基础算法：习题

786.第k个数

#include 

using namespace std;

const int N = 100010;

int q[N];

int quick_sort(int q[], int l, int r, int k)
{
    if (l >= r) return q[l];

    int i = l - 1, j = r + 1, x = q[l + r >> 1];
    while (i < j)
    {
        do i ++ ; while (q[i] < x);
        do j -- ; while (q[j] > x);
        if (i < j) swap(q[i], q[j]);
    }

    if (j - l + 1 >= k) return quick_sort(q, l, j, k);
    else return quick_sort(q, j + 1, r, k - (j - l + 1));
}

int main()
{
    int n, k;
    scanf("%d%d", &n, &k);

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

    cout << quick_sort(q, 0, n - 1, k) << endl;

    return 0;
}

788.逆序对的数量

#include 

using namespace std;

typedef long long LL;

const int N = 1e5 + 10;

int a[N], tmp[N];

LL merge_sort(int q[], int l, int r)
{
    if (l >= r) return 0;

    int mid = l + r >> 1;

    LL res = merge_sort(q, l, mid) + merge_sort(q, mid + 1, r);

    int k = 0, i = l, j = mid + 1;
    while (i <= mid && j <= r)
        if (q[i] <= q[j]) tmp[k ++ ] = q[i ++ ];
        else
        {
            res += mid - i + 1;
            tmp[k ++ ] = q[j ++ ];
        }
    while (i <= mid) tmp[k ++ ] = q[i ++ ];
    while (j <= r) tmp[k ++ ] = q[j ++ ];

    for (i = l, j = 0; i <= r; i ++, j ++ ) q[i] = tmp[j];

    return res;
}

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

    cout << merge_sort(a, 0, n - 1) << endl;

    return 0;
}