Palindrome Partitioning II

class Solution {
    public int minCut(String s) {
        HashMap<String,Integer> memo=new HashMap<String,Integer>();
        return minimumCuts(s,0,s.length()-1,memo);
    }
    private int minimumCuts(String s, int start, int end,HashMap<String,Integer> memo){
        if(isPalindrome(s,start,end)){
            return 0;
        }
        String currentKey=start+"_"+end;
        if(memo.containsKey(currentKey)){
            return memo.get(currentKey);
        }
        int ans=1000000;
        for(int i=start;i<end;i++){
            if(isPalindrome(s,start,i)){
                int tempAns=1+minimumCuts(s,i+1,end,memo);
                ans=Math.min(ans,tempAns);
            }
        }
        memo.put(currentKey,ans);
        return ans;
    }
    
    private boolean isPalindrome(String s, int start, int end){
        while(start<=end){
            if(s.charAt(start)!=s.charAt(end)){
                return false;
            }
            start++;
            end--;
        }
        return true;
    }
}