给定两个整数X和Y ,其中X表示资格要求的得分数, Y表示剩下的比赛数。球队在比赛中获2分,输则1分。任务是找到球队赢得下一轮比赛所需的最少比赛数。
例子:
Input: X = 10, Y = 5
Output: 5
The team needs to win all the matches in order to get 10 points.
Input : X = 6, Y = 5
Output : 1
If the team wins a single match and loses the rest 4 matches, they would still qualify.
一个幼稚的方法是通过对从0到Y的所有值进行迭代来进行检查,并找出给我们X点的第一个值。
一种有效的方法是对要赢得的匹配数执行二进制搜索,以找出最小的匹配数。最初低= 0 ,高= X ,然后检查条件(mid * 2 +(y – mid))≥x 。如果情况仍然存在,则检查左半部分是否存在任何较低的值,即高=中– 1,否则检查右半部分中的任何低值,即低=中+ 1 。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the minimum number of
// matches to win to qualify for next round
int findMinimum(int x, int y)
{
// Do a binary search to find
int low = 0, high = y;
while (low <= high) {
// Find mid element
int mid = (low + high) >> 1;
// Check for condition
// to qualify for next round
if ((mid * 2 + (y - mid)) >= x)
high = mid - 1;
else
low = mid + 1;
}
return low;
}
// Driver Code
int main()
{
int x = 6, y = 5;
cout << findMinimum(x, y);
return 0;
}
Java
// Java implementation of the approach
import java.io.*;
class GFG
{
// Function to return the minimum number of
// matches to win to qualify for next round
static int findMinimum(int x, int y)
{
// Do a binary search to find
int low = 0, high = y;
while (low <= high)
{
// Find mid element
int mid = (low + high) >> 1;
// Check for condition
// to qualify for next round
if ((mid * 2 + (y - mid)) >= x)
high = mid - 1;
else
low = mid + 1;
}
return low;
}
// Driver Code
public static void main (String[] args)
{
int x = 6, y = 5;
System.out.println(findMinimum(x, y));
}
}
// This code is contributed by ajit.
Python 3
# Python 3 implementation of the approach
# Function to return the minimum number of
# matches to win to qualify for next round
def findMinimum(x, y):
# Do a binary search to find
low = 0
high = y
while (low <= high):
# Find mid element
mid = (low + high) >> 1
# Check for condition
# to qualify for next round
if ((mid * 2 + (y - mid)) >= x):
high = mid - 1
else:
low = mid + 1
return low
# Driver Code
if __name__ == '__main__':
x = 6
y = 5
print(findMinimum(x, y))
# This code is contributed by
# Surendra_Gangwar
C#
// C# implementation of the approach
using System;
class GFG
{
// Function to return the minimum number of
// matches to win to qualify for next round
static int findMinimum(int x, int y)
{
// Do a binary search to find
int low = 0, high = y;
while (low <= high)
{
// Find mid element
int mid = (low + high) >> 1;
// Check for condition
// to qualify for next round
if ((mid * 2 + (y - mid)) >= x)
high = mid - 1;
else
low = mid + 1;
}
return low;
}
// Driver code
static public void Main()
{
int x = 6, y = 5;
Console.WriteLine(findMinimum(x, y));
}
}
// This Code is contributed by ajit.
PHP
> 1;
// Check for condition$
// to qualify for next round
if (($mid * 2 + ($y - $mid)) >= $x)
$high = $mid - 1;
else
$low = $mid + 1;
}
return $low;
}
// Driver Code
$x = 6; $y = 5;
echo findMinimum($x, $y);
// This code has been contributed
// by 29AjayKumar
?>
Javascript
输出:
1
时间复杂度: O(log y)
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