Test results - Codility

Tasks Details

medium

1. MinMaxDivision

Divide array A into K blocks and minimize the largest sum of any block.

Task Score

100%

Correctness

100%

Performance

100%

You are given integers K, M and a non-empty array A consisting of N integers. Every element of the array is not greater than M.

You should divide this array into K blocks of consecutive elements. The size of the block is any integer between 0 and N. Every element of the array should belong to some block.

The sum of the block from X to Y equals A[X] + A[X + 1] + ... + A[Y]. The sum of empty block equals 0.

The large sum is the maximal sum of any block.

For example, you are given integers K = 3, M = 5 and array A such that:

A[0] = 2 A[1] = 1 A[2] = 5 A[3] = 1 A[4] = 2 A[5] = 2 A[6] = 2

The array can be divided, for example, into the following blocks:

[2, 1, 5, 1, 2, 2, 2], [], [] with a large sum of 15;

[2], [1, 5, 1, 2], [2, 2] with a large sum of 9;

[2, 1, 5], [], [1, 2, 2, 2] with a large sum of 8;

[2, 1], [5, 1], [2, 2, 2] with a large sum of 6.

The goal is to minimize the large sum. In the above example, 6 is the minimal large sum.

Write a function:

class Solution { public int solution(int K, int M, int[] A); }

that, given integers K, M and a non-empty array A consisting of N integers, returns the minimal large sum.

For example, given K = 3, M = 5 and array A such that:

A[0] = 2 A[1] = 1 A[2] = 5 A[3] = 1 A[4] = 2 A[5] = 2 A[6] = 2

the function should return 6, as explained above.

Write an efficient algorithm for the following assumptions:

N and K are integers within the range [1..100,000];

M is an integer within the range [0..10,000];

each element of array A is an integer within the range [0..M].

Solution

Programming language used Java 8

Time spent on task 5 minutes

Notes

not defined yet

Task timeline

Code: 03:05:04 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        // write your code in Java SE 8
    }
}

Code: 03:05:35 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int maX =0;
    }
}

Code: 03:06:05 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = su
    }
}

Code: 03:06:25 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
        }
    }
}

Code: 03:07:00 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if 
        }
    }
}

Code: 03:07:26 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if () {

            }
        }
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
    }
}

Code: 03:07:56 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if () {

            }
        }
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
        int sum = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum = sum + A[idx];
            if (sum > mid) {
                
            }
        }
    }
}

Code: 03:08:19 UTC, java, autosave

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if () {

            }
        }
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
        int sum = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum = sum + A[idx];
            if (sum > mid) {
                size--;
                sum = A[idx];
            }
            if (size == 0) {
                return false;
            }
        }
        return true;
    }
}

Code: 03:08:40 UTC, java, verify, result: Failed

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if (isDivisable(mid, K, A)) {
                result = mid;
            } else {
                max = mid + 1;
            }
        }
        return result;
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
        int sum = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum = sum + A[idx];
            if (sum > mid) {
                size--;
                sum = A[idx];
            }
            if (size == 0) {
                return false;
            }
        }
        return true;
    }
}

Analysis

expand all Example tests

▶

example
example test

✘

TIMEOUT ERROR
Killed. Hard limit reached: 5.000 sec.

5.000 s

TIMEOUT ERROR, Killed. Hard limit reached: 5.000 sec.

Code: 03:09:11 UTC, java, autosave

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if (isDivisable(mid, K, A)) {
                result = mid;
                sum
            } else {
                max = mid + 1;
            }
        }
        return result;
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
        int sum = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum = sum + A[idx];
            if (sum > mid) {
                size--;
                sum = A[idx];
            }
            if (size == 0) {
                return false;
            }
        }
        return true;
    }
}

Code: 03:09:15 UTC, java, verify, result: Passed

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// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if (isDivisable(mid, K, A)) {
                result = mid;
                sum = mid - 1;
            } else {
                max = mid + 1;
            }
        }
        return result;
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
        int sum = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum = sum + A[idx];
            if (sum > mid) {
                size--;
                sum = A[idx];
            }
            if (size == 0) {
                return false;
            }
        }
        return true;
    }
}

Analysis

expand all Example tests

▶

example
example test

✔

0.008 s

Code: 03:09:21 UTC, java, verify, result: Passed

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if (isDivisable(mid, K, A)) {
                result = mid;
                sum = mid - 1;
            } else {
                max = mid + 1;
            }
        }
        return result;
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
        int sum = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum = sum + A[idx];
            if (sum > mid) {
                size--;
                sum = A[idx];
            }
            if (size == 0) {
                return false;
            }
        }
        return true;
    }
}

Analysis

expand all Example tests

▶

example
example test

✔

0.004 s

Code: 03:09:26 UTC, java, final, score: 100

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

// you can also use imports, for example:
// import java.util.*;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int K, int M, int[] A) {
        int sum = 0;
        int max = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum += A[idx];
            if (A[idx] > max) {
                max = A[idx];
            }
        }
        int result = sum;
        while (max <= sum) {
            int mid = (max + sum) / 2;
            if (isDivisable(mid, K, A)) {
                result = mid;
                sum = mid - 1;
            } else {
                max = mid + 1;
            }
        }
        return result;
    }
    private boolean isDivisable(int mid, int K, int[] A) {
        int size = K;
        int sum = 0;
        for (int idx = 0; idx < A.length; idx++) {
            sum = sum + A[idx];
            if (sum > mid) {
                size--;
                sum = A[idx];
            }
            if (size == 0) {
                return false;
            }
        }
        return true;
    }
}

Analysis summary

The solution obtained perfect score.

Analysis

Detected time complexity:

O(N*log(N+M))

expand all Example tests

▶

example
example test

✔

0.008 s

expand all Correctness tests

▶

extreme_single
single elements

✔

0.004 s

0.008 s

▶

extreme_double
single and double elements

✔

0.008 s

▶

extreme_min_max
maximal / minimal values

✔

0.004 s

0.008 s

0.004 s

0.008 s

▶

simple1
simple tests

✔

0.008 s

0.004 s

▶

simple2
simple tests

✔

0.008 s

▶

tiny_random_ones
random values {0, 1}, N = 100

✔

0.004 s

0.008 s

0.004 s

expand all Performance tests

▶

small_random_ones
random values {0, 1}, N = 100

✔

0.008 s

0.004 s

0.008 s

▶

medium_zeros
many zeros and 99 in the middle, length = 15,000

✔

0.036 s

0.032 s

0.036 s

▶

medium_random
random values {1, 100}, N = 20,000

✔

0.048 s

0.052 s

0.048 s

▶

large_random
random values {0, ..., MAX_INT}, N = 100,000

✔

0.284 s

0.288 s

▶

large_random_ones
random values {0, 1}, N = 100,000

✔

0.188 s

▶

all_the_same
all the same values, N = 100,000

✔

0.308 s

0.320 s

0.316 s