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e2hang
2025-10-24 09:52:24 +08:00
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Exercise/Homework3/Q1双栈做法.cpp Normal file
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#include <bits/stdc++.h>
using namespace std;
//---------------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
//---------------------------------------------
const long long INF = 1LL << 31; // <20><>ĿҪ<C4BF><D2AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Χ [-2^31, 2^31)
//---------------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȼ<EFBFBD><C8BC><EFBFBD><EFBFBD><EFBFBD>
//---------------------------------------------
// <20><><EFBFBD><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȼ<EFBFBD><C8BC>ȼ<EFBFBD><C8BC><EFBFBD><EFBFBD><EFBFBD>ֵԽ<D6B5><D4BD><EFBFBD><EFBFBD><EFBFBD>ȼ<EFBFBD>Խ<EFBFBD>ߣ<EFBFBD>
int level(char op) {
switch (op) {
case '+': case '-': return 1; // <20>Ӽ<EFBFBD><D3BC><EFBFBD><EFBFBD><EFBFBD>
case '*': case '/': return 2; // <20>˳<EFBFBD><CBB3>е<EFBFBD>
case '^': return 3; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
default: return 0; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
}
}
//---------------------------------------------
// <20>ж<EFBFBD><D0B6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƿ<EFBFBD><C7B7><EFBFBD><EFBFBD>ҽ<EFBFBD><D2BD>ϵ<EFBFBD>
//---------------------------------------------
// ֻ<><D6BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>㣨^<5E><><EFBFBD><EFBFBD><EFBFBD>ҽ<EFBFBD><D2BD>ϣ<EFBFBD>a^b^c <20>ȼ<EFBFBD><C8BC><EFBFBD> a^(b^c)
bool rightAssoc(char op) {
return op == '^';
}
//---------------------------------------------
// <20><>ȫ<EFBFBD><C8AB><EFBFBD><EFBFBD><EFBFBD>ݺ<EFBFBD><DDBA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>⣩
//---------------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϵͳ pow<6F><77><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Լ<EFBFBD>д
// ͬʱҪ<CAB1><D2AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƿ񳬹<C7B7><F1B3ACB9><EFBFBD>ĿҪ<C4BF><D2AA><EFBFBD><EFBFBD>Χ<EFBFBD><CEA7><EFBFBD><EFBFBD> int32 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
long long fastpow(long long a, long long b, bool &valid) {
long long res = 1;
while (b > 0) {
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD>λ<EFBFBD><CEBB>1<EFBFBD><31><EFBFBD><EFBFBD>Ҫ<EFBFBD><D2AA>һ<EFBFBD><D2BB>
if (b & 1) {
// <20>ж<EFBFBD><D0B6>Ƿ<EFBFBD><C7B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
if (a != 0 && llabs(res) > (INF - 1) / llabs(a)) {
valid = false;
return 0;
}
res *= a;
}
// ׼<><D7BC>ƽ<EFBFBD><C6BD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
b >>= 1;
if (b) { // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>û<EFBFBD><C3BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ж<EFBFBD>һ<EFBFBD><D2BB>ƽ<EFBFBD><C6BD><EFBFBD>Ƿ<EFBFBD><C7B7><EFBFBD>ȫ
if (llabs(a) > (INF - 1) / llabs(a)) {
valid = false;
return 0;
}
a *= a;
}
}
return res;
}
//---------------------------------------------
// ִ<><D6B4>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD>㣺<EFBFBD><E3A3BA><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ջ<EFBFBD><D5BB>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ͳ<EFBFBD><CDB2><EFBFBD><EFBFBD><EFBFBD>
//---------------------------------------------
bool apply(stack<long long> &num, stack<char> &op) {
if (num.size() < 2 || op.empty()) return false; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
long long b = num.top(); num.pop(); // ע<><D7A2>˳<EFBFBD><CBB3><EFBFBD><EFBFBD><EFBFBD>Ҳ<EFBFBD><D2B2><EFBFBD><EFBFBD><EFBFBD>
long long a = num.top(); num.pop(); // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
char c = op.top(); op.pop(); // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
long long res = 0;
switch (c) {
case '+': res = a + b; break;
case '-': res = a - b; break;
case '*': res = a * b; break;
case '/':
if (b == 0) return false; // <20><><EFBFBD>㱨<EFBFBD><E3B1A8>
res = a / b; // <20><><EFBFBD><EFBFBD><EFBFBD>Զ<EFBFBD><D4B6><EFBFBD>β
break;
case '^': {
if (b < 0) return false; // <20><>Ŀ<EFBFBD><C4BF>ָ֤<D6A4><D6B8><EFBFBD>Ǹ<EFBFBD><C7B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
bool valid = true;
res = fastpow(a, b, valid);
if (!valid) return false; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
break;
}
default:
return false; // <20>Ƿ<EFBFBD><C7B7><EFBFBD><EFBFBD><EFBFBD>
}
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Χ
if (res >= INF || res < -INF) return false;
num.push(res);
return true;
}
//---------------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD>㺯<EFBFBD><E3BAAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD>б<EFBFBD><D0B1><EFBFBD>ʽ
//---------------------------------------------
string calcExpr(const string &s) {
stack<long long> num; // <20><><EFBFBD><EFBFBD>ջ
stack<char> op; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ջ
int n = s.size();
for (int i = 0; i < n; ) {
if (isspace(s[i])) { // <20><><EFBFBD><EFBFBD><EFBFBD>ո<EFBFBD>
i++;
continue;
}
//-------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>֣<EFBFBD>֧<EFBFBD>ֶ<EFBFBD>λ<EFBFBD><CEBB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
//-------------------------------------
if (isdigit(s[i])) {
long long val = 0;
while (i < n && isdigit(s[i])) {
val = val * 10 + (s[i] - '0');
if (val >= INF) return "INVALID"; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Χ
i++;
}
num.push(val);
}
//-------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
//-------------------------------------
else if (s[i] == '(') {
op.push('(');
i++;
}
//-------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ţ<EFBFBD>Ҫ<EFBFBD><D2AA><EFBFBD>㵽<EFBFBD><E3B5BD>һ<EFBFBD><D2BB>'('Ϊֹ
//-------------------------------------
else if (s[i] == ')') {
while (!op.empty() && op.top() != '(') {
if (!apply(num, op)) return "INVALID";
}
if (op.empty()) return "INVALID"; // <20><><EFBFBD>Ų<EFBFBD>ƥ<EFBFBD><C6A5>
op.pop(); // <20><><EFBFBD><EFBFBD> '('
i++;
}
//-------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
//-------------------------------------
else {
char now = s[i];
if (level(now) == 0) return "INVALID"; // <20>Ƿ<EFBFBD><C7B7>ַ<EFBFBD>
// ջ<><D5BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȼ<EFBFBD><C8BC><EFBFBD><EFBFBD>߻<EFBFBD><DFBB><EFBFBD>ͬ<EFBFBD><CDAC><EFBFBD>Ҳ<EFBFBD><D2B2><EFBFBD><EFBFBD>ҽ<EFBFBD><D2BD>ϣ<EFBFBD><CFA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȼ<EFBFBD><C8BC><EFBFBD>
while (!op.empty() && op.top() != '(' &&
(level(op.top()) > level(now) ||
(level(op.top()) == level(now) && !rightAssoc(now)))) {
if (!apply(num, op)) return "INVALID";
}
op.push(now);
i++;
}
}
//-------------------------------------
// <20><><EFBFBD><EFBFBD>ջ<EFBFBD><D5BB>ʣ<EFBFBD><CAA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
//-------------------------------------
while (!op.empty()) {
if (!apply(num, op)) return "INVALID";
}
//-------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ջ<EFBFBD><D5BB>ֹһ<D6B9><D2BB><EFBFBD><EFBFBD>˵<EFBFBD><CBB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʽ<EFBFBD><CABD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
//-------------------------------------
if (num.size() != 1) return "INVALID";
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ս<EFBFBD><D5BD><EFBFBD>
return to_string(num.top());
}
//---------------------------------------------
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>룬ÿ<EBA3AC><C3BF>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ʽ
//---------------------------------------------
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
string s;
while (getline(cin, s)) {
string ans = calcExpr(s);
cout << ans << "\n";
}
return 0;
}