Form Largest Integer With Digits That Add up to Target — LeetCode 1449 Python Solution

The problem

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.

Example

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.

Python solution

class Solution:
    def largestNumber(self, cost: List[int], target: int) -> str:
        f = [[-inf] * (target + 1) for _ in range(10)]
        f[0][0] = 0
        g = [[0] * (target + 1) for _ in range(10)]
        for i, c in enumerate(cost, 1):
            for j in range(target + 1):
                if j < c or f[i][j - c] + 1 < f[i - 1][j]:
                    f[i][j] = f[i - 1][j]
                    g[i][j] = j
                else:
                    f[i][j] = f[i][j - c] + 1
                    g[i][j] = j - c
        if f[9][target] < 0:
            return "0"
        ans = []
        i, j = 9, target
        while i:
            if j == g[i][j]:
                i -= 1
            else:
                ans.append(str(i))
                j = g[i][j]
        return "".join(ans)

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1449. Form Largest Integer With Digits That Add up to Target is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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