基础算法模板——排序

基础算法模板——排序

1. 快速排序

void quick_sort(int q[], int l, int r){
    if(l >= r)
        return ;
    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]);
    }
    quick_sort(q , l  , j) ;
    quick_sort(q, j + 1 , r ) ;
}

利用快速排序找到第k小的数

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

2.归并排序

int a[N], tmp[N];

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

    int mid = l + r >> 1;

    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 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];
}

归并排序的应用——逆序对的数量

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;
}