ALDS1_5_B-MergeSort.

Description:

Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.

Merge(A, left, mid, right)
n1 = mid - left;
n2 = right - mid;
create array L[0...n1], R[0...n2]
for i = 0 to n1-1
do L[i] = A[left + i]
for i = 0 to n2-1
do R[i] = A[mid + i]
L[n1] = SENTINEL
R[n2] = SENTINEL
i = 0;
j = 0;
for k = left to right-1
if L[i] <= R[j]
then A[k] = L[i]
i = i + 1
else A[k] = R[j]
j = j + 1

Merge-Sort(A, left, right){
if left+1 < right
then mid = (left + right)/2;
call Merge-Sort(A, left, mid)
call Merge-Sort(A, mid, right)
call Merge(A, left, mid, right)

Input:

In the first line n is given. In the second line, n integers are given.

Output:

In the first line, print the sequence S. Two consequtive elements should be separated by a space character.

In the second line, print the number of comparisons.

Constraints:

n ≤ 500000
0 ≤ an element in S ≤ 109

SampleInput:

10
8 5 9 2 6 3 7 1 10 4

SampleOutput:

1 2 3 4 5 6 7 8 9 10
34

Codes:

//#define LOCAL

#include <cstdio>

#define M 500010
#define SENTINEL 2000000000
int s = 0, A[M], L[M], R[M];

void merge(int l, int m, int r) {
    int i, j, k, n1 = m-l, n2 = r-m;
    L[n1] = R[n2] = SENTINEL;
    for(i=0; i<n1; ++i) L[i] = A[l+i];
    for(i=0; i<n2; ++i) R[i] = A[m+i];
    i = j = 0;
    for(k=l; k<r; ++k) {
        if(L[i] <= R[j]) A[k] = L[i++];
        else A[k] = R[j++]; ++s;
    }
}

void mergeSort(int l, int r) {
    if(l+1 < r) {
        int m = (l+r)/2;
        mergeSort(l, m);
        mergeSort(m, r);
        merge(l, m, r);
    }
}

int main()
{
    #ifdef LOCAL
        freopen("E:\\Temp\\input.txt", "r", stdin);
        freopen("E:\\Temp\\output.txt", "w", stdout);
    #endif

    int i, n;
    scanf("%d", &n);
    for(i=0; i<n; ++i) scanf("%d", &A[i]);

    mergeSort(0, n);
    for(i=0; i<n; ++i) {
        if(i) printf(" ");
        printf("%d", A[i]);
    }
    printf("\n%d\n", s);

    return 0;
}

ALDS1_6_B-Partition.

Description:

Quick sort is based on the Divide-and-conquer approach. In QuickSort(A, p, r), first, a procedure Partition(A, p, r) divides an array A[p..r] into two subarrays A[p..q-1] and A[q+1..r] such that each element of A[p..q-1] is less than or equal to A[q], which is, inturn, less than or equal to each element of A[q+1..r]. It also computes the index q.

In the conquer processes, the two subarrays A[p..q-1] and A[q+1..r] are sorted by recursive calls of QuickSort(A, p, q-1) and QuickSort(A, q+1, r).

Your task is to read a sequence A and perform the Partition based on the following pseudocode:

Partition(A, p, r)
1 x = A[r]
2 i = p-1
3 for j = p to r-1
4 do if A[j] <= x
5 then i = i+1
6 exchange A[i] and A[j]
7 exchange A[i+1] and A[r]
8 return i+1

Input:

The first line of the input includes an integer n, the number of elements in the sequence A.

In the second line, n elements of the sequence are given separated by space characters.

Output:

Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. The element which is selected as the pivot of the partition should be indicated by [ ].

Constraints:

1 ≤ n ≤ 100,000

SampleInput:

12
13 19 9 5 12 8 7 4 21 2 6 11

SampleOutput:

9 5 8 7 4 2 6 [11] 21 13 19 12

Codes:

//#define LOCAL

#include <cstdio>

#define M 100010
int A[M];

int partition(int p, int r) {
    int i = p-1, a = A[r], j, t;
    for(j=p; j<r; ++j) {
        if(A[j] <= a) {
            ++i;
            t = A[i]; A[i] = A[j]; A[j] = t;
        }
    }
    A[r] = A[i+1]; A[i+1] = a;
    return i+1;
}

int main()
{
    #ifdef LOCAL
        freopen("E:\\Temp\\input.txt&q