AcWing整数二分算法模板

原链接

解释链接

bool check(int x) {/* ... */} // 检查x是否满足某种性质

// 区间[l, r]被划分成[l, mid]和[mid + 1, r]时使用：
int bsearch_1(int l, int r)
{
    while (l < r)
    {
        int mid = l + r >> 1;
        if (check(mid)) r = mid;    // check()判断mid是否满足性质
        else l = mid + 1;
    }
    return l;
}
// 区间[l, r]被划分成[l, mid - 1]和[mid, r]时使用：
int bsearch_2(int l, int r)
{
    while (l < r)
    {
        int mid = l + r + 1 >> 1;
        if (check(mid)) l = mid;
        else r = mid - 1;
    }
    return l;
}

查找不小于x的第一个位置，较为简单

int l = 0, r = n - 1;
while (l < r) {
    int mid = l + r >> 1;
    if (a[mid] < x)  l = mid + 1;
    else    r = mid;
}

y总模板

// 区间[l, r]被划分成[l, mid]和[mid + 1, r]时使用：
int bsearch_1(int l, int r)
{
    while (l < r)
    {
        int mid = l + r >> 1;
        if (check(mid)) r = mid;    // check()判断mid是否满足性质
        else l = mid + 1;
    }
    return l;
}

int l = 0, r = n - 1;
while(l < r)
{
	int mid = l + r >> 1;
	if(a[mid] >= k) r = mid;
	else l = mid + 1;
}

查找不大于x的最后一个位置，便不容易了

错误写法

int l1 = l, r1 = n;
while (l1 + 1 < r1) {
    int mid = l1 + r1 >> 1;
    if (a[mid] <= x)  l1 = mid;
    else    r1 = mid;
}

正确写法

int l = 0, r = n - 1;
while (l < r)
 {
        int mid = l + r + 1 >> 1;
        if (a[mid] <= x) l = mid;
        else r = mid - 1;
 }

int l1 = l, r1 = n - 1;
while (l1 < r1) {
    int mid = l1 + r1 >> 1;
    if (a[mid] <= x)  l1 = mid + 1;
    else    r1 = mid - 1;
}
printf("%d %d\n", l, l1 - (a[l1] == x ? 0 : 1));

y总模板

// 区间[l, r]被划分成[l, mid - 1]和[mid, r]时使用：
int bsearch_2(int l, int r)
{
    while (l < r)
    {
        int mid = l + r + 1 >> 1;
        if (check(mid)) l = mid;
        else r = mid - 1;
    }
    return l;
}

int l = 0, r = n - 1;
while(l < r)
{
	int mid = l + r + 1 >> 1;
	if(a[mid] <= k) l = mid;
	else r = mid - 1;
}