1449. Form Largest Integer With Digits That Add up to Target

Description

Given an array of integers cost and an integer target, return the maximum integer you can paint under the following rules:

• The cost of painting a digit (i + 1) is given by cost[i] (0-indexed).
• The total cost used must be equal to target.
• The integer does not have 0 digits.

Since the answer may be very large, return it as a string. If there is no way to paint any integer given the condition, return "0".

 

Example 1:

Input: cost = [4,3,2,5,6,7,2,5,5], target = 9
Output: "7772"
Explanation: The cost to paint the digit '7' is 2, and the digit '2' is 3. Then cost("7772") = 2*3+ 3*1 = 9. You could also paint "977", but "7772" is the largest number.
Digit    cost
  1  ->   4
  2  ->   3
  3  ->   2
  4  ->   5
  5  ->   6
  6  ->   7
  7  ->   2
  8  ->   5
  9  ->   5

Example 2:

Input: cost = [7,6,5,5,5,6,8,7,8], target = 12
Output: "85"
Explanation: The cost to paint the digit '8' is 7, and the digit '5' is 5. Then cost("85") = 7 + 5 = 12.

Example 3:

Input: cost = [2,4,6,2,4,6,4,4,4], target = 5
Output: "0"
Explanation: It is impossible to paint any integer with total cost equal to target.

 

Constraints:

• cost.length == 9
• 1 <= cost[i], target <= 5000

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n*target)
• Space complexity: O(target)

 

JavaScript

/**
 * @param {number[]} cost
 * @param {number} target
 * @return {string}
 */
const largestNumber = function (cost, target) {
  const n = cost.length;
  const dp = Array.from({ length: target + 1 }, () => '');

  const paintDigit = spendCost => {
    if (spendCost === target) return '';
    if (dp[spendCost] !== '') return dp[spendCost];
    let result = '0';

    for (let index = n - 1; index >= 0; index--) {
      const nextCost = spendCost + cost[index];

      if (nextCost > target) continue;
      const nextInteger = paintDigit(nextCost);

      if (nextInteger === '0') continue;
      const digit = `${index + 1}`;
      const integer = `${digit}${nextInteger}`;

      if (integer.length < result.length) continue;
      if (integer.length === result.length && integer <= result) continue;

      result = integer;
    }

    dp[spendCost] = result;

    return result;
  };

  return paintDigit(0);
};