An imperative solution to the waterflow problem: http://philipnilsson.github.io/Badness10k/articles/waterflow/

waterFill

public static int waterFill(int[] arr){
	
	int rainCount=0;
	int max=arr[0];
	
	for(int i=0;i<arr.length;i++){
		max=(arr[i]>max)?arr[i]:max;
	}
	
	//fill it up
	for(int i=0;i<arr.length;i++){
		rainCount+=max-arr[i];
	}
	

	int height=max;
	int toRemove;
	boolean contained;
	
	//then carve out the space
	while(height>0){
		toRemove=0;
		contained=false;
		for(int i=0;i<arr.length;i++){
			
			if(isWall(height,arr[i])&&!contained){
				contained=true;
				rainCount-=toRemove;
				toRemove=0;
			}else if(isWall(height,arr[i])&&contained){
				toRemove=0;
			}

			if(!isWall(height,arr[i]))
				toRemove++;			
		}
		
		//remove the water that would have fallen out at the end
		if(!isWall(height,arr[arr.length-1])){
			rainCount-=toRemove;
		}
		
		height--;
	}
	
	
	
	return rainCount;
}

private static boolean isWall(int height, int indexHeight){
	return height<=indexHeight;
}