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MinimumNumberOfOperationsToMakeArrayEmpty.java
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MinimumNumberOfOperationsToMakeArrayEmpty.java
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package LordShiva;
class Solution {
/**
https://leetcode.com/problems/minimum-number-of-operations-to-make-array-empty/
Performed the brute-force first, followed up with DP to check if a given number's occurance count is valid or not.
fn(idx) = min(
(fn(idx-3))!=-1?(fn(idx-3)+1):MAX,
(fn(idx-2))!=-1?(fn(idx-2)+1):MAX
), idx>0
= -1, idx==1
= 1, idx==2
= 1, idx==3
Then it hit me, all elements except for 1 have some way of
If we represent all numbers as represented a multiple of 3, we'd have three cases
count = 3x => x = count/3 :: makes count of x
count = 3x+1 = 3(x-1)+3+1 = 3(x-1)+2+2 => x = (count-1)/3 + 1 :: makes count of x+1
count = 3x+2 => x = (count-2)/3 + 1 :: makes count of x+1
#dp #math
**/
public int minOperations(int[] nums) {
int set[] = new int[1000001];
for(int num: nums){
set[num]++;
}
int res = 0;
for(int s: set){
if(s == 1) {
return -1;
} else if (s == 2) {
res++;
} else {
int rem = s % 3;
if(rem == 1) {
res += ((s - 1) / 3) + 1;
} else if(rem == 2) {
res += ((s - 2) / 3) + 1;
} else {
res += s / 3;
}
}
}
return res;
}
}