[pull] master from wisdompeak:master #344

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	class Solution {
	public:
	int minJumps(vector<int>& nums) {
	int MAXA = *max_element(nums.begin(), nums.end());
	vector<int>spf(MAXA+1, 0);
	for (int i=2; i<=MAXA;i++) {
	if (spf[i]) continue;
	for (int j=i; j<=MAXA; j+=i)
	if (!spf[j]) spf[j]=i;
	}

	vector<vector<int>>prime_to_idx(MAXA+1);
	int n = nums.size();
	for (int i=0; i<n; i++) {
	int x = nums[i];
	while (x>1) {
	int p = spf[x];
	prime_to_idx[p].push_back(i);
	while (x%p==0) x/=p;
	}
	}

	const int INF = 1e9;
	vector<int>dist(n, INF);
	vector<int>used_prime(MAXA+1, 0);
	deque<int>q;
	dist[0] = 0;
	q.push_back(0);

	while (!q.empty()) {
	int i = q.front();
	q.pop_front();
	int d = dist[i];
	if (i==n-1)
	return d;

	if (i+1<n && dist[i+1]==INF) {
	dist[i+1] = d+1;
	q.push_back(i+1);
	}
	if (i-1>=0 && dist[i-1]==INF) {
	dist[i-1] = d+1;
	q.push_back(i-1);
	}
	int x = nums[i];
	if (x>1 && spf[x]==x) {
	if (used_prime[x]) continue;
	used_prime[x] = 1;
	for (int j: prime_to_idx[x]) {
	if (dist[j]==INF) {
	dist[j] = d+1;
	q.push_back(j);
	}
	}
	}
	}

	return 0;
	}
	};

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	### 3629.Minimum-Jumps-to-Reach-End-via-Prime-Teleportation

	很容易判断,总体框架必然是BFS。

	此题额外要求预处理nums里的每个质数与其倍数之间的映射关系,存入prime_to_idx中。一个高效的做法是在用埃氏筛判定1到M内的所有质数时,顺便记录下每个自然数的最小质因数(spf)。这样就方便我们对于nums的每个元素x做快速的质因数分解(不断去除以spf[x]),从而建立起它的所有质因子p到x的映射集合。

	BFS的写法比较常规。从队列里弹出index=i后,考察是否需要将`i+1`, `i-1`以及`prime_to_idx[nums[i]]`(仅当nums[i]是质数时)放入队列。注意对于已经处理过的质数需要略过。

1 change: 1 addition & 0 deletions Readme.md

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		[2493.Divide-Nodes-Into-the-Maximum-Number-of-Groups](https://github.com/wisdompeak/LeetCode/tree/master/BFS/2493.Divide-Nodes-Into-the-Maximum-Number-of-Groups) (H-)
		[2812.Find-the-Safest-Path-in-a-Grid](https://github.com/wisdompeak/LeetCode/tree/master/BFS/2812.Find-the-Safest-Path-in-a-Grid) (M+)
		[3552.Grid-Teleportation-Traversal](https://github.com/wisdompeak/LeetCode/tree/master/BFS/3552.Grid-Teleportation-Traversal) (H-)
	[3629.Minimum-Jumps-to-Reach-End-via-Prime-Teleportation](https://github.com/wisdompeak/LeetCode/tree/master/BFS/3629.Minimum-Jumps-to-Reach-End-via-Prime-Teleportation) (M+)
		* ``Multi State``
		[847.Shortest-Path-Visiting-All-Nodes](https://github.com/wisdompeak/LeetCode/tree/master/BFS/847.Shortest-Path-Visiting-All-Nodes) (H-)
		[864.Shortest-Path-to-Get-All-Keys](https://github.com/wisdompeak/LeetCode/tree/master/BFS/864.Shortest-Path-to-Get-All-Keys) (H-)
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