Data_Structure/作業/unit12/all-pairs-shortest-path-v1.c

/*
Program: all-pairs-shortest-path-v1.c (Report comments/bugs to chikh@yuntech.edu.tw)
Function: <EFBFBD><EFBFBD><EFBFBD>@Floyd-Warshall<EFBFBD>t<EFBFBD><EFBFBD><EFBFBD>k<EFBFBD>A<EFBFBD>H<EFBFBD>Ѫ<EFBFBD><EFBFBD><EFBFBD>shortestPath.dat<EFBFBD>ɮק@<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>J 
Notes: 
	1) Floyd-Warshall<EFBFBD>t<EFBFBD><EFBFBD><EFBFBD>k<EFBFBD><EFBFBD><EFBFBD>u<EFBFBD>ʺA<EFBFBD>W<EFBFBD><EFBFBD><EFBFBD>v(dynamic programming)<EFBFBD>k
	2) Ū<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ʃҥε{<EFBFBD><EFBFBD><EFBFBD>X<EFBFBD><EFBFBD><EFBFBD>ۮѪ<EFBFBD><EFBFBD><EFBFBD>shortestPath.c<EFBFBD><EFBFBD><EFBFBD>վ<EFBFBD><EFBFBD>禡<EFBFBD><EFBFBD><EFBFBD>쫬(prototype)<EFBFBD>B<EFBFBD>ץΥ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ܼ<EFBFBD> 
	3) <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ѧ<EFBFBD> https://www.geeksforgeeks.org/floyd-warshall-algorithm-dp-16/
	   <EFBFBD>P https://www.programiz.com/dsa/floyd-warshall-algorithm 
*/

#include <stdio.h>
#include <stdlib.h>	/* for exit() */

#define MAX_V 		100			/* <20>̤j<CCA4><6A><EFBFBD>I<EFBFBD><49> */
#define Inf 		1073741823	/* <20><><EFBFBD><EFBFBD>2^30-1<><31><EFBFBD>j<EFBFBD>Ʀr<C6A6>A<EFBFBD><41><EFBFBD><EFBFBD><EFBFBD>{<7B><><EFBFBD><EFBFBD><EFBFBD>]<5D><><EFBFBD>L<EFBFBD><4C><EFBFBD>j<EFBFBD>ȡF<C8A1>i<EFBFBD><69><EFBFBD><EFBFBD>limits.h<>w<EFBFBD>q<EFBFBD><71>INT_MAX */

void init(int A[][MAX_V], int Y[][MAX_V], int *N)	/* Ū<><C5AA><EFBFBD><EFBFBD><EFBFBD>J<EFBFBD><4A><EFBFBD><EFBFBD><EFBFBD>ɡB<C9A1>]<5D>w<EFBFBD>۾F<DBBE>x<EFBFBD>}<7D>A<EFBFBD><41><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƶ<EFBFBD><C6B5>c<EFBFBD>@<40><><EFBFBD>l<EFBFBD><6C> */ 
{
    FILE *fptr;
    int  i, j;
    int  weight;

    if ((fptr=fopen("shortestPath.dat","r")) == NULL) {	/* <20>}<7D>Ҹ<EFBFBD><D2B8><EFBFBD><EFBFBD><EFBFBD> */ 
        perror("shortestPath.dat");
        exit(1);
    }

    fscanf(fptr,"%d",N);		/* Ū<><C5AA><EFBFBD>ϧθ`<60>I<EFBFBD><49> */
    for (i = 1; i <= *N; i++ )
        for (j = 1; j <= *N; j++) {
            A[i][j] = (i==j)? 0: Inf;	/* <20><><EFBFBD>l<EFBFBD><6C>A[1..N][1..N]<5D>۾F<DBBE>x<EFBFBD>}<7D>A<EFBFBD>Ҧ<EFBFBD><D2A6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>w<EFBFBD>]<5D><><EFBFBD><EFBFBD> */
            Y[i][j] = (i==j)? i: -1;
       	}
 
    while (fscanf(fptr,"%d %d %d",&i,&j,&weight) != EOF) { 
    	A[i][j] = weight;	/* Ū<><C5AA><EFBFBD>s<EFBFBD><73><EFBFBD><EFBFBD><EFBFBD>Ii<49>Pj<50><6A><EFBFBD>䪺<EFBFBD>v<EFBFBD><76><EFBFBD><EFBFBD> */
    	Y[i][j] = i;		/* Y[i][j]<5D>w<EFBFBD>]<5D><>i */ 
    } 
    
	fclose(fptr);
}

/* <20><><EFBFBD>UfloydWarshall()<29>禡<EFBFBD>N<EFBFBD>C<EFBFBD>G<EFBFBD><47><EFBFBD>I(i,j)<29><><EFBFBD><EFBFBD><EFBFBD>p<EFBFBD><70><EFBFBD>̵u<CCB5>Z<EFBFBD><5A><EFBFBD>ȡA<C8A1>ðO<C3B0><4F><EFBFBD>i<EFBFBD>g<EFBFBD>ѭ<EFBFBD><D1AD>Ǥ<EFBFBD><C7A4>~<7E><><EFBFBD>I<EFBFBD>F<EFBFBD><46><EFBFBD>̵u */ 
void floydWarshall(int A[][MAX_V], int Y[][MAX_V], int N) 
{
	int i, j, k;

	for (k = 1; k <= N; k++) 
    	for (i = 1; i < N; i++) 
      		for (j = 1; j <= N; j++) 
        		if (A[i][k] + A[k][j] < A[i][j]) { //if (A[i][k] != Inf && A[k][j] != Inf && A[i][k] + A[k][j] < A[i][j]) { 	
        			A[i][j] = A[i][k] + A[k][j];
					Y[i][j] = Y[k][j]; /* <20><><EFBFBD>g<EFBFBD><67> Y[i][j] = k */
				}
	/* <20>W<EFBFBD><57><EFBFBD>G<EFBFBD>hfor<6F>j<EFBFBD><6A><EFBFBD>Ω<EFBFBD><CEA9>ץ<EFBFBD><D7A5>C<EFBFBD>G<EFBFBD><47><EFBFBD>I(i,j)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Z<EFBFBD><5A><EFBFBD>ȡA<C8A1>˵<EFBFBD><CBB5><EFBFBD><EFBFBD>_<EFBFBD>g<EFBFBD><67>k(<28><><EFBFBD>@<40>ӥi<D3A5>઺<EFBFBD><E0AABA><EFBFBD>~<7E>I)<29><><EFBFBD>o<EFBFBD><6F><EFBFBD><EFBFBD><EFBFBD>p<EFBFBD>Z<EFBFBD><5A><EFBFBD><EFBFBD> */ 
	/* 
	<EFBFBD>d<EFBFBD>Nline 53<EFBFBD><EFBFBD><EFBFBD>g<EFBFBD>k<EFBFBD>A<EFBFBD><EFBFBD><EFBFBD>g<EFBFBD><EFBFBD> Y[i][j] = k<EFBFBD>A<EFBFBD>P<EFBFBD>ǥi<EFBFBD>Ϥ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>t<EFBFBD>O<EFBFBD><EFBFBD>?! 
	<EFBFBD>z<EFBFBD>ѡG<EFBFBD><EFBFBD>line 37<EFBFBD>i<EFBFBD><EFBFBD><EFBFBD>A<EFBFBD>Y<EFBFBD>G<EFBFBD><EFBFBD><EFBFBD>I(i,j)<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>s<EFBFBD>b<EFBFBD>A<EFBFBD>N<EFBFBD><EFBFBD>Y[i][j]<EFBFBD>w<EFBFBD>]<EFBFBD><EFBFBD>i<EFBFBD>C
	<EFBFBD>]<EFBFBD><EFBFBD><EFBFBD>A<EFBFBD>bline 53<EFBFBD><EFBFBD><EFBFBD>A<EFBFBD>Yk<EFBFBD>Pj<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>s<EFBFBD>b<EFBFBD>A<EFBFBD>g<EFBFBD><EFBFBD>Y[k][j]<EFBFBD>P<EFBFBD>g<EFBFBD><EFBFBD>k<EFBFBD><EFBFBD><EFBFBD>N<EFBFBD>q<EFBFBD>ۦP<EFBFBD>A<EFBFBD>N<EFBFBD><EFBFBD><EFBFBD><EFBFBD>j<EFBFBD><EFBFBD><EFBFBD>e<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>~<EFBFBD>I<EFBFBD><EFBFBD>k<EFBFBD>C 
	<EFBFBD><EFBFBD><EFBFBD>Yk<EFBFBD>Pj<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>L<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>s<EFBFBD><EFBFBD><EFBFBD>A<EFBFBD>h<EFBFBD>]Y[i][j] = Y[k][j]<EFBFBD>A<EFBFBD>N<EFBFBD><EFBFBD>i<EFBFBD><EFBFBD>j<EFBFBD><EFBFBD><EFBFBD>̫<EFBFBD><EFBFBD>@<EFBFBD>Ӥ<EFBFBD><EFBFBD>~<EFBFBD>I<EFBFBD>N<EFBFBD>ѱqk<EFBFBD><EFBFBD>j<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>|<EFBFBD>ҰO<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>̫<EFBFBD> 
	<EFBFBD>@<EFBFBD>Ӥ<EFBFBD><EFBFBD>~<EFBFBD>I<EFBFBD>M<EFBFBD>w(Y[k][j]<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ثe<EFBFBD>Ҫ<EFBFBD>k<EFBFBD><EFBFBD>j<EFBFBD>Z<EFBFBD><EFBFBD>j<EFBFBD>̪񪺤<EFBFBD><EFBFBD>~<EFBFBD>I)<EFBFBD>C 
	<EFBFBD>z<EFBFBD>Lline 53<EFBFBD>]<EFBFBD>mY<EFBFBD>x<EFBFBD>}<EFBFBD><EFBFBD><EFBFBD>e<EFBFBD>A<EFBFBD>N<EFBFBD>i<EFBFBD>^<EFBFBD><EFBFBD><EFBFBD>o<EFBFBD><EFBFBD><EFBFBD>̵u<EFBFBD><EFBFBD><EFBFBD>|  
	*/	
}

void printMatrix(int A[][MAX_V], int N) 
{
	int i, j;
	
	printf("\n\n<EFBFBD>B<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>o<EFBFBD><EFBFBD><EFBFBD>I(i,j)<29><><EFBFBD><EFBFBD><EFBFBD>x<EFBFBD>}<7D><><EFBFBD>T<EFBFBD>p<EFBFBD>U<EFBFBD>G\n       ");
	for (i = 1; i <= N; i++) printf("%4d",i);
	for (i = 0; i <= N; i++) printf("%4s",i==0? "\n      +":"----");
		
  	for (i = 1; i <= N; i++) {
  		printf("\n<EFBFBD><EFBFBD><EFBFBD>I%d |",i);
    	for (j = 1; j <= N; j++) {
      		if (A[i][j] == Inf)
        		printf("%5s","<EFBFBD><EFBFBD>");	/* somewhat weird to use %5s instead of %4s here */
      		else
        		printf("%4d",A[i][j]);
    	}
    	//printf("\n");
  	}
}

int backtrack(int A[][MAX_V], int Y[][MAX_V], int source, int dest) 
{
	int distance, k = Y[source][dest];	/* k<><6B>source<63><65>dest<73><74><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>~<7E><><EFBFBD>I */ 
	
	if (source == dest) {
		printf("<EFBFBD><EFBFBD><EFBFBD>I%d <20><>",source);
		return A[source][dest];
	}
	if (Y[source][dest] == -1) {
        printf("<EFBFBD><EFBFBD><EFBFBD>I%d<>P%d<><64><EFBFBD><EFBFBD><EFBFBD>S<EFBFBD><53><EFBFBD><EFBFBD><EFBFBD>|<7C>s<EFBFBD>b:(  ",source,dest);
        return Inf;
    }
    distance = backtrack(A,Y,source,k);
    printf(" %d <20><>",dest);
    
	return distance+A[k][dest];
}

void traverseMatrix(int A[][MAX_V],int Y[][MAX_V]) 
{
	int distance, source, sink; 
	
	printf("\n\n<EFBFBD>d<EFBFBD>ߥ<EFBFBD><EFBFBD>G<EFBFBD>I<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>̵u<EFBFBD><EFBFBD><EFBFBD>|\n<EFBFBD><EFBFBD><EFBFBD>I(0<>h<EFBFBD>X<EFBFBD>d<EFBFBD><64>) => ");
    scanf("%d",&source);
    if (source == 0) return;
    printf("<EFBFBD><EFBFBD><EFBFBD>I(0<>h<EFBFBD>X<EFBFBD>d<EFBFBD><64>) => ");
    scanf("%d",&sink);
    if (sink == 0) return;
	
	printf("<EFBFBD>̵u<EFBFBD><EFBFBD><EFBFBD>|<7C>G");
	distance = backtrack(A,Y,source,sink);
	printf("\b\b (<28>Ҹg<D2B8><67><EFBFBD><EFBFBD><EFBFBD>Z<EFBFBD><5A><EFBFBD>`<60>M=%d)(<28>d<EFBFBD><64>A[%d][%d]=%d)",distance,source,sink,A[source][sink]);	/* <20>ٰ<EFBFBD><D9B0>̫<EFBFBD><CCAB><EFBFBD><EFBFBD>ܦh<DCA6>l<EFBFBD><6C>"<22><>" */ 
}

int main() 
{
	int N, A[MAX_V][MAX_V], Y[MAX_V][MAX_V] = {0};
	/* N<><4E><EFBFBD>ϩҧt<D2A7><74><EFBFBD><EFBFBD><EFBFBD>I<EFBFBD><49><EFBFBD><EFBFBD><EFBFBD>`<60>ơFA[1..N][1..N]<5D><><EFBFBD>ϧΪ<CFA7><CEAA>۾F<DBBE>x<EFBFBD>} */
	/* Y[1..N][1..N]<5D>O<EFBFBD><4F><EFBFBD><EFBFBD><EFBFBD>G<EFBFBD><47><EFBFBD>I(i,j)<29><><EFBFBD><EFBFBD><EFBFBD>Zj<5A>̪񪺤<CCAA><F1AABAA4>~<7E>I<EFBFBD>A<EFBFBD>N<EFBFBD>Ω<EFBFBD><CEA9>̵u<CCB5><75><EFBFBD>|<7C>^<5E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> */
	
	printf("\n*** <20><> all-pairs shortest-path <20><><EFBFBD>D ***");
            
	init(A,Y,&N);			/* Ū<><C5AA><EFBFBD><EFBFBD><EFBFBD>J<EFBFBD><4A><EFBFBD><EFBFBD><EFBFBD>ɡB<C9A1>]<5D>w<EFBFBD>۾F<DBBE>x<EFBFBD>}<7D>A<EFBFBD>ç<EFBFBD><C3A7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƶ<EFBFBD><C6B5>c<EFBFBD>@<40><><EFBFBD>l<EFBFBD><6C> */
  	floydWarshall(A,Y,N);
  	printMatrix(A,N);
  	//printMatrix(Y,N);
  	traverseMatrix(A,Y);
	
	return 0; 
}