簡介:
Floyd算法又稱爲插點法,是一種利用動態規劃的思想尋找給定的加權圖中多源點之間最短路徑的算法,與Dijkstra算法類似。該算法名稱以創始人之一、1978年圖靈獎獲得者、斯坦福大學計算機科學系教授羅伯特·弗洛伊德命名。
樣例求解:
代碼示例:
#include<iostream>
#include<algorithm>
using namespace std;
#define MAX_SIZE 100
#define INT 1e7
int graph[MAX_SIZE][MAX_SIZE];
int D[MAX_SIZE][MAX_SIZE];
int path[MAX_SIZE][MAX_SIZE];
void init_array(){
for(int i = 0; i < MAX_SIZE; i++){
for(int j = 0; j < MAX_SIZE; j++){
graph[i][j] = INT;
}
}
}
void init_graph(int m){
for(int i = 0; i < m; i++){
int x, y, z;
cin >> x >> y >> z;
graph[x][y] = z;
}
}
void floyd(int n){
for(int i = 1; i <= n; i++){
for(int j = 1; j <= n; j++){
D[i][j] = graph[i][j];
if(D[i][j] < INT && i != j)
path[i][j] = i;
else
path[i][j] = -1;
}
}
for(int i = 1; i <= n; i++){
for(int j = 1; j <= n; j++){
for(int k = 1; k <= n; k++){
if(D[i][k] + D[j][i] < D[j][k]){
D[j][k] = D[i][k] + D[j][i];
path[j][k] = path[i][k];
}
}
}
}
}
void print_path(int e, int n){//打印給定頂點到其他頂點的經過路徑
for(int i = 1; i <= n; i++){
if(path[e][i] != -1){
if(e != path[e][i])
cout << e << "," << i << ": " << e << "->" << path[e][i] << "->" << i << endl;
else
cout << e << "," << i << ": " << e << "->" << i << endl;
}
}
}
void print_distance(int e, int n){//打印給定頂點到其他頂點的距離
for(int i = 1; i<= n; i++){
if(D[e][i] != INT)
cout << e << "," << i << ": " << D[e][i] << endl;
}
}
int main(){
int n, m;
cin >> n >> m;
init_array();
init_graph(m);
floyd(n);
print_path(1, n);
print_distance(1, n);
return 0;
}
結果打印:
如上述圖片所示爲例,打印結果。