C - Heavy Transportation——spfa()算法

最新推荐文章于 2022-02-21 09:22:11 发布

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#spfa-算法 #最短路

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本文介绍了一种基于SPFA算法的最短路径问题变形求解方法，重点在于如何找到从起点到终点所有可达路径中权值最小的最大值。通过对比正确与错误的实现代码，强调了数组初始化的重要性。

Think:
1知识点：spfa()算法+最短路径变形
2题意：求n = 1的点到 n = n 的所有可达路径中（当前路径权值最小的）最大值
3反思：注意不要忘记e数组初始化

以下为Wrong Answer代码——题意理解错误

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>

using namespace std;

const int N = 1e3 + 4;
const int inf = 0x3f3f3f3f;

int n, e[N][N], dis[N], vis[N];

void spfa();

int main(){
    int T, k, m, i, u, v, w;
    scanf("%d", &T);
    for(k = 1; k <= T; k++){
        scanf("%d %d", &n, &m);
        memset(e, 0, sizeof(e));
        for(i = 1; i <= m; i++){
            scanf("%d %d %d", &u, &v, &w);
            e[u][v] = e[v][u] = w;
        }
        spfa();
        printf("Scenario #%d:\n", k);
        printf("%d\n", dis[n]);
        printf("\n");
    }
    return 0;
}
void spfa(){
    queue <int> q;
    memset(dis, inf, sizeof(dis));
    memset(vis, 0, sizeof(vis));

    q.push(1), dis[1] = 0, vis[1] = 1;
    while(!q.empty()){
        int t1 = q.front();
        q.pop();
        vis[t1] = 0;
        for(int v = 1; v <= n; v++){
            if(max(dis[t1], e[t1][v]) < dis[v]){
                dis[v] = max(dis[t1], e[t1][v]);
                if(!vis[v]){
                    q.push(v);
                    vis[v] = 1;
                }
            }
        }
    }
}

以下为Wrong Answer代码——e数组未初始化

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>

using namespace std;

const int inf = 0x3f3f3f3f;
const int N = 1014;

int n, m, e[N][N], vis[N], dis[N];

void spfa(int x);

int main(){
    int k = 1, T, i, u, v, w;
    scanf("%d", &T);
    while(T--){
        scanf("%d %d", &n, &m);
        for(i = 0; i < m; i++){
            scanf("%d %d %d", &u, &v, &w);
            e[u][v] = e[v][u] = w;
        }
        spfa(1);
        printf("Scenario #%d:\n", k++);
        printf("%d\n", dis[n]);
        printf("\n");
    }
    return 0;
}
void spfa(int x){
    queue <int> q;
    while(!q.empty()){
        q.pop();
    }
    memset(vis, 0, sizeof(vis));
    memset(dis, 0, sizeof(dis));
    vis[x] = 1, dis[x] = inf;
    q.push(x);
    while(!q.empty()){
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for(int i = 1; i <= n; i++){
            if(min(dis[u], e[u][i]) > dis[i]){
                dis[i] = min(dis[u], e[u][i]);
                if(!vis[i]){
                    vis[i] = 1;
                    q.push(i);
                }
            }
        }
    }
}

以下为Accepted代码

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>

using namespace std;

const int inf = 0x3f3f3f3f;
const int N = 1014;

int n, m, e[N][N], vis[N], dis[N];

void spfa(int x);

int main(){
    int k = 1, T, i, u, v, w;
    scanf("%d", &T);
    while(T--){
        scanf("%d %d", &n, &m);
        memset(e, 0, sizeof(e));/*注意不要忘记初始化*/
        for(i = 0; i < m; i++){
            scanf("%d %d %d", &u, &v, &w);
            e[u][v] = e[v][u] = w;
        }
        spfa(1);
        printf("Scenario #%d:\n", k++);
        printf("%d\n", dis[n]);
        printf("\n");
    }
    return 0;
}
void spfa(int x){
    queue <int> q;
    while(!q.empty()){
        q.pop();
    }
    memset(vis, 0, sizeof(vis));
    memset(dis, 0, sizeof(dis));
    vis[x] = 1, dis[x] = inf;
    q.push(x);
    while(!q.empty()){
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for(int i = 1; i <= n; i++){
            if(min(dis[u], e[u][i]) > dis[i]){
                dis[i] = min(dis[u], e[u][i]);
                if(!vis[i]){
                    vis[i] = 1;
                    q.push(i);
                }
            }
        }
    }
}