Press "Enter" to skip to content

Posts published in “Greedy”

花花酱 LeetCode 1850. Minimum Adjacent Swaps to Reach the Kth Smallest Number

You are given a string num, representing a large integer, and an integer k.

We call some integer wonderful if it is a permutation of the digits in num and is greater in value than num. There can be many wonderful integers. However, we only care about the smallest-valued ones.

  • For example, when num = "5489355142":
    • The 1st smallest wonderful integer is "5489355214".
    • The 2nd smallest wonderful integer is "5489355241".
    • The 3rd smallest wonderful integer is "5489355412".
    • The 4th smallest wonderful integer is "5489355421".

Return the minimum number of adjacent digit swaps that needs to be applied to num to reach the kth smallest wonderful integer.

The tests are generated in such a way that kth smallest wonderful integer exists.

Example 1:

Input: num = "5489355142", k = 4
Output: 2
Explanation: The 4th smallest wonderful number is "5489355421". To get this number:
- Swap index 7 with index 8: "5489355142" -> "5489355412"
- Swap index 8 with index 9: "5489355412" -> "5489355421"

Example 2:

Input: num = "11112", k = 4
Output: 4
Explanation: The 4th smallest wonderful number is "21111". To get this number:
- Swap index 3 with index 4: "11112" -> "11121"
- Swap index 2 with index 3: "11121" -> "11211"
- Swap index 1 with index 2: "11211" -> "12111"
- Swap index 0 with index 1: "12111" -> "21111"

Example 3:

Input: num = "00123", k = 1
Output: 1
Explanation: The 1st smallest wonderful number is "00132". To get this number:
- Swap index 3 with index 4: "00123" -> "00132"

Constraints:

  • 2 <= num.length <= 1000
  • 1 <= k <= 1000
  • num only consists of digits.

Solution: Next Permutation + Greedy

Time complexity: O(k*n + n^2)
Space complexity: O(n)

C++

花花酱 LeetCode 1833. Maximum Ice Cream Bars

It is a sweltering summer day, and a boy wants to buy some ice cream bars.

At the store, there are n ice cream bars. You are given an array costs of length n, where costs[i] is the price of the ith ice cream bar in coins. The boy initially has coins coins to spend, and he wants to buy as many ice cream bars as possible. 

Return the maximum number of ice cream bars the boy can buy with coins coins.

Note: The boy can buy the ice cream bars in any order.

Example 1:

Input: costs = [1,3,2,4,1], coins = 7
Output: 4
Explanation: The boy can buy ice cream bars at indices 0,1,2,4 for a total price of 1 + 3 + 2 + 1 = 7.

Example 2:

Input: costs = [10,6,8,7,7,8], coins = 5
Output: 0
Explanation: The boy cannot afford any of the ice cream bars.

Example 3:

Input: costs = [1,6,3,1,2,5], coins = 20
Output: 6
Explanation: The boy can buy all the ice cream bars for a total price of 1 + 6 + 3 + 1 + 2 + 5 = 18.

Constraints:

  • costs.length == n
  • 1 <= n <= 105
  • 1 <= costs[i] <= 105
  • 1 <= coins <= 108

Solution: Greedy

Sort by price in ascending order, buy from the lowest price to the highest price.

Time complexity: O(nlogn)
Space complexity: O(1)

C++

花花酱 LeetCode 1798. Maximum Number of Consecutive Values You Can Make

You are given an integer array coins of length n which represents the n coins that you own. The value of the ith coin is coins[i]. You can make some value x if you can choose some of your n coins such that their values sum up to x.

Return the maximum number of consecutive integer values that you can make with your coins starting from and including 0.

Note that you may have multiple coins of the same value.

Example 1:

Input: coins = [1,3]
Output: 2
Explanation: You can make the following values:
- 0: take []
- 1: take [1]
You can make 2 consecutive integer values starting from 0.

Example 2:

Input: coins = [1,1,1,4]
Output: 8
Explanation: You can make the following values:
- 0: take []
- 1: take [1]
- 2: take [1,1]
- 3: take [1,1,1]
- 4: take [4]
- 5: take [4,1]
- 6: take [4,1,1]
- 7: take [4,1,1,1]
You can make 8 consecutive integer values starting from 0.

Example 3:

Input: nums = [1,4,10,3,1]
Output: 20

Constraints:

  • coins.length == n
  • 1 <= n <= 4 * 104
  • 1 <= coins[i] <= 4 * 104

Solution: Greedy + Math

We want to start with smaller values, sort input array in ascending order.

First of all, the first number has to be 1 in order to generate sum of 1.
Assuming the first i numbers can generate 0 ~ k.
Then the i+1-th number x can be used if and only if x <= k + 1, such that we can have a consecutive sum of k + 1 by adding x to a sum between [0, k] and the new maximum sum we have will be k + x.

Time complexity: O(nlogn)
Space complexity: O(1)

C++

花花酱 LeetCode 1775. Equal Sum Arrays With Minimum Number of Operations

You are given two arrays of integers nums1 and nums2, possibly of different lengths. The values in the arrays are between 1 and 6, inclusive.

In one operation, you can change any integer’s value in any of the arrays to any value between 1 and 6, inclusive.

Return the minimum number of operations required to make the sum of values in nums1 equal to the sum of values in nums2. Return -1​​​​​ if it is not possible to make the sum of the two arrays equal.

Example 1:

Input: nums1 = [1,2,3,4,5,6], nums2 = [1,1,2,2,2,2]
Output: 3
Explanation: You can make the sums of nums1 and nums2 equal with 3 operations. All indices are 0-indexed.
- Change nums2[0] to 6. nums1 = [1,2,3,4,5,6], nums2 = [6,1,2,2,2,2].
- Change nums1[5] to 1. nums1 = [1,2,3,4,5,1], nums2 = [6,1,2,2,2,2].
- Change nums1[2] to 2. nums1 = [1,2,2,4,5,1], nums2 = [6,1,2,2,2,2].

Example 2:

Input: nums1 = [1,1,1,1,1,1,1], nums2 = [6]
Output: -1
Explanation: There is no way to decrease the sum of nums1 or to increase the sum of nums2 to make them equal.

Example 3:

Input: nums1 = [6,6], nums2 = [1]
Output: 3
Explanation: You can make the sums of nums1 and nums2 equal with 3 operations. All indices are 0-indexed. 
- Change nums1[0] to 2. nums1 = [2,6], nums2 = [1].
- Change nums1[1] to 2. nums1 = [2,2], nums2 = [1].
- Change nums2[0] to 4. nums1 = [2,2], nums2 = [4].

Constraints:

  • 1 <= nums1.length, nums2.length <= 105
  • 1 <= nums1[i], nums2[i] <= 6

Solution: Greedy

Assuming sum(nums1) < sum(nums2),
sort both arrays
* scan nums1 from left to right, we need to increase the value form the smallest one.
* scan nums2 from right to left, we need to decrease the value from the largest one.
Each time, select the one with the largest delta to change.

e.g. nums1[i] = 2, nums[j] = 4, delta1 = 6 – 2 = 4, delta2 = 4 – 1 = 3, Increase 2 to 6 instead of decreasing 4 to 1.

Time complexity: O(mlogm + nlogn)
Space complexity: O(1)

C++

花花酱 LeetCode 1754. Largest Merge Of Two Strings

You are given two strings word1 and word2. You want to construct a string merge in the following way: while either word1 or word2 are non-empty, choose one of the following options:

  • If word1 is non-empty, append the first character in word1 to merge and delete it from word1.
    • For example, if word1 = "abc" and merge = "dv", then after choosing this operation, word1 = "bc" and merge = "dva".
  • If word2 is non-empty, append the first character in word2 to merge and delete it from word2.
    • For example, if word2 = "abc" and merge = "", then after choosing this operation, word2 = "bc" and merge = "a".

Return the lexicographically largest merge you can construct.

A string a is lexicographically larger than a string b (of the same length) if in the first position where a and b differ, a has a character strictly larger than the corresponding character in b. For example, "abcd" is lexicographically larger than "abcc" because the first position they differ is at the fourth character, and d is greater than c.

Example 1:

Input: word1 = "cabaa", word2 = "bcaaa"
Output: "cbcabaaaaa"
Explanation: One way to get the lexicographically largest merge is:
- Take from word1: merge = "c", word1 = "abaa", word2 = "bcaaa"
- Take from word2: merge = "cb", word1 = "abaa", word2 = "caaa"
- Take from word2: merge = "cbc", word1 = "abaa", word2 = "aaa"
- Take from word1: merge = "cbca", word1 = "baa", word2 = "aaa"
- Take from word1: merge = "cbcab", word1 = "aa", word2 = "aaa"
- Append the remaining 5 a's from word1 and word2 at the end of merge.

Example 2:

Input: word1 = "abcabc", word2 = "abdcaba"
Output: "abdcabcabcaba"

Constraints:

  • 1 <= word1.length, word2.length <= 3000
  • word1 and word2 consist only of lowercase English letters.

Solution: Greedy

Always take a single char from the largest word. (NOT just the current char).

E.g.
ans = “”, w1 = “cabba”, w2 = “bcaaa”
w1 > w2, take from w1
ans = “c”, w1 = “abba”, w2 = “bcaaa”
w1 < w2, take from w2
ans = “cb”, w1 = “abba”, w2 = “caaa”
w1 < w2, take from w2
ans = “cbc”, w1 = “abba”, w2 = “aaa”
w1 > w2, take from w1. Note: both start with “a”, but we need to compare the entire word.
ans = “cbca”, w1 = “bba”, w2 = “aaa”
w1 > w2, take from w1
ans = “cbcab”, w1 = “ba”, w2 = “aaa”

Time complexity: O(min(m,n)^2)
Space complexity: O(1)

C++