[leetcode]403. Frog Jump

知道是dp，但是没有思路

Use map to represent a mapping from the stone (not index) to the steps that can be taken from this stone.

so this will be

[0,1,3,5,6,8,12,17]

{17=[], 0=[1], 1=[1, 2], 3=[1, 2, 3], 5=[1, 2, 3], 6=[1, 2, 3, 4], 8=[1, 2, 3, 4], 12=[3, 4, 5]}

Notice that no need to calculate the last stone.

On each step, we look if any other stone can be reached from it, if so, we update that stone's steps by adding step, step + 1, step - 1. If we can reach the final stone, we return true. No need to calculate to the last stone.

Here is the code:

    public boolean canCross(int[] stones) {
        if (stones.length == 0) {
        	return true;
        }
        
        HashMap<Integer, HashSet<Integer>> map = new HashMap<Integer, HashSet<Integer>>(stones.length);
        map.put(0, new HashSet<Integer>());
        map.get(0).add(1);
        for (int i = 1; i < stones.length; i++) {
        	map.put(stones[i], new HashSet<Integer>() );
        }
        
        for (int i = 0; i < stones.length - 1; i++) {
        	int stone = stones[i];
        	for (int step : map.get(stone)) {
        		int reach = step + stone;
        		if (reach == stones[stones.length - 1]) {
        			return true;
        		}
        		HashSet<Integer> set = map.get(reach);
        		if (set != null) {
        		    set.add(step);
        		    if (step - 1 > 0) set.add(step - 1);
        		    set.add(step + 1);
        		}
        	}
        }
        
        return false;
    }