Problem:
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Minimum Spanning Tree

For a given weighted graph $G = (V, E)$, find the minimum spanning tree (MST) of $G$ and print total weight of edges belong to the MST.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, a $n \times n$ adjacency matrix $A$ which represents $G$ is given.
$a_{ij}$ denotes the weight of edge connecting vertex $i$ and vertex $j$. If there is no edge between $i$ and $j$, $a_{ij}$ is given by -1.

Output

Print the total weight of the minimum spanning tree of $G$.

Constraints

$1 \leq n \leq 100$

$0 \leq a_{ij} \leq 2,000$ (if $a_{ij} \neq -1$)

$a_{ij} = a_{ji}$

$G$ is a connected graph

Sample Input 1

5
-1 2 3 1 -1
2 -1 -1 4 -1
3 -1 -1 1 1
1 4 1 -1 3
-1 -1 1 3 -1

Sample Output 1

5

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in C (judge verdict: Time Limit Exceeded)

#include<stdio.h>

#define MAX_N 100
#define MAX_A 2000
int MAP[MAX_N][MAX_N];
int colorflag[MAX_N];

int MinimumSpanningTree(int n) {
	int i, j, k, sum, min, min_ofnode, color[n];

	// 初期化
	k=0;
	colorflag[0] = 1;
	color[0] = k;
	for( i=0; i<n; i++) colorflag[i] = 0;

	while(1) {
		// ノードk個の最小全域木を求める
		min = MAX_A + 1;
		for( i=0; i<k; i++) {
			for( j=i+1; j<n; j++) {
				if(colorflag[j] == 1) continue;
				if(MAP[ color[i] ][j] < 0) continue;
				if(MAP[ color[i] ][j] < min) {
					min = MAP[ color[i] ][j];
					min_ofnode = j;
				}
			}
		}
		
		// ノードk+1個の最小全域木の作成
		if(++k <= n) {
			color[k] = min_ofnode;
			colorflag[min_ofnode] = 1;
			sum += min;
		}
	}

	return sum;
}

int main(void) {
	int n, i, j;

	// input
	scanf("%d", &n);
	for( i=0; i<n; i++) {
		for( j=0; j<n; j++) {
			scanf("%d", &MAP[i][j]);
		}
	}

	// output	
	printf("%d\n", MinimumSpanningTree(n) );
	return 0;
}