立志用最少的代碼做最高效的表達

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PAT甲級最優題解——>傳送門

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As an emergency rescue team leader of a city, you are given a special map of your country. The map shows several scattered cities connected by some roads. Amount of rescue teams in each city and the length of each road between any pair of cities are marked on the map. When there is an emergency call to you from some other city, your job is to lead your men to the place as quickly as possible, and at the mean time, call up as many hands on the way as possible.

Input Specification:
Each input file contains one test case. For each test case, the first line contains 4 positive integers: N (≤500) - the number of cities (and the cities are numbered from 0 to N?1), M - the number of roads, C1 and C2 - the cities that you are currently in and that you must save, respectively. The next line contains N integers, where the i-th integer is the number of rescue teams in the i-th city. Then M lines follow, each describes a road with three integers c1,c2and L, which are the pair of cities connected by a road and the length of that road, respectively. It is guaranteed that there exists at least one path from C1toC2

Output Specification:
For each test case, print in one line two numbers: the number of different shortest paths between C1 and C2, and the maximum amount of rescue teams you can possibly gather. All the numbers in a line must be separated by exactly one space, and there is no extra space allowed at the end of a line.

Sample Input:
5 6 0 2
1 2 1 5 3
0 1 1
0 2 2
0 3 1
1 2 1
2 4 1
3 4 1

Sample Output:
2 4

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題目分析

題意：
n個城市，每個城市都有救火隊，城市間道路雙向連通，要求輸出a城-b城最短路徑的數目，同時這些路徑中最多救火隊的數量

注意：
1、城市間道路雙向連通
2、輸出的不是最短路徑長度，是最短路徑數目（哭，卡了我半個小時）

分析：
本質為求最短路徑問題。

一般來講，求最短路有迪杰斯特拉和DFS兩種算法。個人比較推薦DFS，碼量小，思路更簡潔。

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DFS版代碼

#include<bits/stdc++.h> using namespace std;const int MAX_LEN = 0x3f3f3f3f; const int c_maxn = 500+10; int G[c_maxn][c_maxn]; //城市地圖 int c_pro[c_maxn]; //每個城市的救火隊數量 int vis[c_maxn]; //-1為有回路、0為正在訪問、1為已訪問 int c_n, r_n, sta, fin; //城市數量，道路數量，起點、終點 int Min=MAX_LEN, Max = -1, num_r = 0; //最優路程和救火隊數量 void dfs(int u, int len, int value) {if(len > Min) return; //剪枝 if(u == fin) {if(Min > len) { //如果路程更短，則直接更新 Min = len; Max = value;num_r = 1;} else if(Min == len) { //如果路程相等，則比較救火隊數量 Max = max(value, Max);num_r++;}return;}for(int v = 0; v < c_n; v++) {if(G[u][v] != -1) {if(vis[v] == 1) continue;vis[v] = 1;dfs(v, len+G[u][v], value+c_pro[v]);vis[v] = 0;} // cout << u << ' ' << v << ' ' << G[u][v] << '\n';} }int main() {memset(G, -1, sizeof(G));cin >> c_n >> r_n >> sta >> fin;for(int i = 0; i < c_n; i++) cin >> c_pro[i];for(int i = 0; i < r_n; i++) {int x1, x2, v;cin >> x1 >> x2 >> v;G[x1][x2] = G[x2][x1] = v;}vis[sta] = 1;dfs(sta, 0, c_pro[sta]); //起始節點、道路長度、起始救火隊數量 cout << num_r << ' ' << Max << '\n';return 0; } 超強干貨來襲 云風專訪：近40年碼齡，通宵達旦的技術人生

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