洛谷P1135多题解

 解法1：BFS，有n个节点每个节点最多被访问一次，所以BFS时间复杂度为O(n)。注意a==b的特判。

#include<iostream>
#include<cstring>
#include<queue>
using namespace std;
const int N = 205;
int n, a, b;
int k[N], s[N];
bool st[N];
int dy[2];
int main() {
	cin >> n >> a >> b;
	if (a == b) {
		cout << 0 << endl;
		return 0;
	}
	for (int i = 1; i <= n; i++) {
		cin >> k[i];
	}
	memset(s, -1, sizeof(s));
	s[a] = 0;
	st[a] = true;
	queue<int> q;
	q.push(a);
	while (q.size()) {
		int t = q.front();
		q.pop();
		dy[0] = k[t], dy[1] = -k[t];
		for (int i = 0; i < 2; i++) {
			int u = t + dy[i];
			if (u == b) {
				cout << s[t] + 1 << endl;
				return 0;
			}
			if (u < 1 || u > n || st[u])continue;
			st[u] = true;
			s[u] = s[t] + 1;
			q.push(u);
		}
	}
	cout << -1 << endl;
	return 0;
}

解法2：DFS，时间复杂度是O(2^n)有点大。剪了枝还是TLE

#include<iostream>
#include<climits>
#include<cstring>
using namespace std;
int n, a, b;
int k[205];
bool st[205];
int minn = INT_MAX;
void dfs(int u, int step){
	if(step >= minn)return;
	if(u == b){
		minn = min(minn, step);
		return;
	}
	if(u < 1 || u > n || st[u])return;
	st[u] = true;
	int up = u + k[u];
	if(up <= n){
		dfs(up, step + 1);
	}
	int down = u - k[u];
	if(down >= 1){
		dfs(down, step + 1);
	}
	st[u] = false;
}
int main(){
	cin >> n >> a >> b;
	for(int i = 1; i <= n; i++){
		cin >> k[i];
	}
	dfs(a, 0);
	if(minn == INT_MAX)cout << -1 << endl;
	else cout << minn << endl;
	
	return 0;
}

解法3：迪杰斯特拉堆优化，时间复杂度为O((v+e)logv)

#include<iostream>
#include<cstring>
#include<queue>
using namespace std;
const int N = 205;
int k[N];
bool st[N];
int dist[N];
typedef pair<int, int>PII;
int n, a, b;
int dijkstra(){
	memset(dist, 0x3f, sizeof(dist));
	dist[a] = 0;
	priority_queue<PII, vector<PII>, greater<PII>>heap;
	heap.push({0, a});
	while(heap.size()){
		auto t = heap.top();
		heap.pop();
		int ver = t.second, distance = t.first;
		if(ver == b)return distance;
		if(st[ver])continue;
		st[ver] = true;
		
		int up = ver + k[ver];
		if(up <= n && dist[up] > distance + 1){
			dist[up] = distance + 1;
			heap.push({dist[up], up});
		}
		
		int down = ver - k[ver];
		if(down >= 1 && dist[down] > distance + 1){
			dist[down] = distance + 1;
			heap.push({dist[down], down});
		}
	}
	return -1;
}
int main(){
	cin >> n >> a >> b;
	for(int i = 1; i <= n; i++){
		cin >> k[i];
	}
	int t = dijkstra();
	cout << t << endl;
	
	return 0;
}

解法4：SPFA，