Algorithm: Leetcode Contest 372

2952. Minimum Number of Coins to be Added

You are given a 0-indexed integer array coins, representing the values of the coins available, and an integer target.

An integer x is obtainable if there exists a subsequence of coins that sums to x.

Return the minimum number of coins of any value that need to be added to the array so that every integer in the range [1, target] is obtainable.

A subsequence of an array is a new non-empty array that is formed from the original array by deleting some (possibly none) of the elements without disturbing the relative positions of the remaining elements.

Solution

 public int minimumAddedCoins(int[] coins, int target) {
    Arrays.sort(coins);

    long curRange = 0;
    int res = 0;
    for(int coin: coins) {
        while(curRange + 1 < coin) {
            res++;
            curRange += curRange + 1;
        }
        curRange += coin;
    }

    while(curRange < target) {
        curRange += curRange + 1;
        res++;
    }

    return res;
}

Retrospect

this is a typical problem called the minimum uncomposable sum.

I remember the solution I came up is permuting all coins, get the possible sum, then count how many gaps there are.

Seems I am not familiar with this classic problem so didn’t figure out the right solution.

another two problem is so hard for me… :(