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Program to find minimum largest sum of k sublists in C++
Suppose we have a list of numbers called nums and another value k. We can split the list into k non-empty sublists. We have to find the minimum largest sum of the k sublists.
So, if the input is like nums = [2, 4, 3, 5, 12] k = 2, then the output will be 14, as we can split the list like: [2, 4, 3, 5] and [12].
To solve this, we will follow these steps −
Define a function ok(), this will take array v, k, x,
cnt := 0, sum := 0
for each element i in v −
if sum + i > x, then −
sum := i
(increase cnt by 1)
Otherwise
sum := sum + i
return true when cnt <= k, otherwise false
From the main method do the following −
low := 0, ret := 0, high := 0
for each element i in nums
high := high + i
ret := ret + i
low := maximum of low and i
while low <= high, do −
mid := low + (high - low) / 2
if ok(nums, k - 1, mid) is true, then −
ret := mid
high := mid - 1
Otherwise
low := mid + 1
return ret
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
bool ok(vector <int>& v, int k, int x){
int cnt = 0;
int sum = 0;
for(int i : v){
if(sum + i > x){
sum = i;
cnt++;
}
else{
sum += i;
}
}
return cnt <= k;
}
int solve(vector<int>& nums, int k) {
int low = 0;
int ret = 0;
int high = 0;
for(int i : nums){
high += i;
ret += i;
low = max(low, i);
}
while(low <= high){
int mid = low + ( high - low) / 2;
if(ok(nums, k - 1, mid)){
ret = mid;
high = mid - 1;
}
else{
low = mid + 1;
}
}
return ret;
}
int main(){
vector<int> v = {2, 4, 3, 5, 12};
int k = 2;
cout << solve(v, k);
}Input
{2, 4, 3, 5, 12}, 2Output
14
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