# [LeetCode] 464. Can I Win 我能赢吗

2021年09月15日 阅读数：1

In the "100 game," two players take turns adding, to a running total, any integer from 1..10. The player who first causes the running total to reach or exceed 100 wins.html

What if we change the game so that players cannot re-use integers?java

For example, two players might take turns drawing from a common pool of numbers of 1..15 without replacement until they reach a total >= 100.python

Given an integer `maxChoosableInteger` and another integer `desiredTotal`, determine if the first player to move can force a win, assuming both players play optimally.post

You can always assume that `maxChoosableInteger` will not be larger than 20 and `desiredTotal` will not be larger than 300.this

Exampleurl

```Input:
maxChoosableInteger = 10
desiredTotal = 11

Output:
false

Explanation:
No matter which integer the first player choose, the first player will lose.
The first player can choose an integer from 1 up to 10.
If the first player choose 1, the second player can only choose integers from 2 up to 10.
The second player will win by choosing 10 and get a total = 11, which is >= desiredTotal.
Same with other integers chosen by the first player, the second player will always win.```

Java:orm

```public class Solution {
Map<Integer, Boolean> map;
boolean[] used;
public boolean canIWin(int maxChoosableInteger, int desiredTotal) {
int sum = (1+maxChoosableInteger)*maxChoosableInteger/2;
if(sum < desiredTotal) return false;
if(desiredTotal <= 0) return true;

map = new HashMap();
used = new boolean[maxChoosableInteger+1];
return helper(desiredTotal);
}

public boolean helper(int desiredTotal){
if(desiredTotal <= 0) return false;
int key = format(used);
if(!map.containsKey(key)){
// try every unchosen number as next step
for(int i=1; i<used.length; i++){
if(!used[i]){
used[i] = true;
// check whether this lead to a win (i.e. the other player lose)
if(!helper(desiredTotal-i)){
map.put(key, true);
used[i] = false;
return true;
}
used[i] = false;
}
}
map.put(key, false);
}
return map.get(key);
}

// transfer boolean[] to an Integer
public int format(boolean[] used){
int num = 0;
for(boolean b: used){
num <<= 1;
if(b) num |= 1;
}
return num;
}
}
```

Python:　　htm

```def canIWin(self, maxChoosableInteger, desiredTotal):
"""
:type maxChoosableInteger: int
:type desiredTotal: int
:rtype: bool
"""
if (1 + maxChoosableInteger) * maxChoosableInteger/2 < desiredTotal:
return False
self.memo = {}
return self.helper(range(1, maxChoosableInteger + 1), desiredTotal)

def helper(self, nums, desiredTotal):

hash = str(nums)
if hash in self.memo:
return self.memo[hash]

if nums[-1] >= desiredTotal:
return True

for i in range(len(nums)):
if not self.helper(nums[:i] + nums[i+1:], desiredTotal - nums[i]):
self.memo[hash]= True
return True
self.memo[hash] = False
return False
```

Python:　　blog

```# Memoization solution.
class Solution(object):
def canIWin(self, maxChoosableInteger, desiredTotal):
"""
:type maxChoosableInteger: int
:type desiredTotal: int
:rtype: bool
"""
def canIWinHelper(maxChoosableInteger, desiredTotal, visited, lookup):
if visited in lookup:
return lookup[visited]

mask = 1
for i in xrange(maxChoosableInteger):
if visited & mask == 0:
if i + 1 >= desiredTotal or \
not canIWinHelper(maxChoosableInteger, desiredTotal - (i + 1), visited | mask, lookup):
lookup[visited] = True
return True
mask <<= 1
lookup[visited] = False
return False

if (1 + maxChoosableInteger) * (maxChoosableInteger / 2) < desiredTotal:
return False

return canIWinHelper(maxChoosableInteger, desiredTotal, 0, {})　　```

C++:

```class Solution {
public:
bool canIWin(int maxChoosableInteger, int desiredTotal) {
if (maxChoosableInteger >= desiredTotal) return true;
if (maxChoosableInteger * (maxChoosableInteger + 1) / 2 < desiredTotal) return false;
unordered_map<int, bool> m;
return canWin(maxChoosableInteger, desiredTotal, 0, m);
}
bool canWin(int length, int total, int used, unordered_map<int, bool>& m) {
if (m.count(used)) return m[used];
for (int i = 0; i < length; ++i) {
int cur = (1 << i);
if ((cur & used) == 0) {
if (total <= i + 1 || !canWin(length, total - (i + 1), cur | used, m)) {
m[used] = true;
return true;
}
}
}
m[used] = false;
return false;
}
};
```

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