From 8a7724881974f95d8ec9a583a9a5c6449d9ddd35 Mon Sep 17 00:00:00 2001
From: xingyou wu <3050128610@qq.com>
Date: Thu, 3 Apr 2025 08:55:09 +0800
Subject: [PATCH] =?UTF-8?q?lanqiao=201460=20=E8=B7=AF=E5=BE=84(Dijkstra)?=
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---
 12lanqiao/test5-1.cpp | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 12lanqiao/test5-1.cpp

diff --git a/12lanqiao/test5-1.cpp b/12lanqiao/test5-1.cpp
new file mode 100644
index 0000000..fbe1cc1
--- /dev/null
+++ b/12lanqiao/test5-1.cpp
@@ -0,0 +1,43 @@
+// lanqiao 1460 路径(Dijkstra)
+#include<bits/stdc++.h>
+using namespace std;
+const int N = 3e3 + 10, INF = INT_MAX;
+int g[N][N]; // 领接矩阵
+bool vis[N]; // 标记数组
+int mindis[N]; // 最短路数组
+int s = 1, n = 2021;
+
+// 朴素版dijkstra-时间复杂度 O(n^2)
+void dijkstra(int s){
+    mindis[s] = 0;
+    for(int i = 1; i <= n; i++){
+        int mi = INF, cur = 0;
+        for(int j = 1; j <= n; j++){
+            if(!vis[j] && mindis[j] < mi){
+                mi = mindis[j];
+                cur = j;
+            }
+        }
+        vis[cur] = 1; // 已经确定起点到cur点的最短距离，所以要标记
+        // 以cur点作为中转点去更新起点到其他各点的距离
+        for(int i = 1; i <= n; i++){
+            if(!vis[i]&&g[cur][i] != 0){
+                if(mi + g[cur][i] < mindis[i]){
+                    mindis[i] = mi + g[cur][i];
+                }
+            }
+        }
+    }
+}
+
+int main(){
+    for(int i = 1; i <= n; i++){
+        for(int j = max(i-21, 1); j < min(i+21, 2021); j++){
+            if(i != j) g[i][j] = g[j][i] = lcm(i, j);
+        }
+    }
+    fill(mindis, mindis + N, INF);
+    dijkstra(s);
+    cout << mindis[n] << endl;
+    return 0;
+}