https://leetcode.com/problems/number-of-dice-rolls-with-target-sum/

numberOfDiceRollsWithTargetSum.js

// Memoized Recursive
// O(d*t)
// Unmemoized would be O((d*t)*f^d). I.e., recursive fn with branch factor f and max depth d
var numRollsToTarget = function(d, f, target) {
    
    const memo = {};
    const mod = Math.pow(10, 9) + 7;
    
    const rtt = (d, t) => {
        
        if(t <= 0 || // no dice scores will ever be zero or less
           d <= 0 || // and the question makes no sense with zero or fewer dice
           t < d  || // also, the min score for each die is 1, so t cannot be < d
           t > d*f   // also t cannot exceed the max allowable score
        ) return 0;  // in all such cases, return 0
        if(d === 1) return t<=f ? 1 : 0; // if there's only one dice, there can only be one or zero ways
        
        const key = `${d}:${t}`;
        if(memo[key]) return memo[key];
        
        let result = 0; 
        for(let i=1; i<=f; i++) // for all possible scores for this one die
          result = (result + rtt(d-1, t-i)) % mod; // figure out the result for d-1 dice
        return memo[key] = result % mod;
    };
    
    return rtt(d, target);
};