[a[i]]) {
addedge(a[i], b[i], c[i]);
addedge(b[i], a[i], 0);
}
}
}

int main() {
#ifdef ACM_LOCAL
freopen("./in.txt", "r", stdin);
freopen("./out.txt", "w", stdout);
#endif
ios::sync_with_stdio(false);
long long t;
cin >> t;
while (t--) {
cin >> n >> m;
source = 1;
vertex_num = n + 1;
init();
for (long long i = 0; i < m; i++) {
cin >> a[i] >> b[i] >> c[i];
addedge(a[i], b[i], c[i]);
}
if (!SPFA()) {
cout << '0' << endl;
continue;
}
reISAP();
cout << sap(1, n, n) << endl;
}
return 0;
}