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Merge pull request #335 from cheehwatang/add-1775-EqualSumArraysWithMinimumNumberOfOperations
Add 1775. Equal Sum Arrays With Minimum Number of Operations (Counting)
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‎README.md‎

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<th>Solution</th>
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<th>Topics</th>
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</tr>
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<tr>
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<td align="center">September 14th</td>
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<td>1775. <a href="https://leetcode.com/problems/equal-sum-arrays-with-minimum-number-of-operations/">Equal Sum Arrays With Minimum Number of Operations</a></td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/1775.%20Equal%20Sum%20Arrays%20With%20Minimum%20Number%20of%20Operations/EqualSumArraysWithMinimumNumberOfOperations_Counting.java">Counting</a>
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</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#greedy">Greedy</a>
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</td>
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</tr>
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<tr>
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<td align="center">September 13th</td>
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<td>1814. <a href="https://leetcode.com/problems/count-nice-pairs-in-an-array/">Count Nice Pairs in an Array</a></td>
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<a href="#array">Array</a>
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</td>
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</tr>
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<tr>
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<td align="center">September 9th</td>
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<td>2028. <a href="https://leetcode.com/problems/find-missing-observations/">Find Missing Observations</a></td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/2028.%20Find%20Missing%20Observations/FindMissingObservations.java">Math</a>
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</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#math">Math</a>,
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<a href="#simulation">Simulation</a>
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</td>
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</tr>
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</table>
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</br>
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<hr>
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</td>
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<td></td>
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</tr>
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<tr>
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<td align="center">1775</td>
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<td><a href="https://leetcode.com/problems/equal-sum-arrays-with-minimum-number-of-operations/">Equal Sum Arrays With Minimum Number of Operations</a></td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/1775.%20Equal%20Sum%20Arrays%20With%20Minimum%20Number%20of%20Operations/EqualSumArraysWithMinimumNumberOfOperations_Counting.java">Java</a>
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</td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#greedy">Greedy</a>
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</td>
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<td></td>
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</tr>
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<tr>
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<td align="center">1814</td>
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<td><a href="https://leetcode.com/problems/count-nice-pairs-in-an-array/">Count Nice Pairs in an Array</a></td>
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</td>
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<td></td>
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</tr>
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<tr>
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<td align="center">1775</td>
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<td><a href="https://leetcode.com/problems/equal-sum-arrays-with-minimum-number-of-operations/">Equal Sum Arrays With Minimum Number of Operations</a></td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/1775.%20Equal%20Sum%20Arrays%20With%20Minimum%20Number%20of%20Operations/EqualSumArraysWithMinimumNumberOfOperations_Counting.java">Java</a>
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</td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#greedy">Greedy</a>
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</td>
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<td></td>
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</tr>
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<tr>
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<td align="center">1814</td>
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<td><a href="https://leetcode.com/problems/count-nice-pairs-in-an-array/">Count Nice Pairs in an Array</a></td>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/1578.%20Minimum%20Time%20to%20Make%20Rope%20Colorful/MinimumTimeToMakeRopeColorful_DynamicProgramming.java"><em>Dynamic Programming</em></a>
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</td>
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</tr>
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<tr>
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<td align="center">1775</td>
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<td><a href="https://leetcode.com/problems/equal-sum-arrays-with-minimum-number-of-operations/">Equal Sum Arrays With Minimum Number of Operations</a></td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/1775.%20Equal%20Sum%20Arrays%20With%20Minimum%20Number%20of%20Operations/EqualSumArraysWithMinimumNumberOfOperations_Counting.java">Java</a>
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</td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>,
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<a href="#greedy">Greedy</a>
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</td>
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<td></td>
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</tr>
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<tr>
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<td align="center">1833</td>
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<td><a href="https://leetcode.com/problems/maximum-ice-cream-bars/">Maximum Ice Cream Bars</a></td>

‎solutions/1775. Equal Sum Arrays With Minimum Number of Operations/EqualSumArraysWithMinimumNumberOfOperations_Counting.java‎

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package com.cheehwatang.leetcode;
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// Time Complexity : O(n + m),
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// where 'n' is the length of 'nums1', and 'm' is the length of 'nums2'.
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// We traverse 'nums1' once, and 'nums2' once.
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//
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// Space Complexity : O(1),
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// as the auxiliary space used is independent of the input.
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public class EqualSumArraysWithMinimumNumberOfOperations_Counting {
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// Approach:
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// Using counting array to keep track of the frequency of both arrays.
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// Since both array's elements can be manipulated, the counting array records the inversion of the second array.
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// Example: nums1 = [1,1], nums2 = [6,5,4], counting array = [3,1,1,0,0,0].
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// This is because, to make the sum equal, in this example,
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// we can either increase the 1 in 'nums1' to 6 or decrease the 6 in 'nums2' to 1.
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// In both cases, the 'difference' is decreased by 5.
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// Once we have the counting array, and the sum of both arrays,
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// we get change the smallest number in the counting array first as it has the largest impact on the 'difference'
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// (Greedy Approach).
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public int minOperations(int[] nums1, int[] nums2) {
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// Case where it is impossible to get equal sum,
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// when one array is longer than 6 multiples of the second array length.
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if ((nums1.length * 6 < nums2.length) || (nums1.length > nums2.length * 6)) return -1;
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// Use the countArray to record the frequency of each number in 'nums1',
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// as well as the inversion of the numbers in 'nums2'.
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// Additionally, record the sum of each array.
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int[] countArray = new int[7];
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int sumNum1 = 0;
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for (int number : nums1) {
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countArray[number]++;
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sumNum1 += number;
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}
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int sumNum2 = 0;
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for (int number : nums2) {
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countArray[7 - number]++;
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sumNum2 += number;
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}
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int count = 0;
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int difference = sumNum1 - sumNum2;
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// In both cases, from the number with the largest impact (1 if difference is negative, 6 if difference is positive),
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// the operations to make is either:
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// - all the frequency of the number (with remainders of the difference), or
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// - the remainders of the difference divided by the number.
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if (difference < 0) {
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for (int i = 1; i < 6; i++) {
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int operations = Math.min(countArray[i], -difference / (6 - i) + (-difference % (6 - i) == 0 ? 0 : 1));
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difference += operations * (6 - i);
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count += operations;
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if (difference >= 0) break;
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}
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} else if (difference > 0) {
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for (int i = 6; i > 1; i--) {
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int operations = Math.min(countArray[i], difference / (i - 1) + (difference % (i - 1) == 0 ? 0 : 1));
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difference -= operations * (i - 1);
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count += operations;
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if (difference <= 0) break;
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}
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}
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return count;
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}
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}

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