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NumRollsToTarget.js
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NumRollsToTarget.js
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function numRollsToTarget(n, k, target) {
// MOD is a constant used for taking the modulo to prevent overflow
const MOD = 10 ** 9 + 7;
// dp is a 2D array used for memoization to store intermediate results
const dp = Array.from({ length: n + 1 }, () => Array(target + 1).fill(-1));
// recursion is a helper function that performs the actual recursive computation
const recursion = (dp, n, k, target) => {
// Base case: if both the number of dice and the target are zero, there is one way to achieve it
if (target === 0 && n === 0) return 1;
// Base case: if either the number of dice is zero or the target is less than or equal to zero, there are no ways
if (n === 0 || target <= 0) return 0;
// If the result for the current state (n, target) is already calculated, return it
if (dp[n][target] !== -1) return dp[n][target] % MOD;
// Initialize the ways variable to count the number of ways to achieve the target
let ways = 0;
// Iterate through all possible outcomes of rolling a die (from 1 to k)
for (let i = 1; i <= k; i++) {
// Recursively calculate the number of ways for the next state (n-1, target-i)
ways = (ways + recursion(dp, n - 1, k, target - i)) % MOD;
}
// Store the result in the memoization table and return it
dp[n][target] = ways % MOD;
// console.log(dp);
return dp[n][target];
};
// Start the recursion with the initial values of n, k, and target
return recursion(dp, n, k, target);
}
console.log(numRollsToTarget(2, 6, 7));