Project_Euler-45 题解

题目

思路

非常简单，枚举六边形数字，然后判断他们是不是三角形和五边形数，如果是，那么输出。

代码

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <time.h>

typedef long long ll;

ll triangle(ll n) {
    return (n * (n + 1)) >> 1;
}

ll pentagonal(ll n) {
    return (n * (3 * n - 1)) >> 1;
}

ll hexagonal(ll n) {
    return n * (2 * n - 1);
}

ll is_triangle(ll n) {
    printf("is_triangle: %lld...\n", n);
    ll head = 1, tail = n, mid;
    while (head <= tail) {
        mid = (head + tail) >> 1;
        if (triangle(mid) == n) return 1;
        if (triangle(mid) < n) head = mid + 1;
        else tail = mid - 1;
    }
    printf("is_triangle: %lld is not a triangle.\n", n);
    return 0;
}

ll is_pentagonal(ll n) {
    printf("is_pentagonal: %lld...\n", n);
    ll head = 1, tail = n, mid;
    while (head <= tail) {
        mid = (head + tail) >> 1;
        if (pentagonal(mid) == n) return 1;
        if (pentagonal(mid) < n) head = mid + 1;
        else tail = mid - 1;
    }
    printf("is_pentagonal: %lld is not a pentagonal.\n", n);
    return 0;
}

ll main() {
    ll num = 0;
    for (ll i = 2; num < 2; i++) {
        ll tar = hexagonal(i);
        if (!is_pentagonal(tar)) continue;
        if (!is_triangle(tar)) continue;
        num++;
        printf("%lldth = %lld\n", num, tar);
    }
    return 0;
}

优化思路

发现六边形数字一定是三角形数字，因此枚举六边形数字的画就不需要再判断三角形数字了。

优化代码

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <time.h>

typedef long long ll;

ll pentagonal(ll n) {
    return (n * (3 * n - 1)) >> 1;
}

ll hexagonal(ll n) {
    return n * (2 * n - 1);
}

ll is_pentagonal(ll n) {
    printf("is_pentagonal: %lld...\n", n);
    ll head = 1, tail = n, mid;
    while (head <= tail) {
        mid = (head + tail) >> 1;
        if (pentagonal(mid) == n) return 1;
        if (pentagonal(mid) < n) head = mid + 1;
        else tail = mid - 1;
    }
    printf("is_pentagonal: %lld is not a pentagonal.\n", n);
    return 0;
}

ll main() {
    ll num = 0;
    for (ll i = 2; num < 2; i++) {
        ll tar = hexagonal(i);
        if (!is_pentagonal(tar)) continue;
        num++;
        printf("%lldth = %lld\n", num, tar);
    }
    return 0;
}